Spontaneous Breaking Research Articles

Schottky Anomaly of the Kalb-Ramond-de Sitter Spacetime

In the theory of gravity, the spontaneous breaking of Lorentz symmetry due to the non-minimal coupling between the Kalb-Ramond field and Einstein gravity results in the existence of exactly static and spherically symmetric black hole solutions related to the Lorentz violating parameter. Based on the consideration of the interaction between the black hole and cosmological horizons, this paper studies the thermodynamic properties of Kalb-Ramond-de Sitter (KR-dS) spacetime. The Smarr relation expressed by equivalent thermodynamic quantities is found, and it is proved that the equivalent thermodynamic quantities of the KR-dS spacetime satisfy the universal Euler's theorem. It is discovered that the heat capacity of the KR-dS spacetime with respect to the ratio of the two horizons and the variation curve of the heat capacity with effective temperature possess the characteristics of Schottky specific heat. Moreover, the black hole and the cosmological horizon in the equivalent thermodynamic system are regarded as two different energy levels, and the heat capacity of the KR-dS spacetime is discussed using the general form given by the ordinary two-level system. It is found that the heat capacity of KR-dS spacetime described by equivalent thermodynamic quantities not only conforms to the characteristics of Schottky specific heat but also is consistent with the heat capacity of the ordinary two-level system. This result reflects that when the cosmological constant and the charged carried in the KR-dS spacetime remain unchanged, the heat capacity of the system can be represented by a universal two-level system. By comparing the maximum value of the heat capacity curves, the number of microscopic particles between the two horizons can be estimated, which reflects the quantum properties of the KR-dS spacetime. These studies will open a new perspective to probe the thermodynamics of black holes.

Synthesizing ordered polar patterns in nonpolar SrTiO3 nanofilms via wrinkle-induced flexoelectricity

Ordered polar structures in oxide nanofilms play a pivotal role in the development of nanoelectronic applications. Hitherto, ordered polar structures have been restricted to a limited number of ferroelectric materials, and there is no effective scheme to induce and manipulate ordered polar patterns in centrosymmetric nonpolar nanofilms due to the absence of spontaneous symmetry breaking. Here, we circumvent these limitations by utilizing the wrinkle-induced strain gradient modulation associated with flexoelectricity as a general means of inducing and manipulating ordered polar patterns in nonpolar nanofilms. Leveraging the surface instability caused by strain mismatch between oxide nanofilms and pre-strained compliant substrate, we successfully fabricate striped SrTiO3 wrinkles, where well-ordered strain gradients and corresponding periodic polar patterns are readily achieved. Through in-situ piezoresponse force microscopy experiments, we show that the generated polar patterns can be manipulated by varying strain boundaries. Furthermore, the atomistic resolution images and first-principles calculations reveal that such wrinkle-induced ordered polar patterns primarily emerge from the flexoelectric coupling between the local polarization and strain gradients. These findings provide implications for manipulating polar structures by strain gradient and flexoelectric engineering, which in turn enable the realization of nontrivial polar structures in a broader range of materials.

Dressing vs. Fixing: On How to Extract and Interpret Gauge-Invariant Content

There is solid consensus among physicists and philosophers that, in gauge field theory, for a quantity to be physically meaningful or real, it must be gauge-invariant. Yet, every “elementary” field in the Standard Model of particle physics is actually gauge-variant. This has led a number of researchers to insist that new manifestly gauge-invariant approaches must be established. Indeed, in the foundational literature, dissatisfaction with standard methods for reducing gauge symmetries has been expressed: Spontaneous symmetry breaking is deemed conceptually dubious, while gauge fixing suffers the same limitations and is subject to the same criticisms as coordinate choices in General Relativity. An alternative gauge-invariant proposal was recently introduced in the literature, the so-called “dressing field method” (DFM). It is a mathematically subtle tool, and unfortunately prone to be confused with simple gauge transformations, hence with standard gauge fixings. As a matter of fact, in the physics literature the two are often conflated, and in the philosophy community some doubts have been raised about whether there is any substantial difference between them. Clarifying this issue is of special significance for anyone interested in both the foundational issues of gauge theories and their invariant formulation. It is thus our objective to establish as precisely as possible the technical and conceptual distinctions between the DFM and gauge fixing.

