Symmetry Breaking Research Articles

In this study, we explore the interplay between \mathcal{PT} 𝒫 𝒯 -symmetry and quantum chaos in a non-Hermitian dynamical system. We consider an extension of the standard diagnostics of quantum chaos, namely the complex level spacing ratio and out-of-time-ordered correlators (OTOCs), to study the \mathcal{PT} 𝒫 𝒯 -symmetric quantum kicked rotor model. The kicked rotor has long been regarded as a paradigmatic dynamic system to study classical and quantum chaos. By introducing non-Hermiticity in the quantum kicked rotor, we uncover new phases and transitions that are absent in the Hermitian system. From the study of the complex level spacing ratio, we locate three regimes – one which is integrable and \mathcal{PT} 𝒫 𝒯 -symmetry, another which is chaotic with \mathcal{PT} 𝒫 𝒯 -symmetry and a third which is chaotic but with broken \mathcal{PT} 𝒫 𝒯 -symmetry. We find that the complex level spacing ratio can distinguish between all three phases. Since calculations of the OTOC can be related to those of the classical Lyapunov exponent in the semi-classical limit, we investigate its nature in these regimes and at the phase boundaries. In the phases with \mathcal{PT} 𝒫 𝒯 -symmetry, the OTOC exhibits behaviour akin to what is observed in the Hermitian system in both the integrable and chaotic regimes. Moreover, in the \mathcal{PT} 𝒫 𝒯 -symmetry broken phase, the OTOC demonstrates additional exponential growth stemming from the complex nature of the eigenvalue spectrum at later times. We derive the analytical form of the late-time behaviour of the OTOC. By defining a normalized OTOC to mitigate the effects caused by \mathcal{PT} 𝒫 𝒯 -symmetry breaking, we show that the OTOC exhibits singular behaviour at the transition from the \mathcal{PT} 𝒫 𝒯 -symmetric chaotic phase to the \mathcal{PT} 𝒫 𝒯 -symmetry broken, chaotic phase.

Nonlinear time-dependent (NLTD) electronic structure theories with effective Hamiltonians depending on the time-dependent state can exhibit "complex excitation energy" solutions with exponential rather than oscillatory time-dependence. These instabilities greatly limit the scope of popular NLTD approaches, such as time-dependent Hartree-Fock and density functional theory, as well as some time-dependent correlated wavefunction and Green's function methods. We show that CT symmetry breaking is responsible for these instabilities, where C denotes unitary frequency or quasiparticle charge reversal and T denotes antiunitary time reversal. While CT symmetry is trivially conserved in Hermitian quantum mechanics, it can be broken in NLTD response theories, which are generally non-Hermitian. This non-Hermitian structure is a consequence of the nonanalytic dependence of the effective Hamiltonian on the time-dependent state encountered in most NLTD approaches. Analytic continuation of the underlying many-electron Hilbert space to a Krein space of twice the dimension admits a well-defined response theory. Stable solutions exhibit double "generalized Kramers" degeneracy of solutions and their CT reverses, which can be interpreted as particle-antiparticle pairs of quasiparticle excitations. In non-Hermitian NLTD response theory, real observables and an oscillatory time-evolution are guaranteed by CT symmetry. Electronic stability of the initial state is found to be sufficient, but not necessary, for the conservation of CT symmetry. The results are illustrated for an analytically solvable two-state model.

Abstract The study of strong electron correlations has significantly advanced the frontiers of condensed matter physics, especially in relation to correlation-driven quantum phase transitions (QPTs). In the vicinity of QPTs, quantum critical fluctuations of multiple degrees of freedom enable the emergence of exotic many-body states and quantum critical behaviours beyond the Landau paradigm. Recently, magnetic frustration, traditionally associated with insulating magnets, has been recognized as pivotal to investigating new phases of matter in correlation-driven Kondo breakdown QPTs that are not clearly associated with broken symmetry. The nature of these new phases, however, remains underexplored. Here, we report quantum criticalities emerging from a cluster spin-glass in the heavy-fermion metal TiFexCu2x-1Sb, where frustration originates from intrinsic disorder. Specific heat and magnetic Grüneisen parameter measurements under varying magnetic fields exhibit quantum critical scaling, indicating a quantum critical point (QCP) near 0.13 Tesla. As the magnetic field increases, the cluster spin-glass phase is progressively suppressed. Upon crossing the QCP, resistivity and Hall effect measurements reveal enhanced screening of local moments and an expanding Fermi surface, consistent with the Kondo breakdown scenario. Our findings uncover a new family of iron-based heavy-fermion metals with intricate interplay of multiple degrees of freedom, enabling the exploration of unconventional excitations and exotic quantum critical states and behaviours.

