Symmetry-breaking Phase Transition Research Articles

Spectral signatures of symmetry-breaking dynamical phase transitions.

Large deviation theory provides the framework to study the probability of rare fluctuations of time-averaged observables, opening new avenues of research in nonequilibrium physics. Some of the most appealing results within this context are dynamical phase transitions (DPTs), which might occur at the level of trajectories in order to maximize the probability of sustaining a rare event. While macroscopic fluctuation theory has underpinned much recent progress on the understanding of symmetry-breaking DPTs in driven diffusive systems, their microscopic characterization is still challenging. In this work we shed light on the general spectral mechanism giving rise to continuous DPTs not only for driven diffusive systems, but for any jump process in which a discrete Z_{n} symmetry is broken. By means of a symmetry-aided spectral analysis of the Doob-transformed dynamics, we provide the conditions whereby symmetry-breaking DPTs might emerge and how the different dynamical phases arise from the specific structure of the degenerate eigenvectors. In particular, we show explicitly how all symmetry-breaking features are encoded in the subleading eigenvectors of the degenerate subspace. Moreover, by partitioning configuration space into equivalence classes according to a proper order parameter, we achieve a substantial dimensional reduction which allows for the quantitative characterization of the spectral fingerprints of DPTs. We illustrate our predictions in several paradigmatic many-body systems, including (1) the one-dimensional boundary-driven weakly asymmetric exclusion process (WASEP), which exhibits a particle-hole symmetry-breaking DPT for current fluctuations, (2) the three- and four-state Potts model for spin dynamics, which displays discrete rotational symmetry-breaking DPTs for energy fluctuations, and (3) the closed WASEP which presents a continuous symmetry-breaking DPT into a time-crystal phase characterized by a rotating condensate.

Inhomogeneous disordering at a photoinduced charge density wave transition

Symmetry-breaking phase transitions are ubiquitous in nature. The study of their dynamics in solids has often been performed using homogeneous order parameter theories. By microscopically modeling the photoinduced melting and recovery of a charge density wave, the authors instead show here that the transient dynamics can lead to disordered state, where the average order parameter is not representative of the atomic-scale configuration. This provides a possible minimal model description of the experimentally proposed inhomogeneous disordering pathway in photoinduced phase transitions.

Symmetry-breaking transitions in quiescent and moving solitons in fractional couplers.

We consider phase transitions, in the form of spontaneous symmetry breaking (SSB) bifurcations of solitons, in dual-core couplers with fractional diffraction and cubic self-focusing acting in each core, characterized by Lévy index α. The system represents linearly coupled optical waveguides with the fractional paraxial diffraction or group-velocity dispersion (the latter system was used in a recent experiment [Nat. Commun. 14, 222 (2023)10.1038/s41467-023-35892-8], which demonstrated the first observation of the wave propagation in an effectively fractional setup). By dint of numerical computations and variational approximation, we identify the SSB in the fractional coupler as the bifurcation of the subcritical type (i.e., the symmetry-breaking phase transition of the first kind), whose subcriticality becomes stronger with the increase of fractionality 2-α, in comparison with very weak subcriticality in the case of the nonfractional diffraction, α=2. In the Cauchy limit of α→1, it carries over into the extreme subcritical bifurcation, manifesting backward-going branches of asymmetric solitons which never turn forward. The analysis of the SSB bifurcation is extended for moving (tilted) solitons, which is a nontrivial problem because the fractional diffraction does not admit Galilean invariance. Collisions between moving solitons are studied too, featuring a two-soliton symmetry-breaking effect and merger of the solitons.

Replica symmetry breaking in a Rayleigh backscattering-based random fiber laser

Replica symmetry breaking (RSB) phase transition is observed in disordered photonics systems. The key requirements to observe RSB are provided by random lasers, i.e., gain and disorder. However, in a random fiber laser (RFL) with scattering provided by Rayleigh scattering of light, the condition of quenched disorder is not established due to environment perturbations. Here, RSB is observed in a Rayleigh backscattering-based RFL, where light scattering is due to the inhomogeneity of the optical fiber refractive index. This is done by using short-cavity erbium-RFL with reduced interaction with the environment. Spectral characterization is made, and narrow mode linewidths are demonstrated. The intensity dynamics and laser mode behavior are analyzed showing the presence of gain competition. The results indicate a connection between the replica symmetry or RSB, Lévy-like behavior of intensities, and the presence or not of correlated laser intensity fluctuations.

