Explicit Symmetry Research Articles

Explicit symmetry breaking and effective spin models for four-component interacting Fermi gases in lattice potentials

We study low-temperature properties of the four-component Fermi gas of neutral atoms in optical lattice for several cases of explicit breaking of the SU(4) pseudospin symmetry in the framework of the Fermi–Hubbard model. For a reduced two-site system, we analyze the energy states and effective magnetic couplings in cases, where four interacting spin flavors in the Hubbard Hamiltonian form the symmetry subgroups of the type “three by one” or “two by two” according to their tunneling and interaction amplitudes, independently, and study behavior of the corresponding effective Heisenberg models in the limit of strong interaction. We also obtain and analyze the spatial density distributions of spin components in a harmonic optical trap for each case of explicit symmetry breaking.

Explicit Symmetry Breaking of Generalized Angular Momentum by Second‐Harmonic Generation in Underdense Plasmas

AbstractLight beams possess two intrinsic quantized degrees of freedom, related to spin angular momentum (SAM) and orbital angular momentum (OAM), whose manipulation enables extensive control over the topological properties of electromagnetic fields. In this context, structured fields constructed from a non‐separable combination of SAM and OAM have recently gained sustained interest. Such states are eigenstates of the so‐called generalized angular momentum (GAM), a mixed angular momentum operator encompassing both SAM and OAM components, which can result in astonishing fractional eigenvalues. The demonstration of GAM conservation under harmonic generation has suggested a potential relevance of this new form of angular momentum as a meaningful quantum number. In the present work, the scope of evaluation is expanded by investigating its conservation law with second‐harmonic generation in an underdense isotropic inhomogeneous plasma that relies on dipole‐forbidden interaction implying spin‐orbit coupling. This study reveals that the symmetry and topological properties of the field are disrupted during the nonlinear process, the GAM charge being only conserved on average. This symmetry breaking can be exploited to provide an easily detectable signature of the driving field topology or to create a robust topological attractor.

Kasner interiors from analytic hairy black holes

We conduct an exhaustive study of the interior geometry of a family of asymptotically AdSd+1 hairy black holes in an analytically controllable setup. The black holes are exact solutions to an Einstein-Maxwell-Dilaton theory and include the well-known Gubser-Rocha model. After reviewing the setup, we scrutinize the geometry beyond the horizon, finding that these backgrounds can exhibit timelike or Kasner singularities. We generalize the no inner-horizon theorem for hairy black holes to accommodate these findings. We then consider observables sensitive to the geometry behind the horizon, such as Complexity = Anything and the thermal a-function. In the Kasner case, we propose a new variant of complexity that characterizes the late-time rate by the Kasner exponents, extending previous work by Jørstad, Myers and Ruan. Additionally, we elucidate the power-law behavior of the thermal a-function near the singularity, directly relating it to the Kasner exponents. Finally, we introduce axion-like fields in the Gubser-Rocha model to study the impact of translational symmetry breaking on the black hole interior. We show that Kasner singularities occur for both explicit and spontaneous symmetry breaking, with the Kasner exponents depending on the strength of broken translations only in the latter case.

Revisiting O(N) σ model at unphysical pion masses and high temperatures. II. The vacuum structure and thermal σ pole trajectory with cross-channel improvements

The effective potential of the O(N) model at large N limit is reinvestigated with varying pion mass and temperature. For large pion masses and high temperatures, we find the phenomenologically favored vacuum, located on the upper branch of the double-branched effective potential for physical mπ, moves to the lower branch and becomes no longer a local minimum but a saddle point. The existence and running of the tachyon pole are also discussed. These phenomena indicate that the applicable energy range of the O(N) model is more and more limited as mπ becomes larger and the temperature goes higher. With the effective coupling constant defined from the effective potential, the possible correspondence between the two branches of the effective potential and the two phases of the theory (distinguished by positive or negative coupling) is verified even with nonzero explicit symmetry breaking and at finite temperature. Also, we generalize the N/D modified O(N) model to study the thermal trajectory of the σ pole with the cross-channel contributions considered and find the thermal σ pole trajectory resembles its counterpart with varying pion masses at zero temperature. Published by the American Physical Society 2024

