Symmetry Breaking Research Articles

Spacetime symmetry breaking on nongeodesic leaves and a new form of matter

We examine the permanent damage caused by the historical breakdown of full diffeomorphism invariance induced by a foliation. We focus on the case where the foliation is allowed to be nongeodesic after the interactions with the foliation switch off. Gravity and other forms of matter recover full diffeomorphism invariance only at the expense of introducing a new matterlike component, carrying the nonvanishing Hamiltonian (and momentum, as it turns out) left over from the violating past interactions. This matter form must be stress-free in the preferred frame; this is the only way a matter action can mimic the evolution of the leftover Hamiltonian (and momentum) driven by the Dirac hypersurface deformation algebra. Hence, if the preferred frame is nongeodesic, the equivalent matter component must have energy and a momentum current in this frame, but still no spatial stresses: an unusual form of “matter.” It is equivalent to a fluid with anisotropic stress in some regimes, reducing to dust in others, or even displaying completely new features in extreme situations. Its stress energy tensor is conserved. We provide two examples based on accelerated frames: Rindler space-time and the canonical Schwarzchild frame. Published by the American Physical Society 2024

Depth-dependent study of time-reversal symmetry-breaking in the kagome superconductor AV3Sb5

The breaking of time-reversal symmetry (TRS) in the normal state of kagome superconductors AV3Sb5 stands out as a significant feature, but its tunability is unexplored. Using low-energy muon spin rotation and local field numerical analysis, we study TRS breaking as a function of depth in single crystals of RbV3Sb5 (with charge order) and Cs(V0.86Ta0.14)3Sb5 (without charge order). In the bulk of RbV3Sb5 (>33 nm from the surface), we observed an increase in the internal magnetic field width in the charge-ordered state. Near the surface (<33 nm), the muon spin relaxation rate is significantly enhanced and this effect commences at temperatures significantly higher than the onset of charge order. In contrast, no similar field width enhancement was detected in Cs(V0.86Ta0.14)3Sb5, either in the bulk or near the surface. These observations indicate a strong connection between charge order and TRS breaking and suggest that TRS breaking can occur prior to long-range charge order.

Intercalation-Induced Monolayer Behavior in Bulk NbSe2.

Superconductivity at the 2D limit is significant for advancing fundamental physics, leading to extensive research on monolayer two-dimensional materials. In particular, monolayer transition metal dichalcogenides such as NbSe2 exhibit Ising superconductivity due to broken in-plane inversion symmetry and strong spin-orbit coupling, which has garnered significant attention. In this letter, we adopted an organic cation intercalation technique to modulate the interlayer interaction of NbSe2 by expanding the interlayer distance, thereby making intercalated NbSe2 behave similarly to monolayer NbSe2. The interlayer distances of NbSe2 intercalated with THA+, CTA+, and TDA+ cations are almost double or triple that of pristine NbSe2. The superconducting transition temperature (Tc) of THA-NbSe2 is comparable to that of pristine NbSe2, while the charge density wave (CDW) transition temperature is higher. The Tc of intercalated NbSe2 decreases with a reduced hole concentration, and the enhanced CDW is ascribed to the dimensional reduction. Notably, the in-plane upper critical field of intercalated NbSe2 significantly exceeds the Pauli paramagnetic limit, which is similar to the Ising superconductivity observed in monolayer NbSe2. Our work demonstrates that the organic cations intercalated two-dimensional materials exhibit behavior similar to their monolayer counterparts, providing a convenient platform for exploring and modulating physical phenomena at the two-dimensional limit.

Spontaneous symmetry breaking, gauge hierarchy, and electroweak vacuum metastability

Spontaneous symmetry breaking, gauge hierarchy, and electroweak vacuum metastability

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.

