Showing papers on "Symmetry (physics) published in 2021"

Holographic symmetry algebras for gauge theory and gravity

Abstract: All 4D gauge and gravitational theories in asymptotically flat spacetimes contain an infinite number of non-trivial symmetries. They can be succinctly characterized by generalized 2D currents acting on the celestial sphere. A complete classification of these symmetries and their algebras is an open problem. Here we construct two towers of such 2D currents from positive-helicity photons, gluons, or gravitons with integer conformal weights. These generate the symmetries associated to an infinite tower of conformally soft theorems. The current algebra commutators are explicitly derived from the poles in the OPE coefficients, and found to comprise a rich closed subalgebra of the complete symmetry algebra.

Thermodynamic evidence for a two-component superconducting order parameter in Sr2RuO4

Abstract: Sr2RuO4 has stood as the leading candidate for a spin-triplet superconductor for 26 years1. However, recent NMR experiments have cast doubt on this candidacy2,3 and it is difficult to find a theory of superconductivity that is consistent with all experiments. The order parameter symmetry for this material therefore remains an open question. Symmetry-based experiments are needed that can rule out broad classes of possible superconducting order parameters. Here, we use resonant ultrasound spectroscopy to measure the entire symmetry-resolved elastic tensor of Sr2RuO4 through the superconducting transition. We observe a thermodynamic discontinuity in the shear elastic modulus c66, which implies that the superconducting order parameter has two components. A two-component p-wave order parameter, such as px + ipy, naturally satisfies this requirement. As this order parameter appears to have been precluded by recent NMR experiments, we suggest that two other two-component order parameters, namely $$\{{d}_{xz},{d}_{yz}\}$$ and $$\{{d}_{{x}^{2}-{y}^{2}},{g}_{xy({x}^{2}-{y}^{2})}\}$$ , are now the prime candidates for the order parameter of Sr2RuO4. Ultrasound measurements show that the superconducting order parameter in strontium ruthenate must have two components.

Nonlinear tuning of PT symmetry and non-Hermitian topological states

Abstract: Topology, parity-time (PT) symmetry, and nonlinearity are at the origin of many fundamental phenomena in complex systems across the natural sciences, but their mutual interplay remains unexplored. We established a nonlinear non-Hermitian topological platform for active tuning of PT symmetry and topological states. We found that the loss in a topological defect potential in a non-Hermitian photonic lattice can be tuned solely by nonlinearity, enabling the transition between PT-symmetric and non-PT-symmetric regimes and the maneuvering of topological zero modes. The interaction between two apparently antagonistic effects is revealed: the sensitivity close to exceptional points and the robustness of non-Hermitian topological states. Our scheme using single-channel control of global PT symmetry and topology via local nonlinearity may provide opportunities for unconventional light manipulation and device applications.

Crossing Symmetric Dispersion Relations in Quantum Field Theories.

Abstract: For 2-2 scattering in quantum field theories, the usual fixed t dispersion relation exhibits only two-channel symmetry. This Letter considers a crossing symmetric dispersion relation, reviving certain old ideas from the 1970s. Rather than the fixed t dispersion relation, this needs a dispersion relation in a different variable z, which is related to the Mandelstam invariants s, t, u via a parametric cubic relation making the crossing symmetry in the complex z plane a geometric rotation. The resulting dispersion is manifestly three-channel crossing symmetric. We give simple derivations of certain known positivity conditions for effective field theories, including the null constraints, which lead to two sided bounds and derive a general set of new nonperturbative inequalities. We show how these inequalities enable us to locate the first massive string state from a low energy expansion of the four dilaton amplitude in type II string theory. We also show how a generalized (numerical) Froissart bound, valid for all energies, is obtained from this approach.

Non-Invertible Global Symmetries and Completeness of the Spectrum

Abstract: It is widely believed that consistent theories of quantum gravity satisfy two basic kinematic constraints: they are free from any global symmetry, and they contain a complete spectrum of gauge charges. For compact, abelian gauge groups, completeness follows from the absence of a 1-form global symmetry. However, this correspondence breaks down for more general gauge groups, where the breaking of the 1-form symmetry is insufficient to guarantee a complete spectrum. We show that the correspondence may be restored by broadening our notion of symmetry to include non-invertible topological operators, and prove that their absence is sufficient to guarantee a complete spectrum for any compact, possibly disconnected gauge group. In addition, we prove an analogous statement regarding the completeness of twist vortices: codimension-2 objects defined by a discrete holonomy around their worldvolume, such as cosmic strings in four dimensions. We discuss how this correspondence is modified in various, more general contexts, including non-compact gauge groups, Higgsing of gauge theories, and the addition of Chern-Simons terms. Finally, we discuss the implications of our results for the Swampland program, as well as the phenomenological implications of the existence of twist strings.