Measurement-Induced Continuous Time Crystals.

Strong measurements usually restrict the dynamics of measured finite dimensional systems to the Zeno subspace, where subsequent evolution is unitary due to the suppression of dissipative terms. Here, we show qualitatively different behavior induced by the competition between strong measurements and the thermodynamic limit, inducing a time-translation symmetry breaking phase transition resulting in a continuous time crystal. We consider an undriven spin star model, where the central spin is subject to a strong continuous measurement, and qualify the dynamic behavior of the system in various parameter regimes. We show that above a critical value of measurement strength, the magnetization of the thermodynamically large ancilla spins, along with the central spin, develops limit-cycle oscillations.

Machine Cognition, Control and Embodiment on Landscapes of Fog, Friction and Selection

Real-world cognitive structures — embodied biological, machine or composite entities — are inherently unstable by virtue of the “topological information” imposed upon them by external circumstance, adversarial intent, and other persistent “selection pressures”. Consequently, under the Data Rate Theorem (DRT), they must be constantly controlled by embedding regulators. For example, blood pressure and the stream of consciousness require persistent delicate regulation in higher organisms. Here, using the Rate Distortion Theorem of information theory, we derive a form of the DRT of control theory that characterizes such instability for adiabatically stationary nonergodic systems and uncover novel forms of cognitive dynamics under stochastic challenge. These range from aperiodic stochastic amplification to Yerkes–Dodson signal transduction and outright system collapse. The analysis, deliberately closely adapted from recent purely biological studies, leads toward new statistical tools for data analysis, uncovering groupoid symmetry-breaking phase transition analogs to Fisher Zeros in physical systems that may be important for studies of machine intelligence under real-world, hence embodied, interaction. The challenges facing construction, operation, and stabilization of high-order “workspace” or “multiple-workspace” machine cognition, perhaps backed by rapid pattern-matching “emotional” AI, whether explicitly recognized as conscious or not, will require parallel construction of new analytic machinery. This work provides one example, solidly based on the asymptotic limit theorems of information and control theories.

Broadband yellow and white emission from large octahedral tilting in (110)-oriented layered perovskites: imidazolium-methylhydrazinium lead halides

New (110)-oriented 2D HOIPs exhibit record octahedral tilting implying broadband white and yellow photoluminescence, and an order–disorder symmetry-breaking phase transition at high temperatures.

Bidirectional photoswitchability in an iron(iii) spin crossover complex: symmetry-breaking and solvent effects.

The impact of solvent on spin crossover (SCO) behaviour is reported in two solvates [Fe(qsal-I)2]NO3·2ROH (qsal-I = 4-iodo-2-[(8-quinolylimino)methyl]phenolate; R = Me 1 or Et 2) which undergo abrupt and gradual SCO, respectively. A symmetry-breaking phase transition due to spin-state ordering from a [HS] to [HS-LS] state occurs at 210 K in 1, while T1/2 = 250 K for the EtOH solvate, where complete SCO occurs. The MeOH solvate exhibits LIESST and reverse-LIESST from the [HS-LS] state, revealing a hidden [LS] state. Moreover, photocrystallographic studies on 1 at 10 K reveal re-entrant photoinduced phase transitions to a high symmetry [HS] phase when irradiated at 980 nm or a high symmetry [LS] phase after irradiation at 660 nm. This study represents the first example of bidirectional photoswitchability and subsequent symmetry-breaking from a [HS-LS] state in an iron(iii) SCO material.

DFT insights into the origin of d0 ferromagnetism, mechanical stability, elastic, and acoustic anisotropy in AZrO3 (A= K, rb, Cs) cubic perovskites

The d0 ferromagnetism through hole induction can be realized in oxide perovskites. The electronic and magnetic properties of AZrO3 (A = K, Rb, and Cs) cubic perovskites have been computationally analyzed using generalized gradient approximation (GGA) and modified Becke-Johnson (mBJ) potentials. From the evaluation of tolerance factor, volume optimization, formation energy, and phonon dispersion, their structural, magnetic, and dynamical stabilities in the ferromagnetic cubic phase have been verified. Additionally, Blackman's and Every's diagrams ensure their elastic stability without any symmetry-breaking phase transitions. The three-dimensional surfaces of elastic moduli and acoustic wave velocities indicate the degree of anisotropy in these perovskites. The compounds become more ductile for larger alkali cations. The band structures from both functionals confirm that the localized magnetic moments around oxygen atoms arise only from the exchange spin splitting of O-2p orbitals. The integer magnetic moment of 1 μB and complete spin polarization implies the presence of half-metallic ferromagnetism. Among the proposed compounds, the predicted mean-field curie temperature of CsZrO3 is above room temperature and may serve as optimal magnetic layers in spin-valve sensors and magnetic tunnel junctions.

