Symmetry Breaking Pattern Research Articles

Charged critical behavior and nonperturbative continuum limit of three-dimensional lattice SU(Nc) gauge Higgs models

We consider three-dimensional (3D) lattice SU(Nc) gauge Higgs theories with multicomponent (Nf>1) degenerate scalar fields and U(Nf) global symmetry, focusing on systems with Nc=2, to identify critical behaviors that can be effectively described by the corresponding 3D SU(Nc) gauge Higgs field theory. The field-theoretical analysis of the RG flow allows one to identify a stable charged fixed point for large values of Nf, that would control transitions characterized by the global symmetry-breaking pattern U(Nf)→SU(2)⊗U(Nf−2). Continuous transitions with the same symmetry-breaking pattern are observed in the SU(2) lattice gauge model for Nf≥30. Here we present a detailed finite-size scaling analysis of the Monte Carlo data for several large values of Nf. The results are in substantial agreement with the field-theoretical predictions obtained in the large-Nf limit. This provides evidence that the SU(Nc) gauge Higgs field theories provide the correct effective description of the 3D large-Nf continuous transitions between the disordered and the Higgs phase, where the flavor symmetry breaks to SU(2)⊗U(Nf−2). Therefore, at least for large enough Nf, the 3D SU(Nc) gauge Higgs field theories with multicomponent scalar fields can be nonperturbatively defined by the continuum limit of lattice discretized models with the same local and global symmetries. Published by the American Physical Society 2024

New models of SU(6) grand gauge-Higgs unification

A five dimensional SU(6) grand gauge-Higgs unification compactified on S1/Z2 is discussed. We propose new sets of the SU(6) representations where the quarks and leptons in one generation are embedded and there is no extra massless exotic fermions absent in the Standard Model. The correct electroweak symmetry breaking pattern can be realized by introducing some adjoint fermions. We also analyze whether a viable Higgs mass can be obtained.

The gauge coupling evolutions of an SU(8) theory with the maximally symmetry breaking pattern

We study the renormalizable group equations (RGEs) of the extended strong and weak gauge couplings in an SU(8) theory, where three-generational SM fermions are non-trivially embedded. This framework was previously found to generate the observed SM quark/lepton mass hierarchies and the Cabibbo-Kobayashi-Maskawa mixing pattern through its maximally breaking pattern. The field theoretical two-loop RGEs can not achieve the gauge coupling unification with the minimal setup, unless additional adjoint Higgs fields as well as the gravity-induced d = 5 term to the SU(8) field strength term are included.

A universal formula for the entanglement asymmetry of matrix product states

Abstract Symmetry breaking is a fundamental concept in understanding quantum phases of matter, studied
so far mostly through the lens of local order parameters. Recently, a new entanglement-based probe
of symmetry breaking has been introduced under the name of entanglement asymmetry, which has
been employed to investigate the mechanism of dynamical symmetry restoration. Here, we provide
a universal formula for the entanglement asymmetry of matrix product states with finite bond
dimension, valid in the large volume limit. We show that the entanglement asymmetry of any
compact – discrete or continuous – group depends only on the symmetry breaking pattern, and is
not related to any other microscopic features.

Quantum phases and transitions in spin chains with non-invertible symmetries

Generalized symmetries often appear in the form of emergent symmetries in low energy effective descriptions of quantum many-body systems. Non-invertible symmetries are a particularly exotic class of generalized symmetries, in that they are implemented by transformations that do not form a group. Such symmetries appear in large families of gapless states of quantum matter and constrain their low-energy dynamics. To provide a UV-complete description of such symmetries, it is useful to construct lattice models that respect these symmetries exactly. In this paper, we discuss two families of one-dimensional lattice Hamiltonians with finite on-site Hilbert spaces: one with (invertible) S_3S3 symmetry and the other with non-invertible \mathsf{Rep}(S_3)𝖱𝖾𝗉(S3) symmetry. Our models are largely analytically tractable and demonstrate all possible spontaneous symmetry breaking patterns of these symmetries. Moreover, we use numerical techniques to study the nature of continuous phase transitions between the different symmetry-breaking gapped phases associated with both symmetries. Both models have self-dual lines, where the models are enriched by so-called intrinsically non-invertible symmetries generated by Kramers-Wannier-like duality transformations. We provide explicit lattice operators that generate these non-invertible self-duality symmetries. We show that the enhanced symmetry at the self-dual lines is described by a 2+1d symmetry-topological-order (SymTO) of type JK_4\boxtimes \overline{JK}_4JK4⊠JK¯4. The condensable algebras of the SymTO determine the allowed gapped and gapless states of the self-dual S_3S3-symmetric and \mathsf{Rep}(S_3)𝖱𝖾𝗉(S3)-symmetric models.

