Spontaneous Breaking Research Articles

When the moduli space is an orbifold: spontaneous breaking of continuous non-invertible symmetries

We investigate theories of Nambu-Goldstone bosons where the spontaneously broken continuous symmetry is non-invertible. In such theories, the vacua generically parameterize an orbifold. We study in detail the simplest example of a single free scalar with shift symmetry, modded by reflection symmetry. At singular points of the vacuum manifold, we show that the spectrum of NG excitations is reduced, in particular there are no single-particle states. At the smooth points, on the other hand, single NG modes are present. We show that this is a consequence of the fact that at those points one can construct invertible operators implementing the continuous symmetry on the Hilbert space.

Dynamic mass generation and topological order in overscreened Kondo lattices

Multichannel Kondo lattice models are examples of strongly correlated electronic systems that exhibit non-Fermi-liquid behavior due to the presence of a continuous channel symmetry. Mean-field analyses have predicted that these systems undergo channel symmetry breaking at low temperature. We use the dynamical large-N technique to study temporal and spatial fluctuations of the multichannel Kondo model on a honeycomb lattice and find that this prediction is not generally true. Rather, we find a (2+1)-dimensional conformally invariant fixed point, governed by critical exponents that are found numerically. When we break time-reversal symmetry by adding a Haldane mass to the conduction electrons, three phases, separated by continuous transitions, are discernible: one characterized by dynamic mass generation and spontaneous breaking of the channel symmetry, one where topological defects restore channel symmetry but preserve the gap, and one with a Kondo-coupled chiral spin liquid. We argue that the last phase is a fractional Chern insulator with anyonic excitations. Published by the American Physical Society 2024

Symmetry broken vectorial Kerr frequency combs from Fabry-Pérot resonators

Spontaneous symmetry breaking of a pair of vector temporal cavity solitons has been established as a paradigm to modulate optical frequency combs, and finds many applications in metrology, frequency standards, communications, and photonic devices. While this phenomenon has successfully been observed in Kerr ring resonators, the counterpart exploiting linear Fabry-Pérot cavities is still unexplored. Here, we consider field polarization properties and describe a vector comb generation through the spontaneous symmetry breaking of temporal cavity solitons within coherently driven, passive, Fabry-Pérot cavities with Kerr nonlinearity. Global coupling effects due to the interactions of counter-propagating light restrict the maximum number of soliton pairs within the cavity - even down to a single soliton pair - and force long range polarization conformity in trains of vector solitons.

Spontaneous symmetry breaking on surface defects

Coleman’s theorem states that continuous internal symmetries cannot be spontaneously broken in two-dimensional quantum field theories (QFTs). In this work we consider surface (i.e. two-dimensional) defects in d-dimensional conformal field theories (CFTs) invariant under a continuous internal symmetry group G. We study under which conditions it is possible for a surface defect to break spontaneously a continuous internal symmetry. We find that spontaneous symmetry breaking (SSB) is impossible under reasonable assumptions on the defect Renormalization Group (RG) flow. Counterexamples are possible only for exotic RG flows, that do not terminate at a fixed-point. We discuss an example of this kind. We also illustrate our no-go result with an effective field theory analysis of generic defect RG flows. We find a generic weakly coupled defect universality class (with no SSB), where correlation functions decay logarithmically. Our analysis generalizes the recent discovery by Metlitski of the extraordinary-log boundary universality class in the O(N) model.

Theoretically Motivated Dark Electromagnetism as the Origin of Relativistic Modified Newtonian Dynamics