Kibble-Zurek Mechanism for Dynamical Ordering in a Driven Vortex System.

The Kibble-Zurek mechanism describes the formation of topological defects in systems crossing a continuous symmetry-breaking phase transition at a finite quench rate. While this mechanism has been extensively studied for equilibrium transitions, its applicability to nonequilibrium transitions has not yet been fully examined. Recent simulation has shown the applicability of the Kibble-Zurek mechanism to dynamical ordering transitions in particlelike assemblies, including superconducting vortices, driven over random disorder. Here, we experimentally study the configurational order of vortices in the course of dynamical ordering with various quench rates. We verify a power-law scaling of the defect density with the quench rate and an impulse-adiabatic crossover on the ordered side of the transition, which are key predictions of the Kibble-Zurek mechanism. Our results suggest the applicability of the Kibble-Zurek mechanism to other nonequilibrium phase transitions.

Experimental X-ray Charge-Density Studies─A Suitable Probe for Superconductivity? A Case Study on MgB2.

Case studies of 1T-TiSe2 and YBa2Cu3O7-δ have demonstrated that X-ray diffraction (XRD) studies can be used to trace even subtle structural phase transitions which are inherently connected with the onset of superconductivity in these benchmark systems. However, the utility of XRD in the investigation of superconductors like MgB2 lacking an additional symmetry-breaking structural phase transition is not immediately evident. Nevertheless, high-resolution powder XRD experiments on MgB2 in combination with maximum entropy method analyses hinted at differences between the electron density distributions at room temperature and 15 K, that is, below the Tc of approx. 39 K. The high-resolution single-crystal XRD experiments in combination with multipolar refinements presented here can reproduce these results but show that the observed temperature-dependent density changes are almost entirely due to a decrease of atomic displacement parameters as a natural consequence of a reduced thermal vibration amplitude with decreasing temperature. Our investigations also shed new light on the presence or absence of magnesium vacancies in MgB2 samples─a defect type claimed to control the superconducting properties of the compound. We propose that previous reports on the tendency of MgB2 to form non-stoichiometric Mg1-xB2 phases (1 - x ∼ 0.95) during high-temperature (HT) synthesis might result from the interpretation of XRD data of insufficient resolution and/or usage of inflexible refinement models. Indeed, advanced refinements based on an Extended Hansen-Coppens multipolar model and high-resolution X-ray data, which consider explicitly the contraction of core and valence shells of the magnesium cations, do not provide any significant evidence for the formation of non-stoichiometric Mg1-xB2 phases during HT synthesis.

Belief propagation on the random k-SAT model

Corroborating a prediction from statistical physics, we prove that the belief propagation message passing algorithm approximates the partition function of the random k-SAT model well for all clause/variable densities and all inverse temperatures for which a modest absence of long-range correlations condition is satisfied. This condition is known as “replica symmetry” in physics language. From this result we deduce that a replica symmetry breaking phase transition occurs in the random k-SAT model at low temperature for clause/variable densities below but close to the satisfiability threshold.

Interaction between games give rise to the evolution of moral norms of cooperation.