Generalized Itô’s lemma and the stochastic thermodynamics of diffusion with resetting

Abstract Methods from the theory of stochastic processes are increasingly being used to extend classical thermodynamics to mesoscopic non-equilibrium systems. One characteristic feature of these systems is that averaging the stochastic entropy with respect to an ensemble of stochastic trajectories leads to a second law of thermodynamics that quantifies the degree of departure from thermodynamic equilibrium. A well known mechanism for maintaining a diffusing particle out of thermodynamic equilibrium is stochastic resetting. In its simplest form, the position of the particle instantaneously resets to a fixed position x 0 at a sequence of times generated from a Poisson process of constant rate r. Within the context of stochastic thermodynamics, instantaneous resetting to a single point is a unidirectional process that has no time-reversed equivalent. Hence, the average rate of entropy production calculated using the Gibbs–Shannon entropy cannot be related to the degree of time-reversal symmetry breaking. The problem of unidirectionality can be avoided by considering resetting to a random position or diffusion in an intermittent confining potential. In this paper we show how stochastic entropy production along sample paths of diffusion processes with resetting can be analyzed in terms of extensions of Itô’s formula for stochastic differential equations (SDEs) that include both continuous and discrete processes. First, we use the stochastic calculus of jump-diffusion processes to calculate the rate of stochastic entropy production for instantaneous resetting, and show how previous results are recovered upon averaging over sample trajectories. Second, we formulate single-particle diffusion in a switching potential as a hybrid SDE and develop a hybrid extension of Itô’s stochastic calculus to derive a general expression for the rate of stochastic entropy production. We illustrate the theory by considering overdamped Brownian motion in an intermittent harmonic potential. Finally, we calculate the average rate of entropy production for a population of non-interacting Brownian particles moving in a common switching potential. In particular, we show that the latter induces statistical correlations between the particles, which means that the total entropy is not given by the sum of the 1-particle entropies.

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

Halogen substitution strategy for exploiting high-performance molecular ferroelectrics.

Molecular ferroelectrics are emerging as a robust family of electric-ordered materials due to their distinct structural flexibility, molecular tunability, and versatility. In recent years, diverse chemical design approaches have significantly contributed to discovering and optimizing ferroelectric performances of molecule-based ferroelectric systems. Notably, halogen substitution is one of the most effective strategies for inducing symmetry breaking and optimizing the dipole moments and potential energy barriers. In this minireview, we have summarized recent significant advances of halogen substitution strategy in molecule-based ferroelectrics, including organic-inorganic hybrids and metal-free molecular systems. Subsequently, we discuss the underlying mechanism of halogen substitution to improve ferroelectric performances, including the generation of spontaneous polarization, enhancement of Curie temperature, and bandgap engineering. Finally, the future directions in designing and modulating molecular ferroelectrics by halogen substitution strategy are also highlighted.

Counting and hardness-of-finding fixed points in cellular automata on random graphs

Abstract We study the fixed points of outer-totalistic cellular automata on sparse random regular graphs. These can be seen as constraint satisfaction problems, where each variable must adhere to the same local constraint, which depends solely on its state and the total number of its neighbors in each possible state. Examples of this setting include classical problems such as independent sets or assortative/dissasortative partitions. We analyse the existence and number of fixed points in the large system limit using the cavity method, under both the replica symmetric (RS) and one-step replica symmetry breaking (1RSB) assumption. This method allows us to characterize the structure of the space of solutions, in particular, if the solutions are clustered and whether the clusters contain frozen variables. This last property is conjectured to be linked to the typical algorithmic hardness of the problem. We bring experimental evidence for this claim by studying the performance of the belief-propagation reinforcement algorithm, a message-passing-based solver for these constraint satisfaction problems.

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.

