scispace - formally typeset
Search or ask a question

Showing papers on "Explicit symmetry breaking published in 2008"


Journal ArticleDOI
TL;DR: Xiao et al. as mentioned in this paper showed that inversion symmetry breaking leads to valley contrasted optical selection rules for interband transitions at high symmetry points, which enables valley-dependent interplay of electrons with light of different circular polarizations.
Abstract: Inversion symmetry breaking allows contrasted circular dichroism in different $k$-space regions, which takes the extreme form of optical selection rules for interband transitions at high symmetry points. In materials where band edges occur at noncentral valleys, this enables valley-dependent interplay of electrons with light of different circular polarizations, in analogy to spin dependent optical activities in semiconductors. This discovery is in perfect harmony with the previous finding of valley contrasted Bloch band features of orbital magnetic moment and Berry curvatures from inversion symmetry breaking [D. Xiao, W. Yao, and Q. Niu, Phys. Rev. Lett. 99, 236809 (2007)]. A universal connection is revealed between the $k$-resolved optical oscillator strength of interband transitions, the orbital magnetic moment and the Berry curvatures, which also provides a principle for optical measurement of orbital magnetization and intrinsic anomalous Hall conductivity in ferromagnetic systems. The general physics is demonstrated in graphene where inversion symmetry breaking leads to valley contrasted optical selection rule for interband transitions. We discuss graphene based valley optoelectronics applications where light polarization information can be interconverted with electronic information.

861 citations


Journal ArticleDOI
TL;DR: In this paper, a new method for space-group determination is described based on a symmetry analysis of the structure-factor phases resulting from a structure solution in space group P1.
Abstract: A new method for space-group determination is described. It is based on a symmetry analysis of the structure-factor phases resulting from a structure solution in space group P1. The output of the symmetry analysis is a list of all symmetry operations compatible with the lattice. Each symmetry operation is assigned a symmetry agreement factor that is used to select the symmetry operations that are the elements of the space group of the structure. On the basis of the list of the selected operations the complete space group of the structure is constructed. The method is independent of the number of dimensions, and can also be used in solution of aperiodic structures. A number of cases are described where this method is particularly advantageous compared with the traditional symmetry analysis.

274 citations


Journal ArticleDOI
TL;DR: In this article, the question of whether spontaneous U(1)R breaking can occur in O'Raifeartaigh-type models of spontaneous supersymmetry breaking was studied, and it was shown that in order for it to occur, there must be a field in the theory with R-charge different from 0 or 2.
Abstract: We study the question of whether spontaneous U(1)R breaking can occur in O'Raifeartaigh-type models of spontaneous supersymmetry breaking. We show that in order for it to occur, there must be a field in the theory with R-charge different from 0 or 2. We construct the simplest O'Raifeartaigh model with this property, and we find that for a wide range of parameters, it has a meta-stable vacuum where U(1)R is spontaneously broken. This suggests that spontaneous U(1)R breaking actually occurs in generic O'Raifeartaigh models.

206 citations


Journal ArticleDOI
TL;DR: In this paper, a family of non-Abelian topological models in a lattice that arise by modifying the Kitaev model through the introduction of single-qudit terms was studied.
Abstract: We study a family of non-Abelian topological models in a lattice that arise by modifying the Kitaev model through the introduction of single-qudit terms. The effect of these terms amounts to a reduction in the discrete gauge symmetry with respect to the original systems, which corresponds to a generalized mechanism of explicit symmetry breaking. The topological order is either partially lost or completely destroyed throughout the various models. The systems display condensation and confinement of the topological charges present in the standard non-Abelian Kitaev models, which we study in terms of ribbon operator algebras.

156 citations


Journal ArticleDOI
TL;DR: The symmetry principles of NMR pulse-sequence design are summarized and the selection rules associated with symmetrical pulse sequences are discussed using average Hamiltonian theory.
Abstract: The symmetry principles of NMR pulse-sequence design are summarized. The discussion is guided by an analogy with tiling schemes in the decorative arts. The symmetry operations for NMR pulse sequences are discussed in terms of excitation field modifiers and temporal modifiers. The quantum operators which describe the effect of these modifiers on the excitation field spin Hamiltonian are provided. The symmetry transformations of spin propagators, and the different types of pulse-sequence elements are discussed. The common types of symmetry expansion are treated using the propagator transformations and the Euler angles for the excitation field propagators. The selection rules associated with symmetrical pulse sequences are discussed using average Hamiltonian theory.

