Discrete Symmetry Research Articles

Domain wall networks from first-order phase transitions and gravitational waves

In the first-order phase transitions (PTs) colliding bubble is an important gravitational wave (GW) source. Following bubble collision, domain walls can be formed when degenerate vacua occur as a result of the spontaneous breaking of a discrete symmetry relevant to new physics at electroweak or higher scales. Using lattice simulations, we study the dynamical evolution of domain walls and find that the networks of the domain wall are formed around the completion of PTs and quickly collapse before entering into the scaling regime provide that the degeneracy of true vacua is broken. Our numerical results indicate that domain wall networks continue to produce GWs in the aftermath of PTs, leading to dramatically changing the spectral shape and enhancing the magnitude by about one order. The resulting GW power spectra are peaked at kR*≃π as predicted by the envelop approximation model, above the peak wave number it has a decaying power law close to k−1.2 followed by a slowly decreasing plateau with the UV cutoff at kR*∼O(102). Published by the American Physical Society 2024

Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications

Symmetry algebras of quantum many-body systems with locality can be understood using commutant algebras, which are defined as algebras of operators that commute with a given set of local operators. In this work, we show that these symmetry algebras can be expressed as frustration-free ground states of a local superoperator, which we refer to as a “super-Hamiltonian.” We demonstrate this for conventional symmetries such as Z2, U(1), and SU(2), where the symmetry algebras map to various kinds of ferromagnetic ground states, as well as for unconventional ones that lead to weak ergodicity-breaking phenomena of Hilbert-space fragmentation (HSF) and quantum many-body scars. In addition, we show that the low-energy excitations of this super-Hamiltonian can be understood as approximate symmetries, which in turn are related to slowly relaxing hydrodynamic modes in symmetric systems. This connection is made precise by relating the super-Hamiltonian to the superoperator that governs the operator relaxation in noisy symmetric Brownian circuits and this physical interpretation also provides a novel interpretation for Mazur bounds for autocorrelation functions. We find examples of gapped (gapless) super-Hamiltonians indicating the absence (presence) of slow modes, which happens in the presence of discrete (continuous) symmetries. In the gapless cases, we recover hydrodynamic modes such as diffusion, tracer diffusion, and asymptotic scars in the presence of U(1) symmetry, HSF, and a tower of quantum scars, respectively. In all, this demonstrates the power of the commutant-algebra framework in obtaining a comprehensive understanding of exact symmetries and associated approximate symmetries and hydrodynamic modes, and their dynamical consequences in systems with locality. Published by the American Physical Society 2024

Natural convection in a vertical channel. Part 1. Wavenumber interaction and Eckhaus instability in a narrow domain

In a vertical channel driven by an imposed horizontal temperature gradient, numerical simulations (Gao et al., Phys. Rev. E, vol. 88, 2013, 023010; Phys. Rev. E, vol. 91, 2015, 013006; Phys. Rev. E, vol. 97, 2018, 053107) have previously shown steady, time-periodic and chaotic dynamics. We explore the observed dynamics by constructing invariant solutions of the three-dimensional Oberbeck–Boussinesq equations, characterizing the stability of these equilibria and periodic orbits, and following the bifurcation structure of the solution branches under parametric continuation in Rayleigh number. We find that in a narrow vertically periodic domain of aspect ratio 10, the flow is dominated by the competition between three and four co-rotating rolls. We demonstrate that branches of three- and four-roll equilibria are connected and can be understood in terms of their discrete symmetries. Specifically, the $D_4$ symmetry of the four-roll branch dictates the existence of qualitatively different intermediate branches that themselves connect to the three-roll branch in a transcritical bifurcation due to $D_3$ symmetry. The physical appearance, disappearance, merging and splitting of rolls along the connecting branch provide a physical and phenomenological illustration of the equivariant theory of $D_3$ – $D_4$ mode interaction. We observe other manifestations of the competition between three and four rolls, in which the symmetry in time or in the transverse direction is broken, leading to limit cycles or wavy rolls, respectively. Our work highlights the interest of combining numerical simulations, bifurcation theory and group theory, in order to understand the transitions between and origin of flow patterns.

Quasiparticles with fractional charges in fractionally filled systems

We study systems that approach a state possessing discrete symmetry due to different degenerate realizations for the system. For concreteness, we consider fractionally filled systems where degeneracy comes from the presence of identical sub-lattices. We show that such systems possess a new type of quasiparticles with fractional charges, which we refer to as fractyons. We discuss static and dynamic properties of these quasiparticles.