Spontaneous symmetry breaking in nonlinear binary periodic systems

Spontaneous symmetry breaking in nonlinear binary periodic systems

Global aspects of 3-form gauge theory: implications for axion-Yang-Mills systems

We investigate the proposition that axion-Yang-Mills systems are characterized by a 3-form gauge theory in the deep infrared regime. This hypothesis is rigorously examined by initially developing a systematic framework for analyzing 3-form gauge theory coupled to an axion, specifically focusing on its global properties. The theory consists of a BF term deformed by marginal and irrelevant operators and describes a network of vacua separated by domain walls converging at the junction of an axion string. It encompasses 0- and 3-form spontaneously broken global symmetries. Utilizing this framework, in conjunction with effective field theory techniques and ’t Hooft anomaly-matching conditions, we argue that the 3-form gauge theory faithfully captures the infrared physics of the axion-Yang-Mills system. The ultraviolet theory is an SU(N) Yang-Mills theory endowed with a massless Dirac fermion coupled to a complex scalar and is characterized by chiral and genuine ℤm1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathbb{Z}}_m^{(1)} $$\\end{document} 1-form center symmetries, with a mixed anomaly between them. It features two scales: the vev of the complex scalar, v, and the strong-coupling scale, Λ, with Λ ≪ v. Below v, the fermion decouples and a U(1)(2) 2-form winding symmetry emerge, while the 1-form symmetry is enhanced to ℤN1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathbb{Z}}_N^{(1)} $$\\end{document}. As we flow below Λ, matching the mixed anomaly necessitates introducing a dynamical 3-form gauge field of U(1)(2), which appears as the incarnation of a long-range tail of the color field. The infrared theory possesses spontaneously broken chiral and emergent 3-form global symmetries. It passes several checks, among which: it displays the expected restructuring in the hadronic sector upon transition between the vacua, and it is consistent under the gauging of the genuine ℤm1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathbb{Z}}_m^{(1)} $$\\end{document} ⊂ ℤN1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathbb{Z}}_N^{(1)} $$\\end{document} symmetry.

Laser-target symmetry breaking in high-order harmonic generation: From frequency shift to odd-even intensity modulation

Laser-target symmetry breaking in high-order harmonic generation: From frequency shift to odd-even intensity modulation

Coexistence of linear and non-linear thermoelectricity in graphene-superconductor tunnel junctions

We theoretically analyze the electronic transport properties of a monolayer graphene/insulator/superconductor (GIS) tunnel junction subject to a temperature gradient. For intrinsic graphene, the system shows always dissipative charge transport even in the presence of an electronic temperature difference between the two leads. Differently, the GIS produces a thermoelectric response when the graphene electrochemical potential is lifted to energies comparable to the zero-temperature gap of the superconductor, i.e., the system is particle–hole asymmetric. Indeed, the thermally biased GIS system is able to produce both a short-circuit Peltier current and an open-circuit Seebeck voltage. This thermoelectric effect is made of a linear conventional component, due to the intrinsic particle–hole asymmetry of the system, and a non-linear contribution, due to a further spontaneous particle–hole symmetry breaking. In most of the thermal and charge configurations of the GIS system, the linear component prevails. Concluding, the GIS system could be employed in the design of thermometers, electromagnetic radiation sensors, and heat engines with profound influence in superconducting quantum technologies.

Time-reversal symmetry breaking in the chemosensory array reveals a general mechanism for dissipation-enhanced cooperative sensing

The Escherichia coli chemoreceptors form an extensive array that achieves cooperative and adaptive sensing of extracellular signals. The receptors control the activity of histidine kinase CheA, which drives a nonequilibrium phosphorylation-dephosphorylation reaction cycle for response regulator CheY. Cooperativity and dissipation are both important aspects of chemotaxis signaling, yet their consequences have only been studied separately. Recent single-cell FRET measurements revealed that kinase activity of the array spontaneously switches between active and inactive states, with asymmetric switching times that signify time-reversal symmetry breaking in the underlying dynamics. Here, we present a nonequilibrium lattice model of the chemosensory array, which demonstrates that the observed asymmetric switching dynamics can only be explained by an interplay between the dissipative reactions within individual core units and the cooperative coupling between neighboring units. Microscopically, the switching time asymmetry originates from irreversible transition paths. The model shows that strong dissipation enables sensitive and rapid signaling response by relieving the speed-sensitivity trade-off, which can be tested by future single-cell experiments. Overall, our model provides a general framework for studying biological complexes composed of coupled subunits that are individually driven by dissipative cycles and the rich nonequilibrium physics within.

Efficient Molecular Rectification in Metal-Molecules-Semimetal Junctions.

Molecular rectification is expected to be observed in metal-molecule-metal tunnel junctions in which the resonance levels responsible for their transport properties are spatially localized asymmetrically with respect to the leads. Yet, effects such as electrostatic screening and formation of metal induced gap states reduce the magnitude of rectification that can be realized in such junctions. Here we suggest that junctions of the form metal-molecule(s)-semimetal mitigate these interfacial effects. We report current rectification in junctions based on the semimetal bismuth (Bi) with high rectification ratios (>102) at 1.0 V using alkanethiols, molecules for which rectification has never been observed. In addition to the alleviation of screening and surface states, the efficient rectification is argued to be related to symmetry breaking of the applied bias in these junctions because of a built-in potential within the Bi lead. The significance of this built-in potential and its implications for the future and other applications are discussed.