120 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of an external magnetic field on the dynamics of fundamental flavors in both the confined and deconfined phases of a large N_c gauge theory was studied using the Sakai-Sugimoto model.
Abstract: Using the Sakai-Sugimoto model we study the effect of an external magnetic field on the dynamics of fundamental flavours in both the confined and deconfined phases of a large N_c gauge theory. We find that an external magnetic field promotes chiral symmetry breaking, consistent with the "magnetic catalysis" observed in the field theory literature, and seen in other studies using holographic duals. The external field increases the separation between the deconfinement temperature and the chiral symmetry restoring temperature. In the deconfined phase we investigate the temperature-magnetic field phase diagram and observe, for example, there exists a maximum critical temperature (at which symmetry is restored) for very large magnetic field. We find that this and certain other phenomena persist for the Sakai-Sugimoto type models with probe branes of diverse dimensions. We comment briefly on the dynamics in the presence of an external electric field.

103 citations


Journal ArticleDOI
TL;DR: In this paper, a discrete exchange symmetry can give rise to realistic dark matter candidates in models with warped extra dimensions, where the Higgs is heavier than the experimental bound and new light quark resonances are predicted.
Abstract: We show that a discrete exchange symmetry can give rise to realistic dark matter candidates in models with warped extra dimensions We show how to realize our construction in a variety of models with warped extra dimensions and study in detail a realistic model of gauge-Higgs unification/composite Higgs in which the observed amount of dark matter is naturally reproduced In this model, a realistic pattern of electroweak symmetry breaking typically occurs in a region of parameter space in which the fit to the electroweak precision observables improves, the Higgs is heavier than the experimental bound and new light quark resonances are predicted We also quantify the fine-tuning of such scenarios, and discuss in which sense gauge-Higgs unification models result in a natural theory of electroweak symmetry breaking

100 citations


Journal ArticleDOI
TL;DR: In this paper, a simple model of fermion masses based on a spontaneously broken S 3 × Z 3 flavour group was constructed, and the model predicts θ 23 = π / 4 + O ( λ c 2 ) and θ 13 = O (λ c 2 ).

72 citations


Journal ArticleDOI
TL;DR: In this article, the authors studied dual conformally invariant off-shell four-point Feynman diagrams, and classified all such diagrams through four loops and evaluated 10 new offshell integrals in terms of Mellin-Barnes representations.
Abstract: Evidence has recently emerged for a hidden symmetry of planar scattering amplitudes in N=4 super-Yang-Mills theory called dual conformal symmetry. At weak coupling the presence of this symmetry has been observed through five loops, while at strong coupling the symmetry has been shown to have a natural interpretation in terms of a T-dualized AdS{sub 5}. In this paper we study dual conformally invariant off-shell four-point Feynman diagrams. We classify all such diagrams through four loops and evaluate 10 new off-shell integrals in terms of Mellin-Barnes representations, also finding explicit expressions for their infrared singularities.

69 citations


Journal ArticleDOI
TL;DR: In this paper, a framework for handling flavor symmetry breaking where the symmetry breaking is triggered by boundary conditions of scalar fields in extra-dimensional space is presented, without referring to any details of the scalar potential and its minimization procedure.
Abstract: Flavor symmetry has been widely studied for figuring out the masses and mixing angles of standard model fermions. In this paper we present a framework for handling flavor symmetry breaking where the symmetry breaking is triggered by boundary conditions of scalar fields in extra-dimensional space. The alignment of scalar expectation values is achieved without referring to any details of scalar potential and its minimization procedure. As applications to non-Abelian discrete flavor symmetries, illustrative lepton mass models are constructed where the ${S}_{3}$ and ${A}_{4}$ flavor symmetries are broken down to the directions leading to the tribimaximal form of lepton mixing and realistic mass patterns.