Category of SET orders

We propose the representation principle to study physical systems with a given symmetry. In the context of symmetry enriched topological orders, we give the appropriate representation category, the category of SET orders, which include SPT orders and symmetry breaking orders as special cases. For fusion n-category symmetries, we show that the category of SET orders encodes almost all information about the interplay between symmetry and topological orders, in a natural and canonical way. These information include defects and boundaries of SET orders, symmetry charges, explicit and spontaneous symmetry breaking, stacking of SET orders, gauging of generalized symmetry, as well as quantum currents (SymTFT or symmetry TO). We also provide a detailed categorical algorithm to compute the generalized gauging. In particular, we proved that gauging is always reversible, as a special type of Morita-equivalence. The explicit data for ungauging, the inverse to gauging, is given.

Effect of charm quark on chiral phase transition in Nf=2+1+1 holographic QCD

We investigate the effect of the charm quark on the chiral phase transition of light quarks at finite temperature based on the four-flavor soft-wall holographic QCD model. In the massless limit, we find that the thermal chiral phase transition is of the second order in the four-quark-flavor system. In the case with the massive charm quark and the massless light and strange quarks, the order of the phase transition changes to the first order. This is due to the quark-flavor symmetry breaking which is associated with the violation of the U(1) axial symmetry. Once the light and strange quarks get massive, the explicit chiral symmetry breaking becomes eminent, and then the crossover phase transition is realized at the physical quark masses. We also map the order of the phase transition on a phase diagram in the quark-mass plane where the light- and strange-quark masses are degenerate but differ from the value of the charm-quark mass. This phase diagram is an extension of the conventional Columbia plot to the four-quark-flavor system. The critical exponents related to the chiral phase transition are also addressed. Published by the American Physical Society 2024

A radical solution to the Hubble tension problem

The Hubble tension has proven to be stubbornly persistent, despite widespread efforts to relax it. As a possible resolution of this problem we propose a radical alternative to the way in which cosmological models are viewed. Specifically, we consider building cosmological models from spaces that exhibit intrinsic symmetries, rather than as space-times with explicit symmetry. This change in perspective allows statistical homogeneity and isotropy to be maintained, while relaxing some strong mathematical constraints that the standard approach imposes. We show that a Hubble tension arises naturally in our new approach, and that (as a corollary) a prediction can be made for the radial component of the Baryon Acoustic Oscillations. Our prediction appears to be consistent with the DESI first-year data release, which has otherwise been interpreted as evidence for dynamical dark energy.

Gravity-gauge anomaly constraints on the energy-momentum tensor

We derive constraints on the four dimensional energy-momentum tensor from gravitational and gauge anomalies. Our work can be considered an extension of Duff’s analysis [1] to include parity-odd terms and explicit symmetry breaking. The constraints imply the absence of the parity-odd RR~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ R\\overset{\\sim }{R} $$\\end{document} and FF~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ F\\overset{\\sim }{F} $$\\end{document} terms, for theories whose symmetries are compatible with dimensional regularisation, in a model-independent way. Remarkably, even in the case of explicit symmetry breaking the □R-anomaly is found to be finite and unambiguous after applying the symmetry constraints. We compute mixed gravity-gauge anomalies at leading order and deduce phenomenological consequences for vector bosons associated with global chiral symmetries.

Robustness of the random language model.