The present paper is a modest attempt to initiate the research program outlined in this abstract. We propose that general relativity and relativistic MOND (RelMOND) are analogues of broken electroweak symmetry. That is, SU(2)R×U(1)YDEM→U(1)DEM (DEM stands for dark electromagnetism), and GR is assumed to arise from the broken SU(2)R symmetry and is analogous to the weak force. RelMOND is identified with dark electromagnetism U(1)DEM, which is the remaining unbroken symmetry after the spontaneous symmetry breaking of the dark electro-grav sector SU(2)R×U(1)YDEM. This sector, as well as the electroweak sector, arises from the breaking of an E8×E8 symmetry in a recently proposed model of unification of the standard model with pre-gravitation, with the latter based on an SU(2)R gauge theory. The source charge for the dark electromagnetic force is the square root of mass, motivated by the experimental fact that the ratio of the square roots of the masses of the electron, up-quark, and down-quark is 1:2:3, which is the opposite of the ratio of their electric charges at 3:2:1. The introduction of the dark electromagnetic force helps us understand the peculiar mass ratios of the second and third generations of charged fermions. We also note that in the deep MOND regime, acceleration is proportional to the square root of mass, which motivates us to propose the relativistic U(1)DEM gauge symmetry as the origin of MOND. We explain why the dark electromagnetic force falls inversely with distance, as in MOND, rather than following the inverse square of distance. We conclude that dark electromagnetism effectively mimics cold dark matter, and the two are essentially indistinguishable in cosmological situations where CDM successfully explains observations, such as CMB anisotropies and gravitational lensing.

Demonstration of spontaneous symmetry breaking in self-modulated ring resonators

The demonstration of spontaneous symmetry breaking in a system consisting of a pair of self-modulated ring resonators is performed. In addition, the critical effect of thermal heating induced by optical absorption is studied, where experimental results with numerical calculations reveal that optical absorption contributing as an optical nonlinearity is greatly dominant over the optical Kerr effect under certain operation speeds, depicting a significant impact on the system performance. Our analysis of the operation characteristics outlines important characteristics of self-modulated nonlinear resonators and their function as an optical binary state system. Published by the American Physical Society 2024

Ricci reheating reloaded

A Hubble-induced phase transition is a natural spontaneous symmetry breaking mechanism allowing for explosive particle production in non-oscillatory models of inflation involving non-minimally coupled spectator fields. In this work, we perform a comprehensive characterisation of this type of transitions as a tachyonic Ricci-heating mechanism, significantly extending previous results in the literature. By performing 𝒪 (100) 3+1-dimensional classical lattice simulations, we explore the parameter space of two exemplary scenarios, numerically determining the main timescales in the process. Based on these results, we formulate a set of parametric equations that offer a practical approach for determining the efficiency of the heating process, the temperature at the onset of radiation domination, and the minimum number of e-folds of inflation needed to resolve the flatness and horizon problems in specific quintessential inflation scenarios. These parametric equations eliminate the need for additional lattice simulations, providing a convenient and efficient method for evaluating these key quantities.

Magnetization direction-controlled topological band structure in TlTiX (X = Si, Ge) monolayers

The quantum anomalous Hall (QAH) insulator is a vital material for the investigation of emerging topological quantum effects, but its extremely low working temperature limits experiments. Apart from the temperature challenge, effective regulation of the topological state of QAH insulators is another crucial concern. Here, by first-principles calculations, we find a family of stable two-dimensional materials TlTiX (X = Si, Ge) are large-gap QAH insulators. Their extremely robust ferromagnetic (FM) ground states are determined by both the direct- and super-exchange FM coupling. In the absence of spin–orbit coupling (SOC), there exist a spin-polarized crossing point located at each K and Kʹ points, respectively. The SOC effect results in the spontaneous breaking of C 2 symmetry and introduces a mass term, giving rise to a QAH state with sizable band gap. The tiny magnetocrystalline anisotropic energy (MAE) implies that an external magnetic field can be easily used to align magnetization deviating from z direction to the x–y plane, thereby leading to a transformation of the electronic state from the QAH state to the Weyl half semimetals state, which indicate monolayers TlTiX (X = Si, Ge) exhibit a giant magneto topological band effect. Finally, we examined the impact of stress on the band gap and MAE, which underlies the reasons for the giant magneto topological band effect attributed to the crystal field. These findings present novel prospects for the realization of large-gap QAH states with the characteristic of easily modifiable topological states.