59 citations


Book
20 Feb 2008
TL;DR: The concept of symmetry in science is found in the work of Symmetry as discussed by the authors and science is Founded on symmetry, science is also found on symmetry in physics, and symmetry in mathematics.
Abstract: The Concept of Symmetry.- Science Is Founded on Symmetry.- Symmetry in Physics.- The Symmetry Principle.- Application of Symmetry.- Approximate Symmetry, Spontaneous Symmetry Breaking.- Cosmic Considerations.- The Mathematics of Symmetry: Group Theory.- Group Theory Continued.- The Formalism of Symmetry.- Symmetry in Processes.- Summary of Principles.

Journal ArticleDOI
TL;DR: In this article, the authors present a common explanation of the fermion mass hierarchy and the large lepton mixing angles in the context of a grand unified flavor and gauge theory (GUTF).
Abstract: We present a common explanation of the fermion mass hierarchy and the large lepton mixing angles in the context of a grand unified flavor and gauge theory (GUTF). Our starting point is a SU(3)xU(1) flavor symmetry and a SO(10) GUT, a basic ingredient of our theory which plays a major role is that two different breaking pattern of the flavor symmetry are at work. On one side, the dynamical breaking of SU(3)xU(1) flavor symmetry into U(2)xZ_3 explains why one family is much heavier than the others. On the other side, an explicit symmetry breaking of SU(3) into a discrete flavor symmetry leads to the observed tribimaximal mixing for the leptons. We write an explicit model where this discrete symmetry group is A4. Naturalness of the charged fermion mass hierarchy appears as a consequence of the continuous SU(3) flavor symmetry. Moreover, the same discrete A4-GUT invariant operators are the root of the large lepton mixing, small Cabibbo angle, and neutrino masses.

Journal ArticleDOI
TL;DR: It is shown that the size, in space, of the ‘scar’ over which the order parameter adjusts as it ‘bends’ interpolating between the phases with different symmetries follows from a KZM-like approach, and in quantum phase transitions this spatial scale is directly reflected in the energy spectrum of the system: in particular, it determines the size of the energy gap.
Abstract: We extend the theory of symmetry-breaking dynamics in non-equilibrium second-order phase transitions known as the Kibble–Zurek mechanism (KZM) to transitions where the change of phase occurs not in time but in space. This can be due to a time-independent spatial variation of a field that imposes a phase with one symmetry to the left of where it attains critical value, while allowing spontaneous symmetry breaking to the right of that critical borderline. Topological defects need not form in such a situation. We show, however, that the size, in space, of the ‘scar’ over which the order parameter adjusts as it ‘bends’ interpolating between the phases with different symmetries follows from a KZM-like approach. As we illustrate on the example of a transverse quantum Ising model, in quantum phase transitions this spatial scale—the size of the scar—is directly reflected in the energy spectrum of the system: in particular, it determines the size of the energy gap.

Journal ArticleDOI
TL;DR: In this article, it was shown that radiative breaking of conformal symmetry (and simultaneously electroweak symmetry) in the standard model with right-chiral neutrinos and a minimally enlarged scalar sector induces spontaneous breaking of lepton number symmetry, which naturally gives rise to an axion-like particle with some unusual features.
Abstract: We demonstrate that radiative breaking of conformal symmetry (and simultaneously electroweak symmetry) in the standard model with right-chiral neutrinos and a minimally enlarged scalar sector induces spontaneous breaking of lepton number symmetry, which naturally gives rise to an axion-like particle with some unusual features. The couplings of this ‘axion’ to standard model particles, in particular photons and gluons, are entirely determined (and computable) via the conformal anomaly, and their smallness turns out to be directly related to the smallness of the masses of the light neutrinos.

