Showing papers on "Explicit symmetry breaking published in 2012"

PT symmetry and spontaneous symmetry breaking in a microwave billiard.

Abstract: We demonstrate the presence of parity-time ($\mathcal{P}\mathcal{T}$) symmetry for the non-Hermitian two-state Hamiltonian of a dissipative microwave billiard in the vicinity of an exceptional point (EP). The shape of the billiard depends on two parameters. The Hamiltonian is determined from the measured resonance spectrum on a fine grid in the parameter plane. After applying a purely imaginary diagonal shift to the Hamiltonian, its eigenvalues are either real or complex conjugate on a curve, which passes through the EP. An appropriate basis choice reveals its $\mathcal{P}\mathcal{T}$ symmetry. Spontaneous symmetry breaking occurs at the EP.

Topological Invariants for Spin-Orbit Coupled Superconductor Nanowires

Abstract: We show that the Hamiltonian of a multiband spin-orbit coupled semiconductor nanowire with Zeeman splitting and s-wave superconductivity is approximately chiral symmetric. The chiral symmetry becomes exact when only one pair of confinement bands is occupied and the Zeeman splitting is parallel to the nanowire. In this idealized case the Hamiltonian is in the BDI symmetry class of the topological classification of band Hamiltonians, allowing an arbitrary integer number of zero-energy Majorana fermion modes at each end. In the realistic case of multiband wires (Zeeman splitting still parallel to the length) the chiral symmetry is approximate and results in multiple near-zero-energy end states with increasing Zeeman splitting. The existence of such low energy end states implies the vanishing of the minigap with increased Zeeman splitting which can only be restored by breaking the approximate chiral symmetry by a second Zeeman field.

Magnetic Catalysis: A Review

Abstract: We give an overview of the magnetic catalysis phenomenon. In the framework of quantum field theory, magnetic catalysis is broadly defined as an enhancement of dynamical symmetry breaking by an external magnetic field. We start from a brief discussion of spontaneous symmetry breaking and the role of a magnetic field in its a dynamics. This is followed by a detailed presentation of the essential features of the phenomenon. In particular, we emphasize that the dimensional reduction plays a profound role in the pairing dynamics in a magnetic field. Using the general nature of underlying physics and its robustness with respect to interaction types and model content, we argue that magnetic catalysis is a universal and model-independent phenomenon. In support of this claim, we show how magnetic catalysis is realized in various models with short-range and long-range interactions. We argue that the general nature of the phenomenon implies a wide range of potential applications: from certain types of solid state systems to models in cosmology, particle and nuclear physics. We finish the review with general remarks about magnetic catalysis and an outlook for future research.

Electric–magnetic symmetry and Noether's theorem

Abstract: In the absence of charges, Maxwell's equations are highly symmetrical. In particular, they place the electric and magnetic fields on equal footing. In light of this electric–magnetic symmetry, we introduce a variational description of the free electromagnetic field that is based upon the acknowledgement of both electric and magnetic potentials. We use our description, together with Noether's theorem, to demonstrate that electric–magnetic symmetry is, in essence, an expression of the conservation of optical helicity. The symmetry associated with the conservation of Lipkin's zilches is also identified. We conclude by considering, with care, the subtle separation of the rotation and boost angular momenta of the field into their 'spin' and 'orbital' contributions.

Mechanism for a pairing state with time-reversal symmetry breaking in iron-based superconductors

Abstract: The multipocket Fermi surfaces of iron-based superconductors promote pairing states with both extended $s$-wave and $d$-wave symmetry. We argue that the competition between these two order parameters could lead to a time-reversal symmetry-breaking state with $s+id$ pairing symmetry in the iron-based superconductors, and propose several scenarios in which this phase may be found. To understand the emergence of such a pairing state on a more rigorous footing, we start from a microscopic five-orbital description representative of the pnictides. Using a combined approach of functional renormalization-group and mean-field analysis, we identify the microscopic parameters of the $s+id$ pairing state. There, we find the most promising region for $s+id$ pairing in the electron-doped regime with an enhanced pnictogen height.