The random language model [Phys. Rev. Lett. 122, 128301 (2019)0031-900710.1103/PhysRevLett.122.128301] is an ensemble of stochastic context-free grammars, quantifying the syntax of human and computer languages. The model suggests a simple picture of first-language learning as a type of annealing in the vast space of potential languages. In its simplest formulation, it implies a single continuous transition to grammatical syntax, at which the symmetry among potential words and categories is spontaneously broken. Here this picture is scrutinized by considering its robustness against extensions of the original model, and trajectories through parameter space different from those originally considered. It is shown here that (i) the scenario is robust to explicit symmetry breaking, an inevitable component of learning in the real world, and (ii) the transition to grammatical syntax can be encountered by fixing the deep (hidden) structure while varying the surface (observable) properties. It is also argued that the transition becomes a sharp thermodynamic transition in an idealized limit. Moreover, comparison with human data on the clustering coefficient of syntax networks suggests that the observed transition is equivalent to that normally experienced by children at age 24 months. The results are discussed in light of the theory of first-language acquisition in linguistics, and recent successes in machine learning.

Phases of Pseudo-Nambu-Goldstone bosons

We study the vacuum dynamics of pseudo-Nambu-Goldstone bosons (pNGBs) for SO(N + 1) → SO(N) spontaneous and explicit symmetry breaking. We determine the magnitude of explicit symmetry breaking consistent with an EFT description of the effective potential at zero and finite temperatures. We expose and clarify novel additional vacuum transitions that can arise for generic pNGBs below the initial scale of SO(N + 1) → SO(N) spontaneous symmetry breaking, which may have phenomenological relevance. In this respect, two phenomenological scenarios are analyzed: thermal and supercooled dark sector pNGBs. In the thermal scenario the vacuum transition is first-order but very weak. For a supercooled dark sector we find that, depending on the sign of the explicit symmetry breaking, one can have a symmetry-restoring vacuum transition SO(N – 1) → SO(N) which can be strongly first-order, with a detectable stochastic gravitational wave background signal.

Symmetry breaking in an extended O(2) model

Motivated by attempts to quantum simulate lattice models with continuous Abelian symmetries using discrete approximations, we study an extended-O(2) model in two dimensions that differs from the ordinary O(2) model by the addition of an explicit symmetry breaking term −hqcos(qφ). Its coupling hq allows to smoothly interpolate between the O(2) model (hq=0) and a q-state clock model (hq→∞). In the latter case, a q-state clock model can also be defined for noninteger values of q. Thus, such a limit can also be considered as an analytic continuation of an ordinary q-state clock model to noninteger q. In previous work, we established the phase diagram for noninteger q in the infinite coupling limit (hq→∞). We showed that there is a second-order phase transition at low temperature and a crossover at high temperature. In this work, we seek to establish the phase diagram at finite values of the coupling using Monte Carlo and tensor methods. We show that for noninteger q, the second-order phase transition at low temperature and crossover at high temperature persist to finite coupling. For integer q=2, 3, 4, we know there is a second-order phase transition at infinite coupling (i.e. the well-known clock models). At finite coupling, we find that the critical exponents for q=3, 4 vary with the coupling, and for q=4 the transition may turn into a Berezinskii-Kosterlitz-Thouless transition at small coupling. We comment on the similarities and differences of the phase diagrams with those of quantum simulators of the Abelian-Higgs model based on ladder-shaped arrays of Rydberg atoms. Published by the American Physical Society 2024

Dynamics of the O(4) critical point in QCD: Critical pions and diffusion in model G

We present a detailed study of the finite momentum dynamics of the O(4) critical point of QCD, which lies in the dynamic universality class of “model G.” The critical scaling of the model is analyzed in multiple dynamical channels. For instance, the finite momentum analysis allows us to precisely extract the pion dispersion curve below the critical point. The pion velocity is in striking agreement with the predictions relation and static universality. The pion damping rate and velocity are both consistent with the dynamical critical exponent ζ=3/2 of model G. Similarly, although the critical amplitude for the diffusion coefficient of the conserved O(4) charges is small, it is clearly visible both in the restored phase and with finite explicit symmetry breaking, and its dynamical scaling is again consistent with ζ=3/2. We determine a new set of universal dynamical critical amplitude ratios relating the diffusion coefficient to a suitably defined order parameter relaxation time. We also show that in a finite volume simulation, the chiral condensate diffuses on the coset manifold in a manner consistent with dynamical scaling, and with a diffusion coefficient that is determined by the transport coefficients of hydrodynamic pions. Finally, the amplitude ratios (together with other nonuniversal amplitudes also reported here) compile all relevant information for further studies of model G both in and out of equilibrium. Published by the American Physical Society 2024