Journal ArticleDOI
TL;DR: These measures provide information complementary to the Continuous Symmetry Measures that evaluate the distance between a given structure and the nearest structure which belongs to a selected symmetry point‐group.
Abstract: We introduce a new mathematical tool for quantifying the symmetry contents of molecular structures: the Symmetry Operation Measures. In this approach, we measure the minimal distance between a given structure and the structure which is obtained after applying a selected symmetry operation on it. If the given operation is a true symmetry operation for the structure, this distance is zero; otherwise it gives an indication of how different the transformed structure is from the original one. Specifically, we provide analytical solutions for measures of all the improper rotations, S, including mirror symmetry and inversion, as well as for all pure rotations, C. These measures provide information complementary to the Continuous Symmetry Measures (CSM) that evaluate the distance between a given structure and the nearest structure which belongs to a selected symmetry point-group. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008

Journal ArticleDOI
TL;DR: In this article, the use of Lie symmetry groups in transfinite physics has been studied and a collection of simple examples of transfinite continuation is illustrated and various physically relevant results are obtained.
Abstract: The work addresses the question of extending certain symplectic and exceptional Lie Symmetry groups to the realm of chaotic dynamics. Using a collection of simple examples, the technique of transfinite continuation is illustrated and various physically relevant results are obtained. The paper is intended as an elementary introduction to the use of symmetry groups in transfinite physics and as such is a sequel to a series of previous papers constituting the elementary and advanced mathematical prerequisite for a proper understanding of E-infinity theory.

Journal ArticleDOI
TL;DR: In this article, the spontaneous nonmagnetic time-reversal symmetry breaking in a two-dimensional Fermi liquid without breaking either the translation symmetry or the U(1) charge symmetry was studied.
Abstract: We study the spontaneous nonmagnetic time-reversal symmetry breaking in a two-dimensional Fermi liquid without breaking either the translation symmetry or the U(1) charge symmetry. Assuming the low-energy physics is described by fermionic quasiparticle excitations, we identified an ``emergent'' local $\text{U}{(1)}^{N}$ symmetry in momentum space for an $N$-band model. For a large class of models, including all one-band and two-band models, we found that the time-reversal and chiral symmetry breaking can be described by the $\text{U}{(1)}^{N}$ gauge theory associated with this emergent local $\text{U}{(1)}^{N}$ symmetry. This conclusion enables the classification of the time-reversal symmetry-breaking states as types I and II, depending on the type of accompanying spatial symmetry breaking. The properties of each class are studied. In particular, we show that the states breaking both time reversal and chiral symmetries are described by spontaneously generated Berry phases. We also show examples of the time-reversal symmetry-breaking phases in several different microscopically motivated models and calculate their associated Hall conductance within a mean-field approximation. The fermionic nematic phase with time-reversal symmetry breaking is also presented and the possible realizations in strongly correlated models such as the Emery model are discussed.