In many biological populations, such as human groups, individuals face a complex strategic setting, where they need to make strategic decisions over a diverse set of issues and their behavior in one strategic context can affect their decisions in another. This raises the question of how the interaction between different strategic contexts affects individuals' strategic choices and social norms? To address this question, I introduce a framework where individuals play two games with different structures and decide upon their strategy in a second game based on their knowledge of their opponent's strategy in the first game. I consider both multistage games, where the same opponents play the two games consecutively, and reputation-based model, where individuals play their two games with different opponents but receive information about their opponent's strategy. By considering a case where the first game is a social dilemma, I show that when the second game is a coordination or anti-coordination game, the Nash equilibrium of the coupled game can be decomposed into two classes, a defective equilibrium which is composed of two simple equilibrium of the two games, and a cooperative equilibrium, in which coupling between the two games emerge and sustain cooperation in the social dilemma. For the existence of the cooperative equilibrium, the cost of cooperation should be smaller than a value determined by the structure of the second game. Investigation of the evolutionary dynamics shows that a cooperative fixed point exists when the second game belongs to coordination or anti-coordination class in a mixed population. However, the basin of attraction of the cooperative fixed point is much smaller for the coordination class, and this fixed point disappears in a structured population. When the second game belongs to the anti-coordination class, the system possesses a spontaneous symmetry-breaking phase transition above which the symmetry between cooperation and defection breaks. A set of cooperation supporting moral norms emerges according to which cooperation stands out as a valuable trait. Notably, the moral system also brings a more efficient allocation of resources in the second game. This observation suggests a moral system has two different roles: Promotion of cooperation, which is against individuals' self-interest but beneficial for the population, and promotion of organization and order, which is at both the population's and the individual's self-interest. Interestingly, the latter acts like a Trojan horse: Once established out of individuals' self-interest, it brings the former with itself. Importantly, the fact that the evolution of moral norms depends only on the cost of cooperation and is independent of the benefit of cooperation implies that moral norms can be harmful and incur a pure collective cost, yet they are just as effective in promoting order and organization. Finally, the model predicts that recognition noise can have a surprisingly positive effect on the evolution of moral norms and facilitates cooperation in the Snow Drift game in structured populations.

Unusual thermodynamic signature of topological quantum criticality in two coupled Su-Schrieffer-Heeger chains

Symmetry breaking and topological quantum phase transitions (QPTs) are usually accompanied by a gap opening or closing. For the continuous QPT, it is marked by a quantum critical point. Herein, we study the topological feature of quantum phase boundary-quantum criticality of two coupled Su-Schrieffer-Heeger chains. Two topological nontrivial insulating phases and a trivial one are recapped with two different topological phase boundaries, which are termed as Dirac semimetals (DSMs) with one or two Dirac nodal points within considering spin degeneracy. Specially, a tricritical point holds the character of quadratic contact point semimetal (QCPSM) that is regarded as a parent phase of DSMs. Meanwhile, the QCPSM and DSMs are featured by the quantum critical scaling of thermal Drude weight and specific heat. Furthermore, the Grüneisen ratio serves as a superb tool for the diagnosis of topological semimetals, which is demonstrated with or without self-duality of quantum criticality explicitly.

Spin liquid state in a rare-earth hyperkagome lattice

Quantum fluctuations enhanced by frustration and subtle interplay between competing degrees of freedom offer an ideal ground to realize novel states with fractional quantum numbers in quantum materials that defy standard theoretical paradigms. Quantum spin liquid (QSL) is a highly entangled state wherein frustration induced strong quantum fluctuations preclude symmetry breaking phase transitions down to zero temperature without any order parameter. Experimental realizations of QSL in quantum materials with spin dimensionality greater than one is very rare. Here, we present our thermodynamic, nuclear magnetic resonance, muon spin relaxation and inelastic neutron scattering studies of a new rare-earth hyperkagome compound Li3Yb3Te2O12 in which Yb3+ ions constitute a three dimensional spin-lattice without any detectable disorder. Our comprehensive experiments evince neither signature of magnetic ordering nor spin freezing down to 38 mK that suggest the realization of dynamic liquid-like ground state in this antiferromagnet. The ground state of this material is interpreted by a low energy Jeff = 1/2 degrees of freedom with short range spin correlations. The present results demonstrate a viable basis to explore spin-orbit driven enigmatic correlated quantum states in a new class of rare-earth based three dimensional frustrated magnets that may open new avenues in theoretical and experimental search for spin liquids.

Charge carrier coupling to the soft phonon mode in a ferroelectric semiconductor

Many crystalline solids possess strongly anharmonic ``soft'' phonon modes characterized by diminishing frequency as temperature approaches a critical point associated with a symmetry breaking phase transition. While electron--soft phonon coupling can introduce unique scattering channels for charge carriers in ferroelectrics, recent studies on the nonferroelectric lead halide perovskites have also suggested the central role of anharmonic phonons bearing resemblance to soft modes in charge carrier screening. Here we apply coherent phonon spectroscopy to directly study electron coupling to the soft transverse optical phonon mode in a ferroelectric semiconductor SbSI. Photogenerated charge carriers in SbSI are found to be exceptionally long lived and are associated with a transient electro-optical effect that can be explained by interactions between charge carriers and thermally stimulated soft phonon excitations. These results provide strong evidence for the role of electron--soft phonon coupling in the efficient screening of charge carriers and in reducing charge recombination rates, both desirable properties for optoelectronics.