Dualities in One-Dimensional Quantum Lattice Models: Topological Sectors

It has been a long-standing open problem to construct a general framework for relating the spectra of dual theories to each other. Here, we solve this problem for the case of one-dimensional quantum lattice models with symmetry-twisted boundary conditions. In Ref. [PRX Quantum 4, 020357], dualities are defined between (categorically) symmetric models that only differ in a choice of module category. Using matrix product operators, we construct from the data of module functors explicit symmetry operators preserving boundary conditions as well as intertwiners mapping topological sectors of dual models onto one another. We illustrate our construction with a family of examples that are in the duality class of the spin-12 Heisenberg XXZ model. One model has symmetry operators forming the fusion category Rep(S3) of representations of the group S3. We find that the mapping between its topological sectors and those of the XXZ model is associated with the nontrivial braided autoequivalence of the Drinfel’d center of Rep(S3). Published by the American Physical Society 2024

Approximate higher-form symmetries, topological defects, and dynamical phase transitions

Higher-form symmetries are a valuable tool for classifying topological phases of matter. However, emergent higher-form symmetries in interacting many-body systems are typically not exact due to the presence of topological defects. In this paper, we develop a systematic framework for building effective theories with approximate higher-form symmetries. We focus on a continuous U(1) q-form symmetry and study phases with various patterns of spontaneous and explicit symmetry breaking. We uncover a web of dualities between such phases and highlight their role in describing the presence of dynamical higher-form topological defects. In order to study the out-of-equilibrium dynamics of these phases of matter, we formulate respective hydrodynamic theories and study the spectra of excitations exhibiting higher-form charge relaxation and Goldstone relaxation effects. We show that our framework is able to describe various phase transitions due to proliferation of vortices or defects. This includes the melting transition in smectic crystals, the plasma phase transition from polarized gases to magnetohydrodynamics, the spin-ice transition, the superfluid to neutral fluid transition, and the Meissner effect in superconductors, among many others. Published by the American Physical Society 2024

Anomalous Hall Crystals or Moiré Chern Insulators? Spontaneous versus explicit translational symmetry breaking in graphene pentalayers

Anomalous Hall Crystals or Moiré Chern Insulators? Spontaneous versus explicit translational symmetry breaking in graphene pentalayers

Decays of the tensor glueball in a chiral approach

Glueballs remain an experimentally undiscovered prediction of QCD. Lattice QCD predicts a spectrum of glueballs, with the tensor (JPC = 2++) glueball being the second lightest, behind the scalar glueball. From an effective hadronic model based on spontaneous and explicit chiral symmetry breaking, we compute decay ratios of the tensor glueball into various meson decay chan nels. We find the tensor glueball to primarily decay into 2 vector mesons, dom inated by ρρ and K* K*. These results are compared to experimental data of decay rates of spin 2 mesons. Based on this comparison we make statements on the eligibility of these mesons as potential tensor glueball candidates.

Spontaneous and Explicit Spacetime Symmetry Breaking in Einstein–Cartan Theory with Background Fields

Explicit and spontaneous breaking of spacetime symmetry under diffeomorphisms, local translations, and local Lorentz transformations due to the presence of fixed background fields is examined in Einstein–Cartan theory. In particular, the roles of torsion and violation of local translation invariance are highlighted. The nature of the types of background fields that can arise and how they cause spacetime symmetry breaking is discussed. With explicit breaking, potential no-go results are known to exist, which if not evaded lead to inconsistencies between the Bianchi identities, Noether identities, and the equations of motion. These are examined in detail, and the effects of nondynamical backgrounds and explicit breaking on the energy–momentum tensor when torsion is present are discussed as well. Examples illustrating various features of both explicit and spontaneous breaking of local translations are presented and compared to the case of diffeomorphism breaking.