Category of SET orders

We propose the representation principle to study physical systems with a given symmetry. In the context of symmetry enriched topological orders, we give the appropriate representation category, the category of SET orders, which include SPT orders and symmetry breaking orders as special cases. For fusion n-category symmetries, we show that the category of SET orders encodes almost all information about the interplay between symmetry and topological orders, in a natural and canonical way. These information include defects and boundaries of SET orders, symmetry charges, explicit and spontaneous symmetry breaking, stacking of SET orders, gauging of generalized symmetry, as well as quantum currents (SymTFT or symmetry TO). We also provide a detailed categorical algorithm to compute the generalized gauging. In particular, we proved that gauging is always reversible, as a special type of Morita-equivalence. The explicit data for ungauging, the inverse to gauging, is given.

Entanglement Smectic and Stripe Order

Spontaneous symmetry breaking and more recently entanglement are two cornerstones of quantum matter. We introduce the notion of anisotropic entanglement ordered phases, where the spatial profile of spin-pseudospin entanglement spontaneously lowers the fourfold rotational symmetry of the underlying crystal to a twofold one, while the charge density retains the full symmetry. The resulting phases, which we term and , exhibit a rich Goldstone mode spectrum and a set of phase transitions as a function of underlying anisotropies. We discuss experimental consequences of such anisotropic entanglement phases distinguishing them from more conventional charge or spin stripes. Our discussion of this interplay between entanglement and spontaneous symmetry breaking focuses on multicomponent quantum Hall systems realizing textured Wigner crystals, as may occur in graphene or possibly also in moiré systems, highlighting the rich landscape and properties of possible entanglement ordered phases. Published by the American Physical Society 2024

The interplay between liquid–liquid and ferroelectric phase transitions in supercooled water

The distinctive characteristics of water, evident in its thermodynamic anomalies, have implications across disciplines from biology to geophysics. Considered a valid hypothesis to rationalize its unique properties, a liquid-liquid phase transition in water below the freezing point, in the so-called supercooled regime, has nowadays been observed in several molecular dynamics simulations and is being actively researched experimentally. The hypothesis of ferroelectric phase transition in supercooled water can be traced back to 1977, due to Stillinger. In this work, we highlight intriguing and far-reaching implications of water: The ferroelectric and liquid-liquid phase transitions can be designed as two facets of the same underlying phenomenon. Our results are based on the analysis of extensive molecular dynamics simulations and are explained in the context of a classical density functional theory in mean-field approximation valid for a polar liquid, where dipolar interaction is treated perturbatively. The theory underpins the potential role of ferroelectricity in promoting the liquid-liquid phase transition, being the density-polarization coupling inherent in the dipolar interaction potential. The existence of ferroelectric order in supercooled low-density liquid water is confirmed by the observation in molecular dynamics simulations of collective modes in space-time polarization correlation functions, traceable to spontaneous breaking of continuous rotational symmetry. Our work sheds light on water's supercooled behavior and opens the door to experimental investigations of the static and dynamic behavior of water's polarization.

Revisiting the minimal Nelson-Barr model

We revisit the minimal Nelson-Barr model for solving the strong CP problem through the idea of spontaneous CP breaking. The minimal model suffers from the quality problem, which means that the strong CP angle is generated by higher-dimensional operators and one-loop effects. Consequently, it has been considered that there is a cosmological domain wall problem and that leptogenesis does not work. We point out that just imposing an additional approximate global symmetry solves the quality problem. We also propose a simple solution to the domain wall problem and show that the thermal leptogenesis scenario works.