Journal ArticleDOI
TL;DR: In this paper, the role of particle-hole symmetry on the universality class of various quantum phase transitions corresponding to the onset of superfluidity at zero temperature of bosons in a quenched random medium was studied.
Abstract: We study the role of particle-hole symmetry on the universality class of various quantum phase transitions corresponding to the onset of superfluidity at zero temperature of bosons in a quenched random medium. To obtain a model with an exact particle-hole symmetry it is necessary to use the Josephson junction array, or quantum rotor, Hamiltonian, which may include disorder in both the site energies and the Josephson couplings between wave function phase operators at different sites. The functional integral formulation of this problem in $d$ spatial dimensions yields a $(d+1)$-dimensional classical $XY$ model with extended disorder, constant along the extra imaginary time dimension---the so-called random rod problem. Particle-hole symmetry may then be broken by adding nonzero site energies, which may be uniform or site dependent. We may distinguish three cases: (i) exact particle-hole symmetry, in which the site energies all vanish; (ii) statistical particle-hole symmetry, in which the site energy distribution is symmetric about zero, vanishing on average; and (iii) complete absence of particle-hole symmetry in which the distribution is generic. We explore in each case the nature of the excitations in the nonsuperfluid Mott insulating and Bose glass phases. We show, in particular, that, since the boundary of the Mott phase can be derived exactly in terms of that for the pure, nondisordered system, there can be no direct Mott-superfluid transition. Recent Monte Carlo data to the contrary can be explained in terms of rare region effects that are inaccessible to finite systems. We find also that the Bose glass compressibility, which has the interpretation of a temporal spin stiffness or superfluid density, is positive in cases (ii) and (iii), but that it vanishes with an essential singularity as full particle-hole symmetry is restored. We then focus on the critical point and discuss the relevance of type (ii) particle-hole symmetry-breaking perturbations to the random rod critical behavior, identifying a nontrivial crossover exponent. This exponent cannot be calculated exactly but is argued to be positive and the perturbation therefore relevant. We argue next that a perturbation of type (iii) is irrelevant to the resulting type (ii) critical behavior: The statistical symmetry is restored on large scales close to the critical point, and case (ii) therefore describes the dirty boson fixed point. Using various duality transformations we verify all of these ideas in one dimension. To study higher dimensions, we attempt, with partial success, to generalize the Dorogovtsev--Cardy--Boyanovsky double-epsilon expansion technique to this problem. We find that when the dimension of time ${ϵ}_{\ensuremath{\tau}}l{ϵ}_{\ensuremath{\tau}}^{c}\ensuremath{\simeq}\frac{8}{29}$ is sufficiently small a type (ii) symmetry-breaking perturbation is irrelevant, but that for sufficiently large ${ϵ}_{\ensuremath{\tau}}g{ϵ}_{\ensuremath{\tau}}^{c}$ particle-hole asymmetry is a relevant perturbation and a new stable fixed point appears. Furthermore, for ${ϵ}_{\ensuremath{\tau}}g{ϵ}_{\ensuremath{\tau}}^{c2}\ensuremath{\approx}\frac{2}{3}$, this fixed point is stable also to perturbations of type (iii): at $ϵ={ϵ}_{\ensuremath{\tau}}^{c2}$ the generic type (iii) fixed point merges with the new fixed point. We speculate, therefore, that this new fixed point becomes the dirty boson fixed point when ${ϵ}_{\ensuremath{\tau}}=1$. We point out, however, that ${ϵ}_{\ensuremath{\tau}}=1$ may be quite special. Thus, although the qualitative renormalization group flow picture the double-epsilon expansion technique provides is quite compelling, one should remain wary of applying it quantitatively to the dirty boson problem.

Journal ArticleDOI
TL;DR: In this paper, it was shown that thermodynamic entropy production can be related to the breaking of time-reversal symmetry in the statistical description of these non-equilibrium systems.
Abstract: We here present the complete analysis of experiments on driven Brownian motion and electric noise in an RC circuit, showing that thermodynamic entropy production can be related to the breaking of time-reversal symmetry in the statistical description of these non-equilibrium systems. The symmetry breaking can be expressed in terms of dynamical entropies per unit time, one for the forward process and the other for the time-reversed process. These entropies per unit time characterize dynamical randomness, i.e., temporal disorder, in time series of the non-equilibrium fluctuations. Their difference gives the well-known thermodynamic entropy production, which thus finds its origin in the time asymmetry of dynamical randomness, alias temporal disorder, in systems driven out of equilibrium.

Book
26 May 2008
TL;DR: In this paper, three topics in physics -symmetry, condensed matter physics, and computational methods -were combined into one pedagogical textbook for graduate students in condensed matter, materials science, and chemistry.
Abstract: Unlike existing texts, this book blends for the first time three topics in physics - symmetry, condensed matter physics and computational methods - into one pedagogical textbook. It includes new concepts in mathematical crystallography; experimental methods capitalizing on symmetry aspects; non-conventional applications such as Fourier crystallography, color groups, quasicrystals and incommensurate systems; as well as concepts and techniques behind the Landau theory of phase transitions. Adopting a computational approach to the application of group theoretical techniques to solving symmetry related problems, it dramatically alleviates the need for intensive calculations usually found in the presentation of symmetry. Writing computer programs helps the student achieve a firm understanding of the underlying concepts, and sample programs, based on Mathematica, are presented throughout the book. Containing over 150 exercises, this textbook is ideal for graduate students in condensed matter physics, materials science, and chemistry. Solutions and computer programs are available online at www.cambridge.org/9780521828451.