Flavour Hund’s coupling, Chern gaps and charge diffusivity in moiré graphene

Abstract: Interaction-driven spontaneous symmetry breaking lies at the heart of many quantum phases of matter. In moire systems, broken spin/valley 'flavour' symmetry in flat bands underlies the parent state from which correlated and topological ground states ultimately emerge1-10. However, the microscopic mechanism of such flavour symmetry breaking and its connection to the low-temperature phases are not yet understood. Here we investigate the broken-symmetry many-body ground state of magic-angle twisted bilayer graphene (MATBG) and its nontrivial topology using simultaneous thermodynamic and transport measurements. We directly observe flavour symmetry breaking as pinning of the chemical potential at all integer fillings of the moire superlattice, demonstrating the importance of flavour Hund's coupling in the many-body ground state. The topological nature of the underlying flat bands is manifested upon breaking time-reversal symmetry, where we measure energy gaps corresponding to Chern insulator states with Chern numbers 3, 2, 1 at filling factors 1, 2, 3, respectively, consistent with flavour symmetry breaking in the Hofstadter butterfly spectrum of MATBG. Moreover, concurrent measurements of resistivity and chemical potential provide the temperature-dependent charge diffusivity of MATBG in the strange-metal regime11-a quantity previously explored only in ultracold atoms12. Our results bring us one step closer to a unified framework for understanding interactions in the topological bands of MATBG, with and without a magnetic field.

Lie symmetry analysis for obtaining the abundant exact solutions, optimal system and dynamics of solitons for a higher-dimensional Fokas equation

Abstract: In this article, the Lie group of transformation method via one-dimensional optimal system is proposed to obtain some more exact solutions of the (4+1)-dimensional Fokas equation. Lie infinitesimal generators, possible vector fields, and their commutative and adjoint relations are presented by employing the Lie symmetry method. An optimal system of the one-dimensional subalgebras is also constructed using Lie vectors. Meanwhile, based on the optimal system, Lie symmetry reductions of the Fokas equation is obtained. A repeated process of Lie symmetry reductions, using the single, double, triple, quadruple, and quintuple combinations between the considered vectors, transforms the Fokas equation into nonlinear ordinary differential equations which produce abundant group-invariant solutions. The same problem was studied by Sadat et al. (Chaos Solitons Fractals 140:110134, 2020) using the same Lie symmetry technique via commutative product approach but with the less number of vector fields and therefore could obtain only three exact solutions as compared to the number of analytic solutions in this paper. In order to provide rich localized structures, some solutions are supplemented via numerical simulation, which produces some breather-type solitons, oscillating multi-solitons on the parabolic-shaped surface, fractal dromions, lump-type solitons, and annihilation of different parabolic multi-solitons profiles. The dynamical behaviors of excitation-localized structures are demonstrated graphically via 3D plots for suitable values of the arbitrary free parameters and independent arbitrary functions.

A (2+1)-dimensional Kadomtsev-Petviashvili equation with competing dispersion effect: Painlevé analysis, dynamical behavior and invariant solutions

Abstract: In this paper, we concern ourselves with the nonlinear Kadomtsev–Petviashvili equation (KP) with a competing dispersion effect. First we examine the integrability of governing equation via using the Painleve analysis. We next reduce the KP equation to a one-dimensional with the help of Lie symmetry analysis (LSA). The KP equation reduces to an ODE by employing the Lie symmetry analysis. We formally derive bright, dark and singular soliton solutions of the model. Moreover, we investigate the stability of the corresponding dynamical system via using phase plane theory. Graphical representation of the obtained solitons and phase portrait are illustrated by using Maple software.

Symmetry-resolved entanglement in AdS3/CFT2 coupled to U(1) Chern-Simons theory

Abstract: We consider symmetry-resolved entanglement entropy in AdS3/CFT2 coupled to U(1) Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS3, namely the Ryu-Takayanagi geodesic minimally coupled to the U(1) Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged U(1) vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the U(1) Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincare patch and global AdS3, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level k, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of $$ \hat{\mathfrak{u}}{(1)}_k $$ Kac-Moody type. Employing the $$ \hat{\mathfrak{u}}{(1)}_k $$ Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.