Wilson-Fisher fixed points in the presence of Dirac fermions

Wilson–Fisher expansion near upper critical dimension has proven to be an invaluable conceptual and computational tool in our understanding of the universal critical behavior in the [Formula: see text] field theories that describe low-energy physics of the canonical models, such as Ising, XY, and Heisenberg. Here, I review its application to a class of the Gross–Neveu–Yukawa (GNY) field theories, which emerge as possible universal description of a number of quantum phase transitions in electronic two-dimensional systems such as graphene and d-wave superconductors. GNY field theories may be viewed as minimal modifications of the [Formula: see text] field theories in which the order parameter is coupled to relativistic Dirac fermions through Yukawa term and which still exhibit critical fixed points in the suitably formulated Wilson–Fisher [Formula: see text]-expansion. I discuss the unified GNY field theory for a set of different symmetry-breaking patterns, with focus on the semimetal-Néel-ordered-Mott insulator quantum phase transition in the half-filled Hubbard model on the honeycomb lattice, for which a comparison between the state-of-the-art [Formula: see text]-expansion, quantum Monte Carlo, large N, and functional renormalization-group calculations can be made.

A Goldstone boson equivalence for inflation

The effective field theory of single-field inflation characterizes the inflationary epoch in terms of a pattern of symmetry breaking. An operator acquires a time-dependent vacuum expectation value, defining a preferred spatial slicing. In the absence of dynamical gravity, the fluctuations around the time-dependent background are described by the Goldstone boson associated with this symmetry breaking process. With gravity, the Goldstone is eaten by the metric, becoming the scalar metric fluctuation. In this paper, we will show that in general single-field inflation, the statistics of scalar metric fluctuations are given by the statistics of this Goldstone boson decoupled from gravity up to corrections that are controlled as an expansion in slow-roll parameters. This even holds in the presence of additional parameters, like the speed of sound, that naively enhance the impact of the gravitational terms. In the process, we derive expressions for leading and sub-leading gravitational corrections to all-orders in the Goldstone boson.

Extending global fits of 4D Composite Higgs Models with partially composite leptons

We perform the first convergent Bayesian global fits of 4D Composite Higgs Models with partially-composite third generation quarks and leptons based on the minimal SO(5) → SO(4) symmetry breaking pattern. We consider two models with the τ lepton and its associated neutrino in different representations of SO(5). Fitting each model with a wide array of experimental constraints allows us to analyse the Bayesian evidence and currently-observed fine-tuning of each model by calculating the Kullback-Leibler divergence between their respective priors and posteriors. Notably both models are found to be capable of satisfying all constraints simultaneously at the 3σ level at scales of < 5 TeV. From a Bayesian viewpoint of naturalness the model with leptons in the 14 and 10 representations is preferred over those in the 5 representation due to its lower fine-tuning. Finally, we consider the experimental signatures for the preferred parameters in these models, including lepton partner decay signatures and gluon-fusion produced Higgs signal strengths, and discuss their potential phenomenology at future high-luminosity LHC runs.

Higher-group global symmetry and the bosonic M5 brane

Higher-group symmetries are combinations of higher-form symmetries which appear in various field theories. In this paper, we explain how higher-group symmetries arise in 10d and 11d supergravities when the latter are coupled to brane sources. Motivated by this observation, we study field theories at zero and finite temperature invariant under a class of continuous Abelian higher-group symmetries. We restrict the analysis to the low-energy regime where the dynamical field content exclusively consists of Goldstone fields arising from the spontaneous breaking of higher-group and spacetime symmetries. Invariant quantities are constructed and the phases of matter are classified according to the pattern of spontaneous symmetry breaking. With respect to supergravity, we highlight how such Goldstone effective theories provide a symmetry-based interpretation for the theories living on D/M-branes. As an explicit example we construct a 6-group invariant action for the bosonic M5 brane, consistent with the self-duality of the 3-form field strength on the brane. While the self-duality condition in the bosonic case needs to be imposed externally as a constraint at zero temperature, we find an equilibrium effective action for the bosonic M5 brane at finite temperature that inherently implements self-duality.

Holography for Sp(2Nc) gauge dynamics: from composite Higgs to technicolour

We study Sp(2Nc) gauge dynamics with two Dirac fermion flavours in the fundamental representation. These strongly coupled systems underlie some composite Higgs models with a global symmetry breaking pattern SU(4)→Sp(4), leading to a light quartet of pseudo-Goldstone bosons that can play the role of the Higgs. Including four-fermion interactions can rotate the vacuum to a technicolour breaking pattern. Using gauge/gravity duality, we study the underlying gauge dynamics. Our model incorporates the Nc-specific running of the fermion anomalous dimension and can thus distinguish between specific gauge groups. We determine the bound-state spectrum of the UV SU(4)→Sp(4) symmetry breaking model, also including fermion masses and mass splitting, and display the Nc dependence. The inclusion of a four-fermion interaction shows the emergence of three Goldstone bosons on the path to technicolour dynamics.