Structural transformations of nematic disclinations.

Topological defects (TDs) are a consequence of symmetry breaking phase transitions and are ubiquitous in nature. An ideal testbed for their study are liquid crystals (LCs) owing to their large response to external stimuli and their large electrical and optical anisotropies. In this paper, we perform numerical simulations of topological defects of [Formula: see text] or [Formula: see text] enforced by the confining boundary. We use the Landau-de Gennes phenomenological model in terms of the tensor nematic order parameter and the Jones beam propagation model to simulate polarized optical microscopy images. We demonstrate the structure of closed disclination loops near the boundary known as boojums that can be topologically charged or chargeless. We show that pairs of chargeless disclination loops can interact repulsively or attractively depending on if they are arranged parallel or antiparallel, respectively. Sufficiently closely spaced antiparallel pairs can rewire while parallel pairs simply exhibit stronger bending due to the repulsion.

Fluid-fluid phase transitions in a chiral molecular model.

Molecular chirality is a fundamental phenomenon, underlying both life as we know it and industrial pharmaceutical syntheses. Understanding the symmetry breaking phase transitions exhibited by many chiral molecular substances provides basic insights for topics ranging from the origin of life to the rational design of drug manufacturing processes. In this work, we have performed molecular dynamics simulations to investigate the fluid-fluid phase transitions of a flexible three-dimensional four-site chiral molecular model developed by Latinwo et al. [J. Chem. Phys. 145, 154503 (2016)] and Petsev et al. [J. Chem. Phys. 155, 084105 (2021)]. By introducing a bias favoring local homochiral vs heterochiral interactions, the system exhibits a phase transition from a single achiral phase to a single chiral phase that undergoes infrequent interconversion between the two thermodynamically identical chiral states: the L-rich and D-rich phases. According to the phase rule, this reactive binary system has two independent degrees of freedom and exhibits a density-dependent critical locus. Below the liquid-liquid critical locus, there exists a first-order vapor-liquid coexistence region with a single independent degree of freedom. Our results provide basic thermodynamic and kinetic insights for understanding many-body chiral symmetry breaking phenomena.

On the Inherent Instability of Biocognition: Toward New Probability Models and Statistical Tools.

A central conundrum enshrouds biocognition: almost all such phenomena are inherently unstable and must be constantly controlled by external regulatory machinery to ensure proper function, in much the same sense that blood pressure and the ‘stream of consciousness’ require persistent delicate regulation for the survival of higher organisms. Here, we derive the Data Rate Theorem of control theory that characterizes such instability via the Rate Distortion Theorem of information theory for adiabatically stationary nonergodic systems. We then outline a novel approach to building new statistical tools for data analysis based on those theorems, focusing on groupoid symmetry-breaking phase transitions characterized by Fisher Zero analogs.

History-dependent phase transition character

We consider history-dependent behavior in domain-type configurations in orientational order that are formed in configurations reached via continuous symmetry-breaking phase transitions. In equilibrium, these systems exhibit in absence of impurities a spatially homogeneous order. We focus on cases where domains are formed via (i) Kibble-Zurek mechanism in fast enough quenches or by (ii) Kibble mechanism in strongly supercooled phases. In both cases, domains could be arrested due to pinned topological defects that are formed at domain walls. In systems exhibiting polar or quadrupolar order, point and line defects (disclinations) dominate, respectively. In particular, the disclinations could form complex entangled structures and are more efficient in stabilizing domains. Domain patterns formed by fast quenches could be arrested by impurities imposing a strong enough random-field type disorder, as suggested by the Imry-Ma theorem. On the other hand, domains formed in supercooled systems could be also formed if large enough energy barriers arresting domains are established due to large enough systems’ stiffness. The resulting effective interactions in established domain-type patterns could be described by random matrices. The resulting eigenvectors reveal expected structural excitations formed in such structures. The most important role is commonly played by the random matrix largest eigenvector. Qualitatively different behavior is expected if this eigenvector exhibits a localized or extended character. In the former case, one expects a gradual, non-critical-type transition into a glass-type structure. However, in the latter case, a critical-like phase behavior could be observed.Graphical abstract