Extended corner symmetry, charge bracket and Einstein's equations

Abstract: We develop the covariant phase space formalism allowing for non-vanishing flux, anomalies, and field dependence in the vector field generators. We construct a charge bracket that generalizes the one introduced by Barnich and Troessaert and includes contributions from the Lagrangian and its anomaly. This bracket is uniquely determined by the choice of Lagrangian representative of the theory. We then extend the notion of corner symmetry algebra to include the surface translation symmetries and prove that the charge bracket provides a canonical representation of the extended corner symmetry algebra. This representation property is shown to be equivalent to the projection of the gravitational equations of motion on the corner, providing us with an encoding of the bulk dynamics in a locally holographic manner.

Multipole conservation laws and subdiffusion in any dimension

Abstract: Subdiffusion is a generic feature of chaotic many-body dynamics with multipole conservation laws and subsystem symmetries. We numerically study this subdiffusive dynamics, using quantum automaton random unitary circuits, in a broad range of models including one-dimensional models with dipole and quadrupole conservation, two-dimensional models with dipole conservation, and two-dimensional models with subsystem symmetry on the triangular lattice. Our results are in complete agreement with recent hydrodynamic predictions for such theories.

Faster Digital Quantum Simulation by Symmetry Protection

Abstract: Error reduction of several orders of magnitude in a quantum simulation may be possible by using a technique that explores symmetry protection.

A light-induced phononic symmetry switch and giant dissipationless topological photocurrent in ZrTe5

Abstract: Dissipationless currents from topologically protected states are promising for disorder-tolerant electronics and quantum computation. Here, we photogenerate giant anisotropic terahertz nonlinear currents with vanishing scattering, driven by laser-induced coherent phonons of broken inversion symmetry in a centrosymmetric Dirac material ZrTe5. Our work suggests that this phononic terahertz symmetry switching leads to formation of Weyl points, whose chirality manifests in a transverse, helicity-dependent current, orthogonal to the dynamical inversion symmetry breaking axis, via circular photogalvanic effect. The temperature-dependent topological photocurrent exhibits several distinct features: Berry curvature dominance, particle–hole reversal near conical points and chirality protection that is responsible for an exceptional ballistic transport length of ~10 μm. These results, together with first-principles modelling, indicate two pairs of Weyl points dynamically created by B1u phonons of broken inversion symmetry. Such phononic terahertz control breaks ground for coherent manipulation of Weyl nodes and robust quantum transport without application of static electric or magnetic fields. Femtosecond optical pulses are used to generate coherent phonons that break inversion symmetry and drive anisotropic terahertz photocurrents in the topological material ZrTe5.

Reflection positivity and invertible topological phases

Abstract: We implement an extended version of reflection positivity (Wick-rotated unitarity) for invertible topological quantum field theories and compute the abelian group of deformation classes using stable homotopy theory. We apply these field theory considerations to lattice systems, assuming the existence and validity of low-energy effective field theory approximations, and thereby produce a general formula for the group of symmetry protected topological (SPT) phases in terms of Thom’s bordism spectra; the only input is the dimension and symmetry type. We provide computations for fermionic systems in physically relevant dimensions. Other topics include symmetry in quantum field theories, a relativistic 10–fold way, the homotopy theory of relativistic free fermions, and a topological spin-statistics theorem.

Chiral Photocurrent in Parity-Violating Magnet and Enhanced Response in Topological Antiferromagnet

Abstract: A new classification of photocurrent responses in light of symmetry violations in the presence of magnetic order unveils two new types of photocurrent that can be readily tuned and enhanced by topological electronic structure in solids.

Semilinear elliptic equations involving mixed local and nonlocal operators

Abstract: In this paper, we consider an elliptic operator obtained as the superposition of a classical second-order differential operator and a nonlocal operator of fractional type. Though the methods that we develop are quite general, for concreteness we focus on the case in which the operator takes the form − Δ + ( − Δ)s, with s ∈ (0, 1). We focus here on symmetry properties of the solutions and we prove a radial symmetry result, based on the moving plane method, and a one-dimensional symmetry result, related to a classical conjecture by G.W. Gibbons.

Modular invariant A 4 models for quarks and leptons with generalized CP symmetry

Abstract: We perform a systematical analysis of the A4 modular models with generalized CP for the masses and flavor mixing of quarks and leptons, and the most general form of the quark and lepton mass matrices is given. The CP invariance requires all couplings real in the chosen basis and thus the vacuum expectation value of the modulus τ uniquely breaks both the modular symmetry and CP symmetry. The phenomenologically viable models with minimal number of free parameters and the results of fit are presented. We find 20 models with 7 real free parameters that can accommodate the experimental data of lepton sector. We then apply A4 modular symmetry to the quark sector to explain quark masses and CKM mixing matrix, the minimal viable quark model is found to contain 10 free real parameters. Finally, we give two predictive quark-lepton unification models which use only 16 real free parameters to explain the flavor patterns of both quarks and leptons.