Mean field theory for strongly coupled systems: Holographic approach

In this paper, we develop the holographic mean field theory for strongly interacting fermion systems. We investigate various types of the symmetry-breakings and their effect on the spectral function. We found analytic expressions of fermion Green’s functions in the probe-limit for all types of tensor order parameter fields. We classified the spectral shapes and singularity types from the analytic Green’s function. We calculated the fermions spectral function in the full backreacted background and then compared it with the analytic results to show the reliability of analytic results in the probe limit. The fact that all the main features of the spectral features in the current condensed matter physics including gaps of s-,p- waves, nodal rings and nodal shells, the flat band of dimension 1,2,3, can be obtained in the absence of the lattice as consequences of the order and symmetry breaking pattern, is a pleaseant surprise.

Strong-coupling critical behavior in three-dimensional lattice Abelian gauge models with charged N-component scalar fields and SO(N) symmetry.

We consider a three-dimensional lattice Abelian Higgs gauge model for a charged N-component scalar field ϕ, which is invariant under SO(N) global transformations for generic values of the parameters. We focus on the strong-coupling regime, in which the kinetic Hamiltonian term for the gauge field is a small perturbation, which is irrelevant for the critical behavior. The Hamiltonian depends on a parameter v, which determines the global symmetry of the model and the symmetry of the low-temperature phases. We present renormalization-group predictions, based on a Landau-Ginzburg-Wilson effective description that relies on the identification of the appropriate order parameter and on the symmetry-breaking patterns that occur at the strong-coupling phase transitions. For v=0, the global symmetry group of the model is SU(N); the corresponding model may undergo continuous transitions only for N=2. For v≠0, i.e., in the SO(N) symmetric case, continuous transitions (in the Heisenberg universality class) are possible also for N=3 and 4. We perform Monte Carlo simulations for N=2,3,4,6, to verify the renormalization-group predictions. Finite-size scaling analyses of the numerical data are in full agreement.

The Schwinger-Keldysh coset construction

The coset construction is a tool for systematically building low energy effective actions for Nambu-Goldstone modes. This technique is typically used to compute time-ordered correlators appropriate for S-matrix computations for systems in their ground state. In this paper, we extend this technique to the Schwinger-Keldysh formalism, which enables one to calculate a wider variety of correlators and applies also to systems in a mixed state. We focus our attention on internal symmetries and demonstrate that, after identifying the appropriate symmetry breaking pattern, Schwinger-Keldysh effective actions for Nambu-Goldstone modes can be constructed using the standard rules of the coset construction. Particular emphasis is placed on the thermal state and ensuring that correlators satisfy the KMS relation. We also discuss explicitly the power counting scheme underlying our effective actions. We comment on the similarities and differences between our approach and others that have previously appeared in the literature. In particular, our prescription does not require the introduction of additional “diffusive” symmetries and retains the full non-linear structure generated by the coset construction. We conclude with a series of explicit examples, including a computation of the finite-temperature two-point functions of conserved spin currents in non-relativistic paramagnets, antiferromagnets, and ferromagnets. Along the way, we also clarify the discrete symmetries that set antiferromagnets apart from ferromagnets, and point out that the dynamical KMS symmetry must be implemented in different ways in these two systems.

Topological aspects of brane fields: Solitons and higher-form symmetries

In this note, we classify topological solitons of n-brane fields, which are nonlocal fields that describe n-dimensional extended objects. We consider a class of n-brane fields that formally define a homomorphism from the n-fold loop space \Omega^n X_DΩnXD of spacetime X_DXD to a space Ε_nΕn. Examples of such n-brane fields are Wilson operators in n-form gauge theories. The solitons are singularities of the n-brane field, and we classify them using the homotopy theory of E_nEn-algebras. We find that the classification of codimension {k+1}k+1 topological solitons with {k≥ n}k≥n can be understood using homotopy groups of \mathcal{E}_nℰn. In particular, they are classified by {\pi_{k-n}(\mathcal{E}_n)}πk−n(ℰn) when {n&gt;1}n&gt;1 and by {\pi_{k-n}(\mathcal{E}_n)}πk−n(ℰn) modulo a {\pi_{1-n}(\mathcal{E}_n)}π1−n(ℰn) action when {n=0}n=0 or {1}1. However, for {n&gt;2}n&gt;2, their classification goes beyond the homotopy groups of \mathcal{E}_nℰn when k &lt; n, which we explore through examples. We compare this classification to n-form \mathcal{E}_nℰn gauge theory. We then apply this classification and consider an {n}n-form symmetry described by the abelian group {G^{(n)}}G(n) that is spontaneously broken to {H^{(n)}\subset G^{(n)}}H(n)⊂G(n), for which the order parameter characterizing this symmetry breaking pattern is an {n}n-brane field with target space {\mathcal{E}_n = G^{(n)}/H^{(n)}}ℰn=G(n)/H(n). We discuss this classification in the context of many examples, both with and without ’t Hooft anomalies.