Inducing exceptional points, enhancing plasmon quality and creating correlated plasmon states with modulated Floquet parametric driving

The control of low frequency collective modes in solids by light presents important challenges and opportunities for condensed matter physics. We propose a method to parametrically drive low THz range collective modes in an interacting many body system using Floquet driving at optical frequencies with a modulated amplitude. We demonstrate that it can be used to design plasmonic time-varying media with singular dispersions. Plasmons near resonance with half the modulation frequency exhibit two lines of exceptional points connected by dispersionless states. Above a critical driving strength, resonant plasmon modes become unstable and undergo a continuous transition towards a crystal-like structure stabilized by interactions and nonlinearities. This new state breaks the discrete time translational symmetry of the drive as well as the translational and rotational spatial symmetries of the system and exhibits soft, Goldstone-like phononic excitations. Below the instability threshold, our method can be used to enhance the quality of plasmon resonances.

Topologically ordered time crystals

Time crystals are a dynamical phase of periodically driven quantum many-body systems where discrete time-translation symmetry is broken spontaneously. Time-crystallinity however subtly requires also spatial order, ordinarily related to further symmetries, such as spin-flip symmetry when the spatial order is ferromagnetic. Here we define topologically ordered time crystals, a time-crystalline phase borne out of intrinsic topological order—a particularly robust form of spatial order that requires no symmetry. We show that many-body localization can stabilize this phase against generic perturbations and establish some of its key features and signatures, including a dynamical, time-crystal form of the perimeter law for topological order. We link topologically ordered and ordinary time crystals through three complementary perspectives: higher-form symmetries, quantum error-correcting codes, and a holographic correspondence. Topologically ordered time crystals may be realized in programmable quantum devices, as we illustrate for the Google Sycamore processor.

Higher-order and fractional discrete time crystals in Floquet-driven Rydberg atoms

Higher-order and fractional discrete time crystals (DTCs) are exotic phases of matter where the discrete time translation symmetry is broken into higher-order and non-integer category. Generation of these unique DTCs has been widely studied theoretically in different systems. However, no current experimental methods can probe these higher-order and fractional DTCs in any quantum many-body systems. We demonstrate an experimental approach to observe higher-order and fractional DTCs in Floquet-driven Rydberg atomic gases. We have discovered multiple n-DTCs with integer values of n = 2, 3, and 4, and others ranging up to 14, along with fractional n-DTCs with n values beyond the integers. The system response can transition between adjacent integer DTCs, during which the fractional DTCs are investigated. Study of higher-order and fractional DTCs expands fundamental knowledge of non-equilibrium dynamics and is promising for discovery of more complex temporal symmetries beyond the single discrete time translation symmetry.

Relic abundance of dark matter with [formula omitted](54) flavor symmetry

In this work we discuss the neutrino phenomenology in a Δ(54) discrete flavor symmetry and evaluate the relic abundance of dark matter (DM) and active neutrino-DM mixing angle considering various cosmological constraints. We introduced two Standard Model Higgs particles along with vector-like fermions and a new particle (S) which is a gauge singlet in the Standard Model. This modification leads to a mass matrix that diverges from the tribimaximal neutrino mixing pattern resulting in a non-zero reactor angle (θ13). We also incorporated a Z2⊗Z3⊗Z4 symmetry for the specific interactions in our model. The additional particle S is a sterile neutrino which is considered to be a probable dark matter candidate with mass in keV range.

Motility-Induced Pinning in Flocking System with Discrete Symmetry.

We report a motility-induced pinning transition in the active Ising model for a self-propelled particle system with discrete symmetry. This model was known to exhibit a liquid-gas type flocking phase transition, but a recent study reveals that the polar order is metastable due to droplet excitation. Using extensive MonteCarlo simulations, we demonstrate that, for an intermediate alignment interaction strength, the steady state is characterized by traveling local domains, which renders the polar order short-ranged in both space and time. We further demonstrate that interfaces between colliding domains become pinned as the alignment interaction strength increases. A resonating back-and-forth motion of individual self-propelled particles across interfaces is identified as a mechanism for the pinning. We present a numerical phase diagram for the motility-induced pinning transition, and an approximate analytic theory for the growth and shrink dynamics of pinned interfaces. Our results show that pinned interfaces grow to a macroscopic size preventing the polar order in the regime where the particle diffusion rate is sufficiently smaller than the self-propulsion rate. The growth behavior in the opposite regime and its implications on the polar order remain unresolved and require further investigation.