Higher-form symmetries of 6d and 5d theories

Abstract: We describe general methods for determining higher-form symmetry groups of known 5d and 6d superconformal field theories (SCFTs), and 6d little string theories (LSTs). The 6d theories can be described as supersymmetric gauge theories in 6d which include both ordinary non-abelian 1-form gauge fields and also abelian 2-form gauge fields. Similarly, the 5d theories can also be often described as supersymmetric non-abelian gauge theories in 5d. Naively, the 1-form symmetry of these 6d and 5d theories is captured by those elements of the center of ordinary gauge group which leave the matter content of the gauge theory invariant. However, an interesting subtlety is presented by the fact that some massive BPS excitations, which includes the BPS instantons, are charged under the center of the gauge group, thus resulting in a further reduction of the 1-form symmetry. We use the geometric construction of these theories in M/F-theory to determine the charges of these BPS excitations under the center. We also provide an independent algorithm for the determination of 1-form symmetry for 5d theories that admit a generalized toric construction (i.e. a 5-brane web construction). The 2-form symmetry group of 6d theories, on the other hand, is captured by those elements of the center of the abelian 2-form gauge group that leave all the massive BPS string excitations invariant, which is much more straightforward to compute as it is encoded in the Green-Schwarz coupling associated to the 6d theory.

Spin polarization induced by the hydrodynamic gradients

Abstract: We systematically analyze the effects of the derivatives of the hydrodynamic fields on axial Wigner function that describes the spin polarization vector in phase space. We have included all possible first-order derivative contributions that are allowed by symmetry and compute the associated transport functions at one-loop using the linear response theory. In addition to reproducing known effects due to the temperature gradient and vorticity, we have identified a number of potentially significant contributions that are overlooked previously. In particular, we find that the shear strength, the symmetric and traceless part of the flow gradient, will induce a quadrupole for spin polarization in the phase space. We refer to this novel effect as the shear-induced polarization (SIP). Our results, together with hydrodynamic gradients obtained from hydrodynamic simulations, can be employed as a basis for the interpretation of the $\Lambda$ (anti-$\Lambda$) spin polarization measurement in heavy-ion collisions.

Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond $N$-ality.

Abstract: We study a 3d lattice gauge theory with gauge group $\mathrm{U}(1)^{N-1}\rtimes \mathrm{S}_N$, which is obtained by gauging the $\mathrm{S}_N$ global symmetry of a pure $\mathrm{U}(1)^{N-1}$ gauge theory, and we call it the semi-Abelian gauge theory. We compute mass gaps and string tensions for both theories using the monopole-gas description. We find that the effective potential receives equal contributions at leading order from monopoles associated with the entire $\mathrm{SU}(N)$ root system. Even though the center symmetry of the semi-Abelian gauge theory is given by $\mathbb{Z}_N$, we observe that the string tensions do not obey the $N$-ality rule and carry more detailed information on the representations of the gauge group. We find that this refinement is due to the presence of non-invertible topological lines as a remnant of $\mathrm{U}(1)^{N-1}$ one-form symmetry in the original Abelian lattice theory. Upon adding charged particles corresponding to $W$-bosons, such non-invertible symmetries are explicitly broken so that the $N$-ality rule should emerge in the deep infrared regime.

Holographic entanglement negativity and replica symmetry breaking

Abstract: Since the work of Ryu and Takayanagi, deep connections between quantum entanglement and spacetime geometry have been revealed. The negative eigenvalues of the partial transpose of a bipartite density operator is a useful diagnostic of entanglement. In this paper, we discuss the properties of the associated entanglement negativity and its Renyi generalizations in holographic duality. We first review the definition of the Renyi negativities, which contain the familiar logarithmic negativity as a special case. We then study these quantities in the random tensor network model and rigorously derive their large bond dimension asymptotics. Finally, we study entanglement negativity in holographic theories with a gravity dual, where we find that Renyi negativities are often dominated by bulk solutions that break the replica symmetry. From these replica symmetry breaking solutions, we derive general expressions for Renyi negativities and their special limits including the logarithmic negativity. In fixed-area states, these general expressions simplify dramatically and agree precisely with our results in the random tensor network model. This provides a concrete setting for further studying the implications of replica symmetry breaking in holography.

Topology and Symmetry of Quantum Materials via Nonlinear Optical Responses

Abstract: We review recent progress in the study of photogalvanic effects and optical second-harmonic generation in topological and noncentrosymmetric metals.