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

Light-Driven Spontaneous Phonon Chirality and Magnetization in Paramagnets.

Spin-phonon coupling enables the mutual manipulation of phonon and spin degrees of freedom in solids. In this study, we reveal the inherent nonlinearity within this coupling. Using a paramagnet as an illustration, we demonstrate the nonlinearity by unveiling spontaneous symmetry breaking under a periodic drive. The drive originates from linearly polarized light, respecting a mirror reflection symmetry of the system. However, this symmetry is spontaneously broken in the steady state, manifested in the emergence of coherent chiral phonons accompanied by a nonzero magnetization. We establish an analytical self-consistency equation to find the parameter regime where spontaneous symmetry breaking occurs. Furthermore, we estimate realistic parameters and discuss potential materials that could exhibit this behavior. Our findings shed light on the exploration of nonlinear phenomena in magnetic materials and present possibilities for on-demand control of magnetization.

Electroweak symmetry breaking by gravity

We consider a simple scale-invariant action coupling the Higgs field to the metric scalar curvature R and containing an R2 term that exhibits spontaneous breaking of scale invariance and electroweak symmetry. The coefficient of the R2 term in this case determines the self-coupling of the Higgs boson in the Einstein frame, and the scalaron becomes a dilaton weakly coupled to the Higgs boson. Majorana mass terms for right-handed neutrinos can be generated in a scale-invariant manner by using the Higgs-field invariant; in this case, the existing experimental limits on the Higgs-boson total width rule out Majorana mass values in a certain range. The model inherits the naturalness issues of general relativity connected with the smallness of the gravitational and cosmological constants.

Einstein–Bumblebee-dilaton black hole in Lifshitz spacetimes

We investigate the critical behavior of Lifshitz black holes in Einstein-dilaton gravity in the context of spontaneous Lorentz symmetry breaking. Considering the effects of both the Bumblebee vacuum expectation value (VEV) and the fluctuations over the VEV, we obtained new asymptotically Lifshitz charged solutions in (3 + 1) dimensions. We consider the longitudinal massive mode of Lorentz violation (LV) as thermodynamic pressure, leading us to establish an P-V\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P-V$$\\end{document} extended phase space. Within this framework, we derive the equation of state P(T, V), and subsequently identify the critical points, which manifest as discontinuities in the specific heat at constant pressure. Following this, we compute the Gibbs free energy, revealing a first-order phase transition within the model. Finally, we determine the critical exponents, demonstrating their equivalence to those observed in the Van der Waals system.

Nonreciprocal Frustration: Time Crystalline Order-by-Disorder Phenomenon and a Spin-Glass-like State

Active systems are composed of constituents with interactions that are generically nonreciprocal in nature. Such nonreciprocity often gives rise to situations where conflicting objectives exist, such as in the case of a predator pursuing its prey, while the prey attempts to evade capture. This situation is somewhat reminiscent of those encountered in geometrically frustrated systems where conflicting objectives also exist, which result in the absence of configurations that simultaneously minimize all interaction energies. In the latter, a rich variety of exotic phenomena are known to arise due to the presence of accidental degeneracy of ground states. Here, we establish a direct analogy between these two classes of systems. The analogy is based on the observation that nonreciprocally interacting systems with antisymmetric coupling and geometrically frustrated systems have in common that they both exhibit marginal orbits, which can be regarded as a dynamical system counterpart of accidentally degenerate ground states. The former is shown by proving a Liouville-type theorem. These “accidental degeneracies” of orbits are shown to often get “lifted” by stochastic noise or weak random disorder due to the emergent “entropic force” to give rise to a noise-induced spontaneous symmetry breaking, in a similar manner to the order-by-disorder phenomena known to occur in geometrically frustrated systems. Furthermore, we report numerical evidence of a nonreciprocity-induced spin-glass-like state that exhibits a short-ranged spatial correlation (with stretched exponential decay) and an algebraic temporal correlation associated with the aging effect. Our work establishes an unexpected connection between the physics of complex magnetic materials and nonreciprocal matter, offering a fresh and valuable perspective for comprehending the latter. Published by the American Physical Society 2024