Holographic superfluid with gauge–axion coupling

We have constructed a holographic superfluid with gauge–axion coupling. Depending on whether the coupling is positive or negative, the system displays metallic or insulating behavior in its normal state. A significant feature of the system is the appearance of a mid-IR peak in the alternating current (AC) conductivity in a certain range of parameters. This peak arises due to competition between explicit symmetry breaking (ESB) and spontaneous symmetry breaking (SSB), which results in the presence of a pseudo-Goldstone mode. Moreover, a dip in low-frequency AC conductivity is observed, stemming from the excitation of the SSB Goldstone mode. In the superfluid phase, the effect of gauge–axion coupling on the condensation or superfluid energy gap is only amplified in the presence of strong momentum dissipation. Notably, for the case with negative gauge–axion coupling, a hard-gap-like behavior at low frequency and a pronounced peak at intermediate frequency are observed, indicating that the evolution of the superfluid component is distinct from that of positive coupling.

Composite topological solitons consisting of domain walls, strings, and monopoles in O(N) models

We study various composites of global solitons consisting of domain walls, strings, and monopoles in linear O(N) models with N = 2 and 3. Spontaneous symmetry breaking (SSB) of the O(N) symmetry down to O(N – 1) results in the vacuum manifold SN−1, together with a perturbed scalar potential in the presence of a small explicit symmetry breaking (ESB) interaction. The O(2) model is equivalent to the axion model admitting topological global (axion) strings attached by NDW domain walls. We point out for the NDW = 2 case that the topological stability of the string with two domain walls is ensured by sequential SSBs (ℤ2)2 → ℤ2 → 1, where the first SSB occurs in the vacuum leading to the topological domain wall as a mother soliton, only inside which the second SSB occurs giving rise to a subsequent kink inside the mother wall. From the bulk viewpoint, this kink is identical to a global string as a daughter soliton. This observation can be naturally ex- tended to the O(3) model, where a global monopole as a daughter soliton appears as a kink in a mother string or as a vortex on a mother domain wall, depending on ESB interactions. In the most generic case, the stability of the composite system consisting of the monopole, string, and domain wall is understood by the SSB (ℤ2)3 → (ℤ2)2 → ℤ2 → 1, in which the first SSB at the vacuum gives rise to the domain wall triggering the second one, so that the daughter string appears as a domain wall inside the mother wall triggering the third SSB, which leads to a granddaughter monopole as a kink inside the daughter vortex. We demonstrate numerical simulations for the dynamical evolution of the composite solitons.

Breaking rotations without violating the KSS viscosity bound

We revisit the computation of the shear viscosity to entropy ratio in a holographic p-wave superfluid model, focusing on the role of rotational symmetry breaking. We study the interplay between explicit and spontaneous symmetry breaking and derive a simple horizon formula for η/s, which is valid also in the presence of explicit breaking of rotations and is in perfect agreement with the numerical data. We observe that a source which explicitly breaks rotational invariance suppresses the value of η/s in the broken phase, competing against the effects of spontaneous symmetry breaking. However, η/s always reaches a constant value in the limit of zero temperature, which is never smaller than the Kovtun-Son-Starinets (KSS) bound, 1/4π. This behavior appears to be in contrast with previous holographic anisotropic models which found a power-law vanishing of η/s at small temperature. This difference is shown to arise from the properties of the near-horizon geometry in the extremal limit. Thus, our construction shows that the breaking of rotations itself does not necessarily imply a violation of the KSS bound.