Ferrospintronic Order in Noncentrosymmetric Antiferromagnets: An Avenue toward Spintronic‐Based Computing, Data Storage, and Energy Harvesting

A ferroic order, ferrospintronic (FSp) order, arising in some magnetic materials lacking inversion symmetry is reported on. Emerging from a macroscopic spontaneous symmetry breaking of both the time reversal T and the spatial inversion, while maintaining the symmetry, the order parameter is given by the dipolar moment of the spin density . Herein a model is advanced that fulfills the symmetry requirements mentioned earlier and its properties are investigated. With the aid of a mean‐field theory, its stability against thermal fluctuations is studied and evidence of truly ferroic states that result from breaking its symmetry is provided. Three predictions that can be checked experimentally to distinguish this class of materials from other compounds are provided. In the first place, it is illustrated that FSp systems host the potential for multiferroic behavior. Second, it is shown that the generic FSp system responds under strain by generating spin currents that can be used in spintronic devices, therefore showing a piezospintronic effect. Finally, it is proven that domain walls in the FSp order parameter lead to magnetoresistive effects. All of the findings mentioned earlier are a significant breakthrough in spintronics and multiferroic phenomena and they have wide‐ranging implications for advancing materials and technologies, particularly in computing and energy harvesting.

Spontaneous breaking of symmetry in overlapping cell instance segmentation using diffusion models

Abstract Instance segmentation is the task of assigning unique identifiers to individual objects in images. Solving this task requires breaking the inherent symmetry that semantically similar objects must result in distinct outputs. Deep learning algorithms bypass this break-of-symmetry by training specialized predictors or by utilizing intermediate label representations. However, many of these approaches break down when faced with overlapping labels that are ubiquitous in biomedical imaging, for instance for segmenting cell layers. Here, we discuss the reason for this failure and offer a novel approach for instance segmentation based on diffusion models that breaks this symmetry spontaneously. Our method outputs pixel-level instance segmentations matching the performance of models such as cellpose on the cellpose fluorescent cell dataset while also permitting overlapping labels.

Stacking of charge-density waves in 2H−NbSe2 bilayers

We employ electronic-structure calculations to investigate the charge-density waves and periodic lattice distortions in bilayer 2H−NbSe2. We demonstrate that the vertical stacking can give rise to a variety of patterns that may lower the symmetry of the charge-density waves exhibited separately by the two composing 1H−NbSe2 monolayers. The general tendency to a spontaneous symmetry breaking observed in the ground state and the first excited states is shown to originate from a non-negligible interlayer coupling. Simulated images for scanning tunneling microscopy as well as geometric structure factors show signatures of the different stacking orders. This may not only be useful to reinterpret past experiments on surfaces and thin films, but it may also be exploited to devise ad hoc experiments for the investigation of the stacking order in 2H−NbSe2. We anticipate that our analysis not only applies to the 2H−NbSe2, but is also relevant for thin films and bulk, whose smallest centrosymmetric component is indeed the bilayer. Finally, our results illustrate clearly that the vertical stacking is not only important for 1T structures, as exemplified by the metal-to-insulator transition observed in 1T−TaS2, but seems to be a general feature of metallic layered transition metal dichalcogenides as well. Published by the American Physical Society 2024

Building 1D lattice models with $G$-graded fusion category

We construct a family of one-dimensional (1D) quantum lattice models based on GG-graded unitary fusion category \mathcal{C}_G𝒞G. This family realize an interpolation between the anyon-chain models and edge models of 2D symmetry-protected topological states, and can be thought of as edge models of 2D symmetry-enriched topological states. The models display a set of unconventional global symmetries that are characterized by the input category \mathcal{C}_G𝒞G. While spontaneous symmetry breaking is also possible, our numerical evidence shows that the category symmetry constrains the models to the extent that the low-energy physics has a large likelihood to be gapless.