Griffiths-Type Theorems for Short-Range Spin Glass Models

We establish relations between different characterizations of order in spin glass models. We first prove that the broadening of the replica overlap distribution indicated by a nonzero standard deviation of the replica overlap R1,2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R^{1,2}$$\\end{document} implies the non-differentiability of the two-replica free energy with respect to the replica coupling parameter λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document}. In Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {Z}}_2$$\\end{document} invariant models such as the standard Edwards–Anderson model, the non-differentiability is equivalent to the spin glass order characterized by a nonzero Edwards–Anderson order parameter. This generalization of Griffiths’ theorem is proved for any short-range spin glass models with classical bounded spins. We also prove that the non-differentiability of the two-replica free energy mentioned above implies replica symmetry breaking in the literal sense, i.e., a spontaneous breakdown of the permutation symmetry in the model with three replicas. This is a general result that applies to a large class of random spin models, including long-range models such as the Sherrington-Kirkpatrick model and the random energy model. There is a 25-minute video that explains the main results of the present work:https://youtu.be/BF3hJiY1xvI

Angle-resolved transport non-reciprocity and spontaneous symmetry breaking in twisted trilayer graphene.

The identification and characterization of spontaneous symmetry breaking is central to our understanding of strongly correlated two-dimensional materials. In this work, we utilize the angle-resolved measurements of transport non-reciprocity to investigate spontaneous symmetry breaking in twisted trilayer graphene. By analysing the angular dependence of non-reciprocity in both longitudinal and transverse channels, we are able to identify the symmetry axis associated with the underlying electronic order. We report that a hysteretic rotation in the mirror axis can be induced by thermal cycles and a large current bias, supporting the spontaneous breaking of rotational symmetry. Moreover, the onset of non-reciprocity with decreasing temperature coincides with the emergence of orbital ferromagnetism. Combined with the angular dependence of the superconducting diode effect, our findings uncover a direct link between rotational and time-reversal symmetry breaking. These symmetry requirements point towards exchange-driven instabilities in momentum space as a possible origin for transport non-reciprocity in twisted trilayer graphene.

Symmetry breaking of 3-dimensional AdS in holographic semiclassical gravity

We show that 3-dimensional AdS spacetime can be semiclassically unstable due to strongly interacting quantum field effects. In our previous paper, we have pointed out the possibility of such an instability of AdS3 by inspecting linear perturbations of the (covering space of) static BTZ black hole with AdS4 gravity dual in the context of holographic semiclassical problems. In the present paper, we further study this issue from thermodynamic viewpoint by constructing asymptotically AdS3 semiclassical solutions and computing free energies of the solutions. We find two asymptotically AdS3 solutions to the semiclassical Einstein equations with non-vanishing source term: the one whose free energy is smaller than that of the BTZ with vanishing source term and the other whose free energy is smaller than that of the global AdS3 with no horizon (thus manifestly zero-temperature background). The instability found in this paper implies the breakdown of the maximal symmetries of AdS3, and its origin is different from the well-known semiclassical linear instability since our holographic semiclassical Einstein equations in 3-dimensions do not involve higher order derivative terms.

A symmetry principle for gauge theories with fractons

Fractonic phases are new phases of matter that host excitations with restricted mobility. We show that a certain class of gapless fractonic phases are realized as a result of spontaneous breaking of continuous higher-form symmetries whose conserved charges do not commute with spatial translations. We refer to such symmetries as nonuniform higher-form symmetries. These symmetries fall within the standard definition of higher-form symmetries in quantum field theory, and the corresponding symmetry generators are topological. Worldlines of particles are regarded as the charged objects of 1-form symmetries, and mobility restrictions can be implemented by introducing additional 1-form symmetries whose generators do not commute with spatial translations. These features are realized by effective field theories associated with spontaneously broken nonuniform 1-form symmetries. At low energies, the theories reduce to known higher-rank gauge theories such as scalar/vector charge gauge theories, and the gapless excitations in these theories are interpreted as Nambu-Goldstone modes for higher-form symmetries. Due to the nonuniformity of the symmetry, some of the modes acquire a gap, which is the higher-form analogue of the inverse Higgs mechanism of spacetime symmetries. The gauge theories have emergent nonuniform magnetic symmetries, and some of the magnetic monopoles become fractonic. We identify the ’t Hooft anomalies of the nonuniform higher-form symmetries and the corresponding bulk symmetry-protected topological phases. By this method, the mobility restrictions are fully determined by the choice of the commutation relations of charges with translations. This approach allows us to view existing (gapless) fracton models such as the scalar/vector charge gauge theories and their variants from a unified perspective and enables us to engineer theories with desired mobility restrictions.