The Lie symmetry analysis and exact Jacobi elliptic solutions for the Kawahara–KdV type equations

Abstract: In this article, we aim to employ two analytical methods including, the Lie symmetry method and the Jacobi elliptical solutions finder method to acquire exact solitary wave solutions in various forms of (1+1)-dimensional Kawahara-KdV type equation and modified Kawahara-KdV type equation. These models are famous models that arise in the modeling of many complex physical phenomena. At the outset, we have generated geometric vector fields and infinitesimal generators of Kawahara KdV type equations. The (1+1)-dimensional Kawahara-KdV type equations reduced into ordinary differential equations (ODEs) using Lie symmetry reductions. Furthermore, numerous exact solitary wave solutions are obtained utilizing the Jacobi elliptical solutions finder method with the help of symbolic computation with Maple. The obtained results are new in the formulation, and more useful to explain complex physical phenomena. The results reveal that these mathematical approaches are straightforward, effective, and powerful methods that can be adopted for solving other nonlinear evolution equations.

A model of solitary waves in a nonlinear elastic circular rod: Abundant different type exact solutions and conservation laws

Abstract: In this study, we have dealt with a wave equation containing 4th order nonlinear mixed derivative. This model corresponds to solitary waves in nonlinear elastic circular rod. One dimensional optimal systems corresponding to Lie symmetry generator sub-algebras, symmetry reductions, and group invariant solutions corresponding to these systems have been systematically produced by Lie symmetry analysis of this model. In addition, traveling wave solutions were obtained with the help of an useful integration scheme of the model. These solutions are structures with physical properties of hyperbolic, trigonometric and rational solution types. Numerical simulations of the obtained solutions for different values of the parameters were made. The stability property of the obtained solutions is tested to show the ability of obtained solutions. In addition, the local conservation laws of the model were obtained with the help of the multiplier homotopy method.

Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models

Abstract: We consider the problem of the decomposition of the Renyi entanglement entropies in theories with a non-abelian symmetry by doing a thorough analysis of Wess-Zumino-Witten (WZW) models. We first consider SU(2)k as a case study and then generalise to an arbitrary non-abelian Lie group. We find that at leading order in the subsystem size L the entanglement is equally distributed among the different sectors labelled by the irreducible representation of the associated algebra. We also identify the leading term that breaks this equipartition: it does not depend on L but only on the dimension of the representation. Moreover, a log log L contribution to the Renyi entropies exhibits a universal prefactor equal to half the dimension of the Lie group.

Two-fold symmetric superconductivity in few-layer NbSe2

Abstract: The strong Ising spin–orbit coupling in certain two-dimensional transition metal dichalcogenides can profoundly affect the superconducting state in few-layer samples. For example, in NbSe2, this effect combines with the reduced dimensionality to stabilize the superconducting state against magnetic fields up to ~35 T, and could lead to topological superconductivity. Here we report a two-fold rotational symmetry of the superconducting state in few-layer NbSe2 under in-plane external magnetic fields, in contrast to the three-fold symmetry of the lattice. Both the magnetoresistance and critical field exhibit this two-fold symmetry, and it also manifests deep inside the superconducting state in NbSe2/CrBr3 superconductor-magnet tunnel junctions. In both cases, the anisotropy vanishes in the normal state, demonstrating that it is an intrinsic property of the superconducting phase. We attribute the behaviour to the mixing between two closely competing pairing instabilities, namely the conventional s-wave instability typical of bulk NbSe2 and an unconventional d- or p-wave channel that emerges in few-layer NbSe2. Our results demonstrate the unconventional character of the pairing interaction in few-layer transition metal dichalcogenides and highlight the exotic superconductivity in this family of two-dimensional materials. A two-fold rotational symmetry is observed in the superconducting state of NbSe2. This is strikingly different from the three-fold symmetry of the lattice, and suggests that a mixed conventional and unconventional order parameter exists in this material.

Generalized global symmetries of T[M] theories. Part I

Abstract: We study reductions of 6d theories on a d-dimensional manifold Md, focusing on the interplay between symmetries, anomalies, and dynamics of the resulting (6 − d)-dimensional theory T[Md]. We refine and generalize the notion of “polarization” to polarization on Md, which serves to fix the spectrum of local and extended operators in T[Md]. Another important feature of theories T[Md] is that they often possess higher-group symmetries, such as 2-group and 3-group symmetries. We study the origin of such symmetries as well as physical implications including symmetry breaking and symmetry enhancement in the renormalization group flow. To better probe the IR physics, we also investigate the ’t Hooft anomaly of 5d Chern-Simons matter theories. The present paper focuses on developing the general framework as well as the special case of d = 0 and 1, while an upcoming paper will discuss the case of d = 2, 3 and 4.