Exploring global symmetry-breaking superradiant phase via phase competition.

Superradiant phase transitions play a fundamental role in understanding the mechanism of collective light-matter interaction at the quantum level. Here we investigate multiple superradiant phases and phase transitions with different symmetry-breaking patterns in a two-mode V-type Dicke model. Interestingly, we show that there exists a quadruple point where one normal phase, one global symmetry-breaking superradiant phase, and two local symmetry-breaking superradiant phases meet. Such a global phase results from the phase competition between two local superradiant phases and cannot occur in the standard Λ- and Ξ-type three-level configurations in quantum optics. Moreover, we exhibit a sequential first-order quantum phase transition from one local to the global again to the other local superradiant phase. Our study opens up a perspective of exploring multilevel quantum critical phenomena with global symmetry breaking.

Equivalence of EFTs and timelike extra dimensions

A flat 3-brane probing a five-dimensional anti–de Sitter space has the same symmetries and symmetry breaking pattern as one probing a five-dimensional de Sitter space with two time directions. Despite the seemingly different physical setups, we show that the effective field theory of the brane bending mode is identical in both cases. In particular, despite “wrong” signs in the Dirac-Born-Infeld (DBI) action for the two-time de Sitter case, the theories have the same S-matrix. This is consistent with the expectation that effective field theories are determined solely by their degrees of freedom and pattern of symmetry breaking, even in the case of spacetime symmetries. We comment further on the equivalence between the Weyl/dilaton and DBI representations of the EFT of broken conformal symmetry. Published by the American Physical Society 2024

Entanglement-enabled symmetry-breaking orders

A spontaneous symmetry-breaking order is conventionally described by a tensor-product wavefunction of some few-body clusters; some standard examples include the simplest ferromagnets and valence bond solids. We discuss a type of symmetry-breaking orders, dubbed entanglement-enabled symmetry-breaking orders, which cannot be realized by any such tensor-product state. Given a symmetry breaking pattern, we propose a criterion to diagnose if the symmetry-breaking order is entanglement-enabled, by examining the compatibility between the symmetries and the tensor-product description. For concreteness, we present an infinite family of exactly solvable gapped models on one-dimensional lattices with nearest-neighbor interactions, whose ground states exhibit entanglement-enabled symmetry-breaking orders from a discrete symmetry breaking. In addition, these ground states have gapless edge modes protected by the unbroken symmetries. We also propose a construction to realize entanglement-enabled symmetry-breaking orders with spontaneously broken continuous symmetries. Under the unbroken symmetries, some of our examples can be viewed as symmetry-protected topological states that are beyond the conventional classifications.

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

Complex localization mechanisms in networks of coupled oscillators: Two case studies.

Localized phenomena abound in nature and throughout the physical sciences. Some universal mechanisms for localization have been characterized, such as in the snaking bifurcations of localized steady states in pattern-forming partial differential equations. While much of this understanding has been targeted at steady states, recent studies have noted complex dynamical localization phenomena in systems of coupled oscillators. These localized states can come in the form of symmetry-breaking chimera patterns that exhibit coexistence of coherence and incoherence in symmetric networks of coupled oscillators and gap solitons emerging in the bandgap of parametrically driven networks of oscillators. Here, we report detailed numerical continuations of localized time-periodic states in systems of coupled oscillators, while also documenting the numerous bifurcations they give way to. We find novel routes to localization involving bifurcations of heteroclinic cycles in networks of Janus oscillators and strange bifurcation diagrams resembling chaotic tangles in a parametrically driven array of coupled pendula. We highlight the important role of discrete symmetries and the symmetric branch points that emerge in symmetric models.

AdS2 holography and effective QFT

We discuss AdS2 quantum gravity from an unconventional perspective that emphasizes bulk geometry. In our approach, AdS2 has no boundary, there are no divergences that require renormalization, and the dilaton of JT-gravity can be omitted altogether. The result is the standard Schwarzian theory. However, it may be advantageous that our derivation just relies on conventional AdS/CFT correspondence and effective quantum field theory. For example, it clarifies the symmetry breaking pattern. It also puts the non-compact AdS2 topology on the same footing as compact Riemann surfaces.