Toward distinguishing Dirac from Majorana neutrino mass with gravitational waves

We propose a new method toward distinguishing the Dirac versus Majorana nature of neutrino masses from the spectrum of gravitational waves (GWs) associated with neutrino mass genesis. Motivated by the principle of generating small neutrino masses without tiny Yukawa couplings, we assume generic seesaw mechanisms for both Majorana and Dirac neutrino masses. For Majorana neutrinos, we further assume a spontaneously broken gauged U(1)B−L symmetry, independently of the type of Majorana seesaw mechanism, which gives a cosmic string induced GW signal flat over a wide range of frequencies. For Dirac neutrinos, we assume the spontaneous breaking of a Z2 symmetry, the minimal symmetry choice associated with all Dirac seesaw mechanisms, which is softly broken, generating a peaked GW spectrum from the annihilation of the resulting domain walls. In fact, the GW spectra for all types of Dirac seesaws with such a broken Z2 symmetry are identical, subject to a mild caveat. As an illustrative example, we study the simplest respective type-I seesaw mechanisms, and show that the striking difference in the shapes of the GW spectra can help differentiate between these Dirac and Majorana seesaws, complementing results of neutrinoless double beta decay experiments. We also discuss detailed implications of the recent NANOGrav data for Majorana and Dirac seesaw models. Published by the American Physical Society 2024

Nonlinear topological symmetry protection in a dissipative system

We investigate experimentally and theoretically a system ruled by an intricate interplay between topology, nonlinearity, and spontaneous symmetry breaking. The experiment is based on a two-mode coherently-driven optical resonator where photons interact through the Kerr nonlinearity. In presence of a phase defect, the modal structure acquires a synthetic Möbius topology enabling the realization of spontaneous symmetry breaking in inherently bias-free conditions without fine tuning of parameters. Rigorous statistical tests confirm the robustness of the underlying symmetry protection, which manifests itself by a periodic alternation of the modes reminiscent of period-doubling. This dynamic also confers long term stability to various localized structures including domain walls, solitons, and breathers. Our findings are supported by an effective Hamiltonian model and have relevance to other systems of interacting bosons and to the Floquet engineering of quantum matter. They could also be beneficial to the implementation of coherent Ising machines.

Spontaneous symmetry breaking from an on-shell perspective

We show how the well known patterns of masses and interactions that arise from spontaneous symmetry breaking can be determined from an entirely on-shell perspective, that is, without reference to Lagrangians, gauge symmetries, or fields acquiring a vacuum expectation value. To do this, we review how consistent factorization of 2 → 2 tree level scattering can lead to the familiar structures of Yang-Mills theories, and extend this to find structures of Yukawa theories. Considering only spins-0, 1/2 and 1 particles, we construct all the allowed on-shell UV amplitudes under a symmetry group G, and consider all the possible IR amplitudes. By demanding that on-shell IR amplitudes match onto on-shell UV amplitudes in the high energy limit, we reproduce the Higgs mechanism and generate masses for spins-1/2 and 1, find that there is a subgroup H ⊆ G in the IR, and other interesting relations. To highlight the results, we show the breaking pattern of the Standard Model U(1)EM ⊂ SU(2)L × U(1)Y, along with the generation of the masses and interactions of the particles.