Symmetry protected topological order and spin susceptibility in superfluid 3He-B.

Abstract: We here demonstrate that the superfluid $^{3}\mathrm{He}\mathrm{\text{\ensuremath{-}}}B$ under a magnetic field in a particular direction stays topological due to a discrete symmetry, that is, in a symmetry protected topological order. Because of the symmetry protected topological order, helical surface Majorana fermions in the $B$ phase remain gapless and their Ising spin character persists. We unveil that the competition between the Zeeman magnetic field and dipole interaction involves an anomalous quantum phase transition in which a topological phase transition takes place together with spontaneous symmetry breaking. Based on the quasiclassical theory, we illustrate that the phase transition is accompanied by anisotropic quantum criticality of spin susceptibilities on the surface, which is detectable in NMR experiments.

Vortices and Chirality in Multi-Band Superconductors

Abstract: We investigate some significant properties of multi-band superconductors. They are time-reversal symmetry breaking, chirality and fractional quantum flux vortices in three-band superconductors. The Bardeen–Cooper–Schrieffer (BCS) gap equation has a solution with time-reversal symmetry breaking in some cases. We derive the Ginzburg–Landau free energy from the BCS microscopic theory. The frustrating pairing interaction among Fermi surfaces leads to a state with broken time-reversal symmetry, that is, a chiral solution. The Ginzburg–Landau equation for three-component superconductors leads to a double sine-Gordon model. A kink solution exists to this equation as in the conventional sine-Gordon model. In the chiral region of the double sine-Gordon model, an inequality of Bogomol'nyi type holds, and fractional-π kink solutions exist with the topological charge Q . This yields multi-vortex bound states in three-band superconductors.

On the influence of a Coulomb-like potential induced by the Lorentz symmetry breaking effects on the harmonic oscillator

Abstract: In this work, we obtain bound states for a nonrelativistic spin-half neutral particle under the influence of a Coulomb-like potential induced by the Lorentz symmetry breaking effects. We present a new possible scenario of studying the Lorentz symmetry breaking effects on a nonrelativistic quantum system defined by a fixed space-like vector field parallel to the radial direction interacting with a uniform magnetic field along the z -axis. Furthermore, we also discuss the influence of a Coulomb-like potential induced by Lorentz symmetry violation effects on the two-dimensional harmonic oscillator.

Symmetries of hadrons after unbreaking the chiral symmetry

Abstract: We study hadron correlators upon artificial restoration of the spontaneously broken chiral symmetry. In a dynamical lattice simulation we remove the lowest lying eigenmodes of the Dirac operator from the valence quark propagators and study the evolution of the hadron masses obtained. All mesons and baryons in our study, except for a pion, survive the unbreaking of the chiral symmetry and their exponential decay signals become essentially better. From the analysis of the observed spectroscopic patterns we conclude that confinement still persists while the chiral symmetry is restored. All hadrons fall into different chiral multiplets. The broken $U(1{)}_{A}$ symmetry does not get restored upon unbreaking the chiral symmetry. We also observe signals of some higher symmetry that includes chiral symmetry as a subgroup. Finally, from comparison of the $\ensuremath{\Delta}\ensuremath{-}N$ splitting before and after the unbreaking of the chiral symmetry, we conclude that both the color-magnetic and the flavor-spin quark-quark interactions are of equal importance.

Review of AdS/CFT Integrability, Chapter V.2: Dual Superconformal Symmetry

Abstract: Scattering amplitudes in planar N = 4 super Yang-Mills theory reveal a remarkable symmetry structure. In addition to the superconformal symmetry of the La- grangian of the theory, the planar amplitudes exhibit a dual superconformal symmetry. The presence of this additional symmetry imposes strong restrictions on the amplitudes and is connected to a duality relating scattering amplitudes to Wilson loops dened on polygonal light-like contours. The combination of the superconformal and dual super- conformal symmetries gives rise to a Yangian, an algebraic structure which is known to be related to the appearance of integrability in other regimes of the theory. We discuss two dual formulations of the symmetry and address the classication of its invariants.