Long-lived topological time-crystalline order on a quantum processor

Topologically ordered phases of matter elude Landau’s symmetry-breaking theory, featuring a variety of intriguing properties such as long-range entanglement and intrinsic robustness against local perturbations. Their extension to periodically driven systems gives rise to exotic new phenomena that are forbidden in thermal equilibrium. Here, we report the observation of signatures of such a phenomenon—a prethermal topologically ordered time crystal—with programmable superconducting qubits arranged on a square lattice. By periodically driving the superconducting qubits with a surface code Hamiltonian, we observe discrete time-translation symmetry breaking dynamics that is only manifested in the subharmonic temporal response of nonlocal logical operators. We further connect the observed dynamics to the underlying topological order by measuring a nonzero topological entanglement entropy and studying its subsequent dynamics. Our results demonstrate the potential to explore exotic topologically ordered nonequilibrium phases of matter with noisy intermediate-scale quantum processors.

Magic of discrete Lattice Gauge theories

Simulation of quantum field theories and fundamental interactions is one of the most challenging tasks in modern particle physics. Classical computers generally fail to reproduce accurate results when it comes to strongly coupled theories such as QCD. Recent developments in quantum technologies open up the possibility of simulating such physical regimes by using quantum computers. In this paper, we study the quantum resource related to the simulability of a quantum theory, i.e. non-stabilizerness for Lattice Gauge Theory (LGT) with discrete symmetry gauge groups. We show that enforcing gauge constraints for [Formula: see text] LGTs has no cost in terms of this resource and discuss the relation between non-abelianity of the gauge group with the average non-stabilizerness of the gauge invariant Hilbert space.

Note on higher-group structure in 6d self-dual gauge theory

We analyze higher-group structure of a 6d model coupled with a self-dual 2-form gauge field. This model is defined from 6d axion-electrodynamics with a 1-form Chern-Weil(CW) symmetry gauged dynamically. The gauging leads to a Green-Schwarz-West-Sagnotti(GSWS) term, which gives rise to an anomaly through a GSWS transformation acting on the 2-form gauge field. We cancel this anomaly by gauging a 3-form CW symmetry in 6d axion-electrodynamics. We find out the global symmetries in the resultant model and derive the gauge invariant action in the presence of the background gauge fields. It is argued that a discrete 1-form symmetry is anomalous because turning on the associated background gauge field causes quantum inconsistency due to an operator-valued ambiguity. Higher-group structure in this model that is manifested as a Green-Schwarz-like transformation for CW background gauge fields is discussed.

Finding discrete symmetry groups via machine learning.

We introduce a machine-learning approach (denoted symmetry seeker neural network) capable of automatically discovering discrete symmetry groups in physical systems. This method identifies the finite set of parameter transformations that preserve the system's physical properties. Remarkably, the method accomplishes this without prior knowledge of the system's symmetry or the mathematical relationships between parameters and properties. Demonstrating its versatility, we showcase examples from mathematics, nanophotonics, and quantum chemistry.

Characters are quantum numbers

Abstract Character tables represent an invaluable tool for applications of group theory in physics and chemistry. They are useful, among other applications, to carry out the projection of functions which later on constitute the basis to simplify the calculations and establish the selection rules. However, the physical interpretation of the character tables as quantum numbers is not visible. In this contribution we prove that the characters are indeed conserved quantities associated with the discrete symmetry of a molecule. In the process, the eigenfunction method of symmetry projection emerges in natural form, an approach not discussed in traditional textbooks. A non trivial example involving the octahedral group ${\cal O}_h$ is presented.

The breaking of μ − τ reflection symmetry in a B − L extended 3HDM with (Z2 × Z4)⋊Z2 (II) symmetry

We propose a new neutrino mass matrix texture satisfying the μ−τ reflection symmetry in a B−L model with three Higgs doublets based on non-Abelian discrete symmetry (Z2×Z4)⋊Z2(II). The Dirac and Majorana mass matrices, which is motivated in the framework of the Type I seesaw mechanism in association with (Z2×Z4)⋊Z2(II) symmetry, hint for a realistic lepton mixing pattern where the co-bimaximal mixing pattern is broken by the charged-lepton contribution. The hierarchy of lepton masses is naturally achieved and the constraints on the effective neutrino mass are consistent with the recent experimental limits.

Kitaev honeycomb antiferromagnet in a field: quantum phase diagram for general spin

We use tensor-network methods and high-order linked-cluster expansions to explore the quantum phase diagram of the antiferromagnetic Kitaev honeycomb model in a magnetic field for general spin S values. Tensor network calculations for the pure Kitaev model confirm the absence of fluxes and spin-spin correlations beyond nearest neighbors, while revealing discrete orientational symmetry breaking for S ∈ 1, 3/2, 2, consistent with the semiclassical limit. An intermediate region between Kitaev phases and the high-field polarized phase is identified for all considered spin values, showing a sequence of potential phases characterized by distinct local magnetization patterns while the total magnetization increases smoothly as a function of the field. Linked-cluster expansions for the high-field zero-momentum gap and spectral weight indicate a quantum critical breakdown of the polarized phase, suggesting exotic physics at intermediate Kitaev couplings.