Journal ArticleDOI
TL;DR: In this paper, it was shown that in O'Raifeartaigh models of spontaneous supersymmetry breaking, R-symmetries can be broken by nonzero values of fields at tree level, rather than by vacuum expectation values of pseudomoduli at loop level.
Abstract: We show that in O'Raifeartaigh models of spontaneous supersymmetry breaking, R-symmetries can be broken by non-zero values of fields at tree level, rather than by vacuum expectation values of pseudomoduli at loop level. As a complement of the recent result by Shih, we show that there must be a field in the theory with R-charge different from zero and two in order for R-symmetry breaking to occur, no matter whether the breaking happens at tree or loop level. We review the example by CDFM, and construct two types of tree level R-symmetry breaking models with a wide range of parameters and free of runaway problem. And the R-symmetry is broken everywhere on the pseudomoduli space in these models. This provides a rich set of candidates for SUSY model building and phenomenology.

Journal ArticleDOI
TL;DR: In this article, a modification of the five-dimensional description of dynamical electroweak symmetry breaking inspired by the AdS/CFT correspondence was studied, where conformal symmetry is lost in the low-energy region near the IR brane by a power-law departure from the pure AdS background.
Abstract: We study a modification of the five-dimensional description of dynamical electroweak symmetry breaking inspired by the AdS/CFT correspondence. Conformal symmetry is broken in the low-energy region near the IR brane by a power-law departure from the pure AdS background. Such a modification--while not spoiling the identification of the IR brane with the scale of confinement--has a dramatic effect on both the coupling of the first composite states to the standard model currents and their self-couplings. Chiral symmetry breaking can take place at a scale larger than the IR cutoff. This study shows that observables, such as the precision parameter S-circumflex, which depend on the couplings of the lightest composite states to the currents, are very sensitive to the details of the dynamics in the low-energy region where conformal symmetry is lost and electroweak symmetry is broken just above the scale of confinement. Therefore results of calculations of these observables in AdS/CFT inspired scenarios should be interpreted conservatively. The most important phenomenological consequence for physics at the Large Hadron Collider is that the bound on the mass scale of the heavy excitations (technirho mesons) in a realistic model is in general lower than in the pure AdS background with a simplemore » hard-wall cutoff in the IR.« less

Journal ArticleDOI
TL;DR: In this paper, the authors show that supersymmetry and R-symmetry can be dynamically broken in a long-lived metastable vacuum of SQCD with massive and massless flavors.
Abstract: We show that supersymmetry and R-symmetry can be dynamically broken in a long-lived metastable vacuum of SQCD with massive and massless flavors. The vacuum results from a competition of a (leading) two-loop effect and small "Planck" suppressed higher-dimension operators. This mechanism provides a particularly simple realization of dynamical SUSY and R-symmetry breaking, and as such it is a good starting point for building phenomenologically viable models of gauge mediation. We take a preliminary step in this direction by constructing a complete model of minimal gauge mediation. Here we find that the parameters of the model are surprisingly constrained by the hidden sector. Similar mechanisms for creating long-lived states operate in a large class of models.

Journal ArticleDOI
TL;DR: In this article, a functional approach was employed to investigate the confinement problem in quenched Landau gauge QCDs and showed that a linear rising potential between massive quarks is generated by infrared singularities in the dressed quark-gluon vertex.
Abstract: We employ a functional approach to investigate the confinement problem in quenched Landau gauge QCD. We demonstrate analytically that a linear rising potential between massive quarks is generated by infrared singularities in the dressed quark–gluon vertex. The self-consistent mechanism that generates these singularities is driven by the scalar Dirac amplitudes of the full vertex and the quark propagator. These can only be present when chiral symmetry is broken. We have thus uncovered a novel mechanism that directly links chiral symmetry breaking with confinement.

Journal ArticleDOI
TL;DR: The stability properties of models of spontaneous mirror symmetry breaking in chemistry are characterized algebraically and the critical parameter controlling the chiral symmetry breaking transition from racemic to chiral steady-state solutions is identified.