Chiral symmetry breaking and external fields in the Kuperstein-Sonnenschein model

Abstract: A novel holographic model of chiral symmetry breaking has been proposed by Kuperstein and Sonnenschein by embedding non-supersymmetric probe D7 and anti-D7 branes in the Klebanov-Witten background. We study the dynamics of the probe flavours in this model in the presence of finite temperature and a constant electromagnetic field. In keeping with the weakly coupled field theory intuition, we find the magnetic field promotes spontaneous breaking of chiral symmetry whereas the electric field restores it. The former effect is universally known as the “magnetic catalysis” in chiral symmetry breaking. In the presence of an electric field such a condensation is inhibited and a current flows. Thus we are faced with a steady-state situation rather than a system in equilibrium. We conjecture a definition of thermodynamic free energy for this steady-state phase and using this proposal we study the detailed phase structure when both electric and magnetic fields are present in two representative configurations: mutually perpendicular and parallel.

Chiral symmetry breaking in graphene

Abstract: The question of whether the Coulomb interaction is strong enough to break the sublattice symmetry of undoped graphene is discussed. We formulate a strong coupling expansion where the ground state of the Coulomb Hamiltonian is found exactly and the kinetic hopping Hamiltonian is treated as a perturbation. We argue that many of the properties of the resulting system would be shared by graphene with a Hubbard model interaction. In particular, the best candidate sublattice symmetry-breaking ground state is an antiferromagnetic Mott insulator. We discuss the results of some numerical simulations which indicate that the Coulomb interaction is indeed subcritical. We also point out the curious fact that if the electron did not have spin degeneracy, the tendency to break chiral symmetry would be much greater and even relatively weak Coulomb interactions would likely gap the spectrum.

Spontaneous breaking of continuous translational invariance

Abstract: Unbroken continuous translational invariance is often taken as a basic assumption in discussions of spontaneous symmetry breaking (SSB), which singles out SSB of translational invariance itself as an exceptional case. We present a framework that allows us to treat translational invariance on the same footing as other symmetries. It is shown that existing theorems on SSB can be straightforwardly extended to this general case. As a concrete application, we analyze the Nambu-Goldstone modes in a (ferromagnetic) supersolid. We prove on the ground of the general theorems that the Bogoliubov mode stemming from a spontaneously broken internal U(1) symmetry and the longitudinal phonon due to a crystalline order are distinct physical modes.

Question of Peccei-Quinn symmetry and quark masses in the economical 3-3-1 model

Abstract: We show that there is an infinite number of $U(1)$ symmetries like Peccei-Quinn symmetry in the 3-3-1 model with minimal scalar sector---two scalar triplets. Moreover, all of them are completely broken due to the model's scalars by themselves (notice that these scalars as known to have been often used to break the gauge symmetry and to generate the masses for the model's particles). There is not any residual Peccei-Quinn symmetry. Because of the minimal scalar content, there are some quarks that are massless at tree level, but they can get consistent mass contributions at one loop due to this fact. Interestingly, axions as associated with the mentioned $U(1)$s breaking (including Majoron due to lepton-charge breaking) are all gauged away because they are also the Goldstone bosons responsible for the gauge symmetry breaking as usual.

Infra-red effects of Non-linear sigma model in de Sitter space

Abstract: We extend our investigation on a possible de Sitter symmetry breaking mechanism in nonlinear sigma models. The scale invariance of the quantum fluctuations could make the cosmological constant time dependent signaling the de Sitter symmetry breaking. To understand such a symmetry breaking mechanism, we investigate the energy-momentum tensor. We show that the leading infra-red logarithms cancel to all orders in perturbation theory in a generic non-linear sigma model. When the target space is an N sphere, the de Sitter symmetry is preserved in the large N limit. For a less symmetric target space, the infra-red logarithms appear at the three loop level. However there is a counter term to precisely cancel it. The leading infra-red logarithms do not cancel for higher derivative interactions. We investigate such a model in which the infra-red logarithms first appear at the three loop level. A nonperturbative investigation in the large N limit shows that they eventually grow as large as the one loop effect.