Topological transport of a classical droplet in a lattice of time

AbstractThouless charge pumps are quantum mechanical devices whose operation relies on topology. They provide the means for transporting quantum matter in space lattices with a single quantum precision. Contrasting space crystals that spontaneously break a continuous spatial translation symmetry and form crystals in space, time crystals have emerged as novel states of matter that organise into time lattices and spontaneously break a discrete time translation symmetry. The utility of Thouless pumps that enable topologically protected quantised transport of electrons and neutral atoms in spatial superlattices leads to the question if corresponding devices exist for time crystals. Here we show that topological pumps can be realised for time solids by transporting droplets of a liquid forward and backward in time lattices and we measure the topological index that characterises such pumping processes. By exploiting a synthetic time dimension, classical time crystals can circumvent the quantum tunnelling that underpins Thouless charge pumps. Our results establish topological pumping through time instead of space and pave the way for applications of time crystals.Key Points Periodically driven fluid droplets can be made to bounce persistently in a gravitational field and may undergo spontaneous time translation symmetry breaking forming classical time crystals. These classical time crystals can be pumped from one time site to another, and this pumping process is characterised by a topological index. Our observations establish a classical temporal counterpart to Thouless pumping of quantum particles in space lattices.

Numerical investigation of the late-time tails of the solutions of the Fackerell–Ipser equation

The late-time behaviour of the solutions of the Fackerell–Ipser equation (which is a wave equation for the spin-zero component of the electromagnetic field strength tensor) on the closure of the domain of outer communication of sub-extremal Kerr spacetime is studied numerically. Within the Kerr family, the case of Schwarzschild background is also considered. Horizon-penetrating compactified hyperboloidal coordinates are used, which allow the behaviour of the solutions to be observed at the event horizon and at future null infinity as well. For the initial data, pure multipole configurations that have compact support and are either stationary or non-stationary are taken. It is found that with such initial data the solutions of the Fackerell–Ipser equation converge at late times either to a known static solution (up to a constant factor) or to zero. As the limit is approached, the solutions exhibit a quasinormal ringdown and finally a power-law decay. The exponents characterizing the power-law decay of the spherical harmonic components of the field variable are extracted from the numerical data for various values of the parameters of the initial data, and based on the results a proposal for a Price’s law relevant to the Fackerell–Ipser equation is made. Certain conserved energy and angular momentum currents are used to verify the numerical implementation of the underlying mathematical model. In the construction of these currents a discrete symmetry of the Fackerell–Ipser equation, which is the product of an equatorial reflection and a complex conjugation, is also taken into account.

Froggatt-Nielsen ALP

The Froggatt-Nielsen (FN) mechanism, a prominent framework for explaining the observed flavor hierarchies, generically predicts the existence of an axion-like particle (ALP). This work examines a class of FN models based on ℤN discrete symmetries. We chart the allowed parameter space from a set of theoretical considerations and construct explicit renormalizable completions with minimal field content necessary to generate consistent textures. We then conduct comprehensive phenomenological analyses of two particularly elegant ℤ4 and ℤ8 models, highlighting the interplay between the effects of the ALP and the associated UV fields. We find that the FN scale can be as low as a few TeV.

Nematic Superconductivity and Its Critical Vestigial Phases in the Quasicrystal.

We propose a general mechanism to realize nematic superconductivity (SC) and reveal its exotic vestigial phases in the quasicrystal (QC). Starting from a Penrose-Hubbard model, our microscopic studies suggest that the Kohn-Luttinger mechanism driven SC in the QC is usually gapless due to violation of Anderson's theorem, rendering that both chiral and nematic SCs are common. The nematic SC in the QC can support novel vestigial phases driven by pairing phase fluctuations above its T_{c}. Our combined renormalization group and MonteCarlo studies provide a phase diagram in which, besides the conventional charge-4e SC, two critical vestigial phases emerge, i.e., the quasinematic (QN) SC and QN metal. In the two QN phases, discrete lattice rotation symmetry is counterintuitively "quasibroken" with power-law decaying orientation correlation. They separate the phase diagram into various phases connected via Berezinskii-Kosterlitz-Thouless (BKT) transitions. These remarkable critical vestigial phases, which resemble the intermediate BKT phase in the q state (q≥5) clock model, are a consequence of the fivefold (or higher) anisotropy field brought about by the unique QC symmetry, which are absent in conventional crystalline materials.