Global shift symmetry on an ADM hypersurface: Toward emergent gravity

Generalized symmetries and their spontaneous breakdown serve as the fundamental concept to constrain the many-body entanglement structure, which allows us to characterize quantum phases of matter and emergent collective excitations. For example, emergent photons may be understood by spontaneous 1-form symmetry breaking, which results from a long-ranged entanglement structure between UV microscopic degrees of freedom. In this study, we show that emergent “gravity” may also arise in a similar fashion, where quotes have been used to emphasize that the symmetry-constrained gravitons show unconventional properties compared to usual gravitons. As the electric 1-form symmetry in Maxwell theory is realized as a global shift symmetry of the spatial component of the U(1) gauge field, generated by the electric field, we demonstrate that a constant shift of the Arnowitt-Deser-Misner (ADM) metric on the spatial hypersurface can be viewed as a global symmetry, generated by the ADM canonical momentum. Deriving a vector-type conserved charge from the variation of action, we construct a shift symmetry operator. Considering a Wick rotation, we demonstrate that a gravitational Wilson loop is charged under the action of this shift symmetry operator, which thus confirms the existence of a generalized global symmetry on the ADM hypersurface. Based on the Ward identity, we show that the spontaneous breaking of this global shift symmetry may give rise to a nonpropagating massless symmetric gauge field at the boundary of the hypersurface. Published by the American Physical Society 2024

Weak field deflection angle and analytical parameter estimation of the Lorentz-violating Bumblebee parameter through the black hole shadow using EHT data

We explored how the Lorentz symmetry breaking parameter ℓ affects the Reissner-Nordstöm BH solution in the context of weak field deflection angle, and the black hole shadow. We aim to derive the general expression for the weak deflection angle using the non-asymptotic version of the Gauss-Bonnet theorem, and we presented a way to simplify the calculations under the assumption that the distance of the source and the receiver are the same. Through the Solar System test, ℓ is constrained from around orders of magnitude to 0, implying challenging detection of ℓ through the deflection of light rays from the Sun. We also studied the black hole shadow in an analytic way, where we applied the EHT results under the far approximation in obtaining an estimate expression for ℓ. Using the realistic values of the black hole mass and observer distance for Sgr. A* and M87*, it was shown that is satisfied, implying the relevance and potential promise of the spontaneous Lorentz symmetry breaking parameter's role on the shadow radius uncertainties as measured by the EHT. We find constraints for ℓ to be negatively valued, where the upper and lower bounds are ∼ - 1.94 and ∼ - 2.04, respectively.

Linear and nonlinear coupling of light in twin-resonators with Kerr nonlinearity

Nonlinear effects in microresonators are efficient building blocks for all-optical computing and telecom systems. With the latest advances in microfabrication, coupled microresonators are used in a rapidly growing number of applications. In this work, we investigate the coupling between twin-resonators in the presence of Kerr nonlinearity. We use an experimental setup with controllable coupling between two high-Q resonators and discuss the effects caused by the simultaneous presence of linear and nonlinear coupling between the optical fields. Linear-coupling-induced mode splitting is observed at low input powers, with the controllable coupling leading to a tunable mode splitting. At high input powers, the hybridized resonances show spontaneous symmetry breaking (SSB) effects, in which the optical power is unevenly distributed between the resonators. Our experimental results are supported by a detailed theoretical model of nonlinear twin-resonators. With the recent interest in coupled resonator systems for neuromorphic computing, quantum systems, and optical frequency comb generation, our work provides important insights into the behavior of these systems at high circulating powers.

Observable gravitational waves and ΔNeff with global lepton number symmetry and dark matter

We study the possibility of testing a dark matter (DM) scenario embedded in a global lepton number symmetry U(1)L via gravitational waves (GWs) and cosmic microwave background (CMB) observations. The spontaneous breaking of U(1)L symmetry generates the seesaw scale as well as DM mass dynamically. The (pseudo-)Nambu-Goldstone boson, known as a Majoron, acquires nonzero mass due to soft symmetry-breaking terms of quadratic type in the scalar potential, which eventually breaks U(1)L to its Z2 subgroup. The spontaneous symmetry breaking, which effectively breaks Z2, leads to the formation of domain walls (DWs), posing a threat to successful cosmology, if allowed to dominate. As gravity does not respect any global symmetries, we consider higher-dimensional operators suppressed by the scale of quantum gravity (QG), namely, ΛQG, which introduces the required bias leading to DW annihilation and emission of stochastic GWs observable at near future experiments. The same operators also lead to decay of DM bringing interesting indirect detection aspects. While DM is produced nonthermally via scalar portal interactions, light Majorons can give rise to additional ΔNeff within reach of future CMB experiments. Published by the American Physical Society 2024

Intrinsic Magnetocrystalline Anisotropy Induced 3m-Symmetry Dependent Field-Free Switching in Epitaxial Garnet Films.