Lattice dynamics reveals a local symmetry breaking in the emergent dipole phase of PbTe

Abstract: Local symmetry breaking in complex materials is emerging as an important contributor to materials properties but is inherently difficult to study. Here we follow up an earlier structural observation of such a local symmetry broken phase in the technologically important compound PbTe with a study of the lattice dynamics using inelastic neutron scattering (INS). We show that the lattice dynamics are responsive to the local symmetry broken phase, giving key insights in the behavior of PbTe, but also revealing INS as a powerful tool for studying local structure. The new result is the observation of the unexpected appearance upon warming of a new zone center phonon branch in PbTe. In a harmonic solid the number of phonon branches is strictly determined by the contents and symmetry of the unit cell. The appearance of the new mode indicates a crossover to a dynamic lower symmetry structure with increasing temperature. No structural transition is seen crystallographically, but the appearance of the new mode in inelastic neutron scattering coincides with the observation of local Pb off-centering dipoles observed in the local structure. The observation resembles relaxor ferroelectricity, but since there are no inhomogeneous dopants in pure PbTe this anomalous behavior is an intrinsic response of the system. We call such an appearance of dipoles out of a nondipolar ground-state ``emphanisis'' meaning the appearance out of nothing. It cannot be explained within the framework of conventional phase transition theories such as soft-mode theory and challenges our basic understanding of the physics of materials.

Rayleigh-Taylor instability in a two-component Bose-Einstein condensate with rotational symmetry

Abstract: The interfacial instability and subsequent dynamics in a phase-separated two-component Bose-Einstein condensate with rotational symmetry are studied. When the interatomic interaction or the trap frequency is changed, the Rayleigh-Taylor instability breaks the rotational symmetry of the interface, which is subsequently deformed into nonlinear patterns including mushroom shapes.

Gauge-invariant formalism with a Dirac-mode expansion for confinement and chiral symmetry breaking

Abstract: Using the eigenmode of the Dirac operator $\mathrm{D\ensuremath{\llap{ ot\;}}}={\ensuremath{\gamma}}^{\ensuremath{\mu}}{D}^{\ensuremath{\mu}}$ in quantum chromodynamics (QCD), we develop a manifestly gauge-covariant expansion and projection of the QCD operators such as the Wilson loop and the Polyakov loop. With this method, we perform a direct analysis of the correlation between confinement and chiral symmetry breaking in lattice QCD Monte Carlo calculation on ${6}^{4}$ at $\ensuremath{\beta}=5.6$. Even after removing the low-lying Dirac modes, which are responsible for chiral symmetry breaking, we find that the Wilson loop obeys the area law, and the slope parameter corresponding to the string tension, or confinement force, is almost unchanged. We find also that the Polyakov loop remains to be almost zero even without the low-lying Dirac modes, which indicates the ${Z}_{3}$-unbroken confinement phase. These results indicate that one-to-one correspondence does not hold between confinement and chiral symmetry breaking in QCD.

Condensation in the inhomogeneous zero-range process: an interplay between interaction and diffusion disorder

Abstract: We analyze the role of the interplay between on-site interaction and inhomogeneous diffusion on the phenomenon of condensation in the zero-range process. We predict a universal phase diagram in the plane of two exponents, respectively characterizing the interactions and the diffusion disorder. The most prominent outcome is the existence of an extended condensed phase. In the latter phase, which originates as a result of the combined effects of strong enough interaction and weak enough disorder, a typical high-density configuration has a unique condensate on top of a critical background, but the condensate may be located at any site of a large hosting set of favored sites, whose size grows sub-extensively. The novel extended condensed phase thus interpolates continuously between the two scenarios associated so far with the condensation transition, namely spontaneous symmetry breaking and explicit symmetry breaking.