Defects are typically regarded as detrimental in crystalline systems whose physical properties rely on symmetry. However, lattice defects are known to be an effective solution for applications requiring energy localization. Here, we report the experimental observation of spin wave localization in a one-dimensional magnonic crystal with broken translational symmetry. By operating in the diffractive regime, we directly image energy localization in both space and time using a magneto-inductive probe. This work provides the first direct space- and time-resolved experimental evidence of spin wave localization in a diffractive regime due to a single structural defect. These findings are in good agreement with theoretical simulations, validating the underlying physical mechanism.

We study a two-dimensional topological insulator in the presence of a static nonuniform gravitational field, which mimics the variations in the temperature distribution. We derive an effective boundary free energy functional for the gravitational field and show that, in contrast to the case of massive Dirac fermions, the addition of a Newtonian mass term significantly modifies the quantum anomalous behavior of the system. A nonzero bulk thermal current appears, which violates the Wiedemann-Franz law. The systematic approach we develop to calculate the contribution of edge states to thermal Hall conductivity and energy magnetization can easily be extended to other models.

We determine the possible trajectories the Universe may have followed in the quantum chromodynamics (QCD) phase diagram during the QCD epoch. We focus on the roles of chiral symmetry breaking and pion condensation under high imbalances in lepton asymmetry. Adopting the quark-meson model as an effective description of QCD at finite temperature, charge and baryon chemical potentials we show that, for sufficiently large but physically motivated asymmetries, the Universe may have entered the pion condensation phase through a first-order phase transition, followed by a second-order phase transition when exiting it. Such a first-order phase transition represents a new possible source of primordial gravitational waves during the QCD epoch.

We analytically investigate the charge parity (CP) violation, neutrino masses, and leptogenesis in the Standard Model (SM) with an extension to Dirac neutrinos, building on our previous quark sector analysis. Using systematic top-down diagonalization of fermion mass matrices and experimental neutrino mass-squared differences, we predict the complete neutrino mass spectrum and assess leptogenesis viability. We find that our analysis yields specific mass predictions: mh≈5.01×10−2 eV, ml≈6.09×10−3 eV, and a bimodal middle mass (mm≈4.97×10−2 eV for inverted ordering, mm≈1.05×10−2 eV for normal ordering). Four viable scenarios emerge with parameter constraints ranging from highly restrictive (1<g<1.01512) to moderately broad (1<g<5.9). Crucially, Dirac neutrino leptogenesis is about 71 orders of magnitude weaker than baryogenesis, indicating that Standard Model leptogenesis is negligible and Beyond Standard Model physics is needed for significant leptogenesis contributions. CP violation emerges through SN symmetry breaking, with mass degeneracies controlled by model parameters. Remarkably, while mass-squared differences are small, individual neutrino masses can be significantly larger, potentially addressing dark matter mass requirements and enhancing cosmological significance. This work provides testable predictions for neutrino experiments and establishes a unified analytical approach to CP violation across fermion sectors.

Topological insulators exhibit boundary states protected by bulk band topology, a principle first established in quantum systems and later extended to classical waves, including phononics. Conventionally, an $n$-dimensional bulk with nontrivial topology hosts $(n-1)$-dimensional topologically protected boundary states, which may be further gapped out by breaking the symmetry that protects them, potentially leading to the emergence of $(n-2)$-dimensional, or even lower-dimensional topological states, as in higher-order topological insulators. In this work, we introduce an alternative mechanism for \textcolor{blue}{gapping out topological states and forming new topological modes within the resulting gap without further unit-cell symmetry breaking or dimension reduction.} Using one- and two-dimensional Su-Schrieffer-Heeger (SSH) models, we show that controlled repositioning of topological domain walls enables the construction of hierarchical unit cells that gap out the original domain-wall states while preserving the underlying symmetry. This process produces \textcolor{blue}{higher-hierarchical-level topological states}, characterized by a generalized winding number, and can be iterated to realize multiple - potentially infinite - hierarchical levels of topological states. Our approach expands the conventional topological classification and offers a versatile route for engineering complex networks of protected modes in higher dimensions.