Robust edge photogalvanic effect in thin-film WTe2

The photogalvanic effect (PGE) in Weyl semimetals, such as WTe2 and MoTe2, has been widely observed and is considered a promising phenomenon for advancing Weyl semimetal-based optoelectronic devices. However, as device dimensions continue to shrink, edge effects on photocurrent generation and modulation become increasingly significant and cannot be overlooked. Herein, we have discovered a locally enhanced edge linear photogalvanic effect at the edge of WTe2 thin-film devices using a home-built polarization-modulated scanning photocurrent system, which arises from symmetry breaking. Furthermore, the magnitude and direction of this edge photocurrent are modulated by the polarization direction of the incident light. This research provides valuable insights for the development of polarization-sensitive photodetectors based on layered type-II Weyl semimetals.

Topological Polar Networks in Twisted Rhombohedral-Stacked Bilayer WSe2 Moiré Superlattices.

Sliding ferroelectricity enables materials with intrinsic centrosymmetric symmetry to generate spontaneous polarization via stacking engineering, extending the family of ferroelectric materials and enriching the field of low-dimensional ferroelectric physics. Vertical ferroelectric domains, where the polarization is perpendicular to atomic motion, have been discovered in twisted bilayers of inversion symmetry broken systems such as hexagonal boron nitride, graphene, and transition metal chalcogenides. In this study, we demonstrate that this symmetry breaking also induces lateral polar networks in twisted bilayer rhombohedral-stacked WSe2, as determined through symmetry considerations and vector piezoresponse force microscopy (V-PFM) results. Lateral polarization (LP) in saddle point (SP) regions forms head-to-tail triangular vortices, exhibiting elliptical domain shapes with widths up to 40 nm. The LP encloses the vertical polarization (VP), forming a network of Bloch-type merons and antimerons. Our work enhances the understanding of domain distribution and polarization orientation in moiré ferroelectrics.

Probing the effects of broken symmetries in machine learning

Abstract Symmetry is one of the most central concepts in physics, and it is no surprise that it has also been widely adopted as an inductive bias for machine-learning models applied to the physical sciences. &amp;#xD;This is especially true for models targeting the properties of matter at the atomic scale. Both established and state-of-the-art approaches, with almost no exceptions, are built to be exactly equivariant to translations, permutations, and rotations of the atoms.&amp;#xD;Incorporating symmetries -- rotations in particular -- constrains the model design space and implies more complicated architectures that are often also computationally demanding. There are indications that unconstrained models can easily learn symmetries from data, and that doing so can even be beneficial for the accuracy of the model.&amp;#xD;We demonstrate that an unconstrained architecture can be trained to achieve a high degree of rotational invariance, testing the impacts of the small symmetry breaking in realistic scenarios involving simulations of gas-phase, liquid, and solid water. &amp;#xD;We focus specifically on physical observables that are likely to be affected -- directly or indirectly -- by non-invariant behavior under rotations, finding negligible consequences when the model is used in an interpolative, bulk, regime. Even for extrapolative gas-phase predictions, the model remains very stable, even though symmetry artifacts are noticeable. &amp;#xD;We also discuss strategies that can be used to systematically reduce the magnitude of symmetry breaking when it occurs, and assess their impact on the convergence of observables.

Static or dynamic pear shapes in radioactive nucleus 224Rn?

We report a comprehensive study on low-lying parity doublet states of 224Rn by mixing both quadrupole- and octupole-shaped configurations in multireference covariant density functional theory, in which broken symmetries in configurations are restored using projection techniques. The low-lying energy spectrum is reasonably reproduced when the shape fluctuations in both the quadrupole and octupole shapes are considered. Electric octupole transition strength in 224Rn is found to be B(E3;31-→01+)=43\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B(E3; 3^-_1 \\rightarrow 0^+_1)=43$$\\end{document} W.u., comparable to that in 224Ra, whose data are 42(3) W.u.. Our results indicate that 224Rn shares similar low-energy structure with 224Ra despite the excitation energy of first 3-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3^-$$\\end{document} state of the former nucleus is higher than that of the latter. This study suggests 224Rn is a candidate for the search for permanent electric dipole moment.