Spin liquid correlations, anisotropic exchange, and symmetry breaking in Tb 2 Ti 2 O 7

Abstract: We have studied the low-energy spin dynamics between 4.6 and 0.07 K in a Tb${}_{2}$Ti${}_{2}$O${}_{7}$ single-crystal sample by means of inelastic neutron scattering experiments. The spectra consist in a dual response, with a static and an inelastic contribution, showing striking $Q$ dependencies. We propose an interpretation involving an anisotropic exchange interaction in combination with a breaking of the threefold symmetry at the rare earth site. Simulations of the $Q$-dependent scattering in the random phase approximation account well for the inelastic response.

Collective Symmetry Breaking and Resonant Non-Gaussianity

Abstract: We study inflationary models that produce a nearly scale-invariant power spectrum while breaking scale invariance significantly in the bispectrum. Under most circumstances, such models are finely-tuned, as radiative corrections generically induce a larger signal in the power spectrum. However, when scale invariance is broken collectively (i.e., it requires more than one coupling to break the symmetry), these radiative corrections may be suppressed. We illustrate the features and limitations of collective symmetry breaking in the context of resonant non-gaussianity. We discuss two examples where oscillatory features can arise predominantly in the bispectrum.

Consistent interactions and involution

Abstract: Starting from the concept of involution of field equations, a universal method is proposed for constructing consistent interactions between the fields. The method equally well applies to the Lagrangian and non-Lagrangian equations and it is explicitly covariant. No auxiliary fields are introduced. The equations may have (or have no) gauge symmetry and/or second class constraints in Hamiltonian formalism, providing the theory admits a Hamiltonian description. In every case the method identifies all the consistent interactions.

Massless or heavy due to two-fold symmetry: Surface-state electrons at W(110)

Abstract: The C2v symmetry of the W(110) surface influences strongly the spin-polarized Dirac-cone-like surface state within a spin-orbit-induced symmetry gap. We present a detailed angle-resolved photoemission study with s -a nd p-polarized light along three different symmetry lines. The Dirac-cone-like feature appears alongHa ndS, while it is strongly deformed alongN. A two-fold � 3 symmetry of the d-type surface state is identified from photoemission experiments using linearly polarized light. Our results are well described by model calculations based on an effective Hamiltonian with C2v symmetry. The flattened Dirac cone of the surface state is caused by hybridization with bulk continuum states of � 1 and � 2 symmetry. The spin texture of this state obtained from the model calculations shows a quasi-one-dimensional behavior. This finding opens a new avenue in the study of d-electron-based persistent spin helix systems and/or weak topological insulators.

Momentum routing invariance in Feynman diagrams and quantum symmetry breakings

Abstract: We illustrate with examples that quantum symmetry breakings in perturbation theory are connected to breakdown of momentum routing invariance (MRI) in the loops of a Feynman diagram. We show that MRI is a necessary and sufficient condition to preserve abelian gauge symmetry at arbitrary loop order. We adopt the implicit regularization framework in which surface terms that are directly connected to momentum routing can be constructed to arbitrary loop order. The interplay between momentum routing invariance, surface terms and anomalies is discussed. We also illustrate that MRI is important to preserve supersymmetry. For theories with poor symmetry content, such as scalar field theories, MRI is shown to be important in the calculation of renormalization group functions.

Probing the superconducting pairing symmetry from spin excitations in BiS$_2$ based superconductors

Abstract: Starting from a two-orbital model and based on the random phase approximation, spin excitations in the superconducting state of the newly discovered BiS$_2$ superconductors with three possible pairing symmetries are studied theoretically. We show that spin response is uniquely determined by the pairing symmetry. Possible spin resonance excitations might occur for the d-wave symmetry at an incommensurate momentum about $(0.7\pi,0.7\pi)$. For the p-wave symmetry the transverse spin excitation near $(0,0)$ is enhanced. For the s-wave pairing symmetry there is no spin resonance signature. These distinct features may be used for probing or determining the pairing symmetry in this newly discovered compound.