A bstract In holography, flavour probe branes are used to introduce fundamental matter to the AdS/CFT correspondence. At a technical level, the probes are described by extremizing the DBI action and solving the Euler-Lagrange equations of motion. I report on applications of artificial neural networks that allow direct minimization of the regularized DBI action (interpreted as a free energy) without the need to derive and solve the equations of motion. I consider, as examples, magnetic catalysis of chiral symmetry breaking and the meson melting phase transition in the D3/D7 holographic set-up. Finally, I provide a framework which allows the simultaneous learning of the embeddings and the relevant aspects of the dual geometry based on field theory data.

Among the various mysteries in cuprate high temperature superconductors, the pseudogap (PG) phase stands out for the difficulty in pinning down its origin and its close connection to unconventional superconductivity. It appears above the superconducting transition temperature ​, where part of the low energy spectral weight becomes depleted and several competing or intertwined orders such as charge and pair density waves, nematicity, and spin fluctuations begin to develop. A persistent challenge lies in the systematic discrepancies revealed by different experimental probes, as transport measurements locate the critical doping near , spectroscopic studies around , and symmetry sensitive techniques close to . These variations reflect the distinct sensitivities of each probe to correlation length scales and electronic coherence rather than experimental inconsistency. This review brings together evidence from angle resolved photoemission spectroscopy (ARPES), scanning tunneling microscopy or spectroscopy (STM or STS), nuclear magnetic resonance (NMR), resonant X ray scattering (RXS), and optical conductivity, showing that the pseudogap is a spatially heterogeneous, symmetry breaking electronic state whose onset temperature decreases roughly linearly with doping and terminates sharply at . Three complementary theoretical frameworks, namely quantum criticality, Mott physics, and intertwined orders, collectively describe these observations. Experiments showing the abrupt disappearance of nematic order and a logarithmic rise in the electronic specific heat coefficient suggest that the pseudogap terminates at a quantum critical point. This transition appears to separate a correlation dominated pseudogapped metal from a coherent Fermi liquid phase rather than occurring through a gradual crossover. The doping level identified from transport data aligns with optimal superconductivity, implying that the recovery of long range phase coherence rather than the complete removal of pseudogap features is what ultimately enhances . Unresolved questions include reconciling probe dependent boundaries through systematic cross technique studies on identical crystals and developing correlation length resolved probes to distinguish spatial scales of electronic reconstruction. A major theoretical challenge remains to unify competing frameworks and to elucidate how the pseudogap terminates and coherence emerges at , which represents a key step toward a microscopic theory of high temperature superconductivity in cuprates.

In this paper, we showcase how flow obstruction by a deformable object can lead to symmetry breaking in curved domains subject to angular acceleration. Our analysis is motivated by the deflection of the cupula, a soft tissue located in the inner ear that is used to perceive rotational motion as part of the vestibular system. The cupula is understood to block the rotation-induced flow in a toroidal region with the flow-induced deformation of the cupula used by the brain to infer motion. By asymptotically solving the governing equations for this flow, we characterise regimes for which the sensory system is sensitive to either angular velocity or angular acceleration. Moreover, we show the fluid flow is not symmetric in the latter case. Finally, we extend our analysis of symmetry breaking to understand the formation of vortical flow in cavernous regions within channels. We discuss the implications of our results for the sensing of rotation by mammals.

Semimetals exhibit intriguing characteristics attributed to the coexistence of both electrons and holes. In rhombohedral multilayer graphene, a strong trigonal warping effect gives rise to a semi-metallic state near the Fermi surface, offering unique opportunities to explore the interplay of semi-metallic properties with strong correlations and topologies. Here, the observation of quarter semimetals in rhombohedral multilayer graphene by introducing spin-orbit coupling (SOC) is reported. The semi-metallic characteristics of rhombohedral graphene manifest as nearly vanished Hall resistance and parabolic longitudinal resistance. The strong correlations arising from the surface flat band lead to spontaneous symmetry breaking. SOC proximitized by WSe2 further lifts the valley degeneracy, resulting in the spontaneous time-reversal symmetry breaking, as evidenced by the hysteretic anomalous Hall effect. The coexistence of fully polarized electrons and holes allows for the observation of a nonmonotonic temperature dependence of the anomalous Hall resistance. Furthermore, the application of moderate magnetic fields induces a phase transition from quarter semimetals to Chern insulators. These findings establish rhombohedral multilayer graphene as an ideal platform for studying strong correlations and topologies in semimetals.