The electrical control of perpendicular magnetization without the need for external magnetic fields holds significant potential for next-generation spintronic devices. In this Letter, we have identified a 3m-symmetry dependent field-free switching phenomenon in (111)-oriented Tm_{3}Fe_{5}O_{12} single-crystal films capped with a platinum (Pt) layer. We demonstrate that this distinctive property arises due to the spontaneous breaking of mirror symmetry in magnetocrystalline anisotropy (MCA) for (111)-oriented magnetic films with a cubic structure, which results in a local out-of-plane MCA effective field with a 3m-symmetry dependence on the azimuth angle when the magnetization lies in the (111) plane. The observed field-free switching, facilitated by this MCA effective field, is validated by numerical simulations based both on macro-spin model and on micromagnetic theory. Our findings not only underscore the instrumental role of intrinsic MCA in enabling field-free magnetization switching but also enrich the fundamental understanding of the underlying switching dynamics.

Inhomogeneous confinement and chiral symmetry breaking induced by imaginary angular velocity

We investigate detailed properties of imaginary rotating matter with gluons and quarks at high temperature. Previously, we showed that imaginary rotation induces perturbative confinement of gluons at the rotation center. We perturbatively calculate the Polyakov loop potential and find inhomogeneous confinement above a certain threshold of imaginary angular velocity. We also evaluate the quark contribution to the Polyakov loop potential and confirm that spontaneous chiral symmetry breaking occurs in the perturbatively confined phase.

Application of Clifford’s Algebra to Describe the Early Universe

This article is a shortened review of previous results obtained by the author. The advantages of describing the geometric nature of the physical properties of the early universe using the Clifford algebra approach are demonstrated. A geometric representation of the wave function of the early universe is used, and a new mechanism of spontaneous symmetry breaking with different degrees of freedom is proposed. A possible supersymmetry is revealed, and it is shown that the energy of the initial vacuum can be considered equal to zero. The origin of baryonic asymmetry and the nature of dark matter can be explained using a geometric representation of the wave function of the early universe.

Spontaneous symmetry breaking in generative diffusion models*

Abstract Generative diffusion models have recently emerged as a leading approach for generating high-dimensional data. In this paper, we show that the dynamics of these models exhibit a spontaneous symmetry breaking phenomenon that divides the generative dynamics into two distinct phases: (1) a linear steady-state dynamics around a central fixed-point and, (2) an attractor dynamics directed towards the data manifold. These two ‘phases’ are separated by the change in stability of the central fixed-point, with the resulting window of instability being responsible for the diversity of the generated samples. Using both theoretical and empirical evidence, we show that an accurate simulation of the early dynamics does not significantly contribute to the final generation, since early fluctuations are reverted to the central fixed point. To leverage this insight, we propose a Gaussian late initialization scheme, which significantly improves model performance, achieving up to 3× Fréchet inception distance improvements on fast samplers, while also increasing sample diversity (e.g. racial composition of generated CelebA images). Our work offers a new way to understand the generative dynamics of diffusion models that has the potential to bring about higher performance and less biased fast-samplers.

Baryon violating first order phase transitions and gravitational waves

We propose a scenario in which the matter-antimatter asymmetry arises following the post-electroweak spontaneous breaking of baryon (B) number symmetry. This B-symmetry undergoes a first-order phase transition, which can be sufficiently violent to generate gravitational waves across a broad parameter space. Specifically, we explore a concrete realization of this mechanism that induces a Majorana mass for the neutron, rather than the neutrino. We demonstrate that this model exhibits rich phenomenology, including the generation of gravitational waves from baryon first-order phase transitions (B-FOPTs) and implications for neutron-antineutron oscillations.