Journal ArticleDOI
TL;DR: In this paper, the exact dynamics of harmonic systems in the presence of an arbitrary radiation field are studied and necessary conditions for phase controllability are identified and are shown to be identical in quantum and classical mechanics.
Abstract: Necessary conditions for generating phase-controllable asymmetry in spatially symmetric systems using lasers are identified and are shown to be identical in quantum and classical mechanics. First, by studying the exact dynamics of harmonic systems in the presence of an arbitrary radiation field, it is demonstrated that anharmonicities in the system's potential are a necessary requirement for phase controllability. Then, by analysing the space-time symmetries of the laser-driven Liouville dynamics for classical and quantum systems, a common set of temporal symmetries for the driving field that need to be violated to induce transport is identified. The conditions apply to continuous wave lasers and to symmetry breaking effects that do not rely on the control of the absolute phase of the field. Known examples of laser fields that can induce transport in symmetric systems are seen to be particular cases of these symmetry constraints.

Journal ArticleDOI
TL;DR: In this article, the authors derived the effective potential to next-to-leading (NLO) order and showed that it can be renormalized in a temperature-independent manner.
Abstract: We study relativistic Bose-Einstein condensation at finite density and temperature using the linear sigma model in the one-particle-irreducible 1/N expansion. We derive the effective potential to next-to-leading (NLO) order and show that it can be renormalized in a temperature-independent manner. As a particular application, we study the thermodynamics of the pion gas in the chiral limit as well as with explicit symmetry breaking. At nonzero temperature we solve the NLO gap equation and show that the results describe the chiral-symmetry-restoring second-order phase transition in agreement with general universality arguments. However, due to nontrivial regularization issues, we are not able to extend the NLO analysis to nonzero chemical potential.

Journal ArticleDOI
TL;DR: It is demonstrated that a swarm under the DAR has unperceived and inherent singularities, and it is shown that the compelled symmetry-breaking effects at or near the singularities contribute fundamentally to the emergence of the collective behavior.
Abstract: A large-scale system consisting of self-propelled particles, moving under the directional alignment rule (DAR), can often self-organize to an ordered state that emerges from an initially rotationally symmetric configuration. It is commonly accepted that the DAR, which leads to effective long-range interactions, is the underlying mechanism contributing to the collective motion. However, in this paper, we demonstrate that a swarm under the DAR has unperceived and inherent singularities. Furthermore, we show that the compelled symmetry-breaking effects at or near the singularities, as well as the topological connectivity of the swarm in the evolution process, contribute fundamentally to the emergence of the collective behavior; and the elimination or weakening of singularities in the DAR will induce an unexpected sharp transition from coherent movement to isotropic dispersion. These results provide some insights into the fundamental issue of collective dynamics: What is the underlying mechanism causing the spontaneous symmetry breaking and leading to eventual coherent motion?

Journal ArticleDOI
TL;DR: It is shown, within the linearized theory, that a DOPO with spherical mirrors, in which the signal and idler fields correspond to first-order Laguerre- Gauss modes, produces a perfectly squeezed vacuum with the shape of a Hermite-Gauss mode.
Abstract: We predict squeezed light generation through the spontaneous rotational symmetry breaking occurring in a degenerate optical parametric oscillator (DOPO) pumped above threshold. We show, within the linearized theory, that a DOPO with spherical mirrors, in which the signal and idler fields correspond to first-order Laguerre-Gauss modes, produces a perfectly squeezed vacuum with the shape of a Hermite-Gauss mode. This occurs at any pumping level above threshold; hence, the phenomenon is noncritical. Imperfections of the rotational symmetry, due, e.g., to cavity anisotropy, are shown to have a small impact.

Journal ArticleDOI
TL;DR: In this paper, the bipartite and multipartite entanglement for the ground state of the one-dimensional $XY$ model in a transverse magnetic field in the thermodynamical limit was analyzed.
Abstract: We analyze the bipartite and multipartite entanglement for the ground state of the one-dimensional $XY$ model in a transverse magnetic field in the thermodynamical limit. We explicitly take into account the spontaneous symmetry breaking in order to explore the relation between entanglement and quantum phase transitions. As a result we show that while both bipartite and multipartite entanglement can be enhanced by spontaneous symmetry breaking deep into the ferromagnetic phase, only the latter is affected by it in the vicinity of the critical point. This result adds to the evidence that multipartite, and not bipartite, entanglement is the fundamental indicator of long-range correlations in quantum phase transitions.