Abstract In this paper, we consider a Hénon-type equation for the Grushin operator. After proving a radial lemma, we establish the existence of a solution for a superlinear and supercritical problem. Additionally, we derive a symmetry-breaking result for ground-state solutions in the subcritical case.

This study investigates stochastic bifurcation in a generalized tristable Rayleigh–Duffing oscillator with fractional inertial force under both additive and multiplicative recycling noises. The system’s dynamic behavior is influenced by its inherent spatial symmetry, represented by the potential function, as well as by temporal symmetry breaking caused by fractional memory effects and recycling noise. First, an approximate integer-order equivalent system is derived from the original fractional-order model using a harmonic balance method, with minimal mean square error (MSE). The steady-state probability density function (sPDF) of the amplitude is then obtained via stochastic averaging. Using singularity theory, the conditions for stochastic P bifurcation (SPB) are identified. For different fractional derivative’s orders, transition set curves are constructed, and the sPDF is qualitatively analyzed within the regions bounded by these curves—especially under tristable conditions. Theoretical results are validated through Monte Carlo simulations and the Radial Basis Function Neural Network (RBFNN) approach. The findings offer insights for designing fractional-order controllers to improve system response control.

We study the quantum chromodynamics (QCD) phase transitions in the complex chemical potential plane via the Dyson-Schwinger equation approach, incorporating a constant gluonic background field that represents the confining dynamics. We solve the quark gap equation and the background field equation self-consistently, which allows us to directly explore the confinement phase transition and furthermore, evaluate the impact of the back-coupling of confinement on chiral symmetry breaking. Moreover, within such a coupled framework toward the complex chemical potential region, we demonstrate the emergence of Roberge-Weiss (RW) symmetry and investigate the trajectory of Lee-Yang edge singularities (LYESs). Our analysis reveals that the LYESs scaling behavior is similar to our previous findings without the background field condensate. However, a significant difference from our earlier work is that the trajectory of LYESs terminates when the imaginary part of the singularity becomes 1 / 3 π T . We elaborate that this cutoff behavior is caused by the RW symmetry that is symmetric to the imaginary chemical potential Im μ = 1 / 3 π T .

Presented here is the first synergistic experimental observation and computational prediction of nonantiperiodic nonlinear electrophoresis (NANEP), obtained by imposing a sinusoidal nonantiperiodic voltage on negatively charged colloidal (polystyrene) particles in a microfluidic device. The motion of micrometer-sized polystyrene particles driven by NANEP was experimentally observed and predicted computationally, demonstrating that a net particle drift can be obtained with the application of a (spatially uniform) AC signal without the need of a DC bias. Experiments applying AC voltages with amplitudes of 150 and 500 V while toggling on and off the nonantiperiodic signal were conducted, from which particle position was measured and compared with the predictions from simulations of the full nonlinear electrokinetic equations, obtaining good agreement in the amplitude of the particle position oscillation and its net drift. Further experiments varying the amplitude of the applied voltage signal were used to build a net drift speed profile as a function of the electric field peak-to-peak amplitude. The numerical simulations identified fore-aft spatial symmetry breaking in the period-averaged velocity profile and electric field around the particle as the mechanism for generating nonzero net particle drift.

Abstract Metasurfaces that support bound states in the continuum (BICs) enable extreme spectral selectivity by suppressing radiative leakage; controlled symmetry breaking converts ideal BICs into quasi-BICs with finite yet ultra-high quality factors. Here, we design and numerically validate an all-dielectric silicon metasurface on SiO₂ that, under normal incidence, supports five quasi-BIC resonances in the 0.8–1.0 THz band. The metasurface unit cell comprises two semi-elliptical silicon elements; introducing a narrow slit in one element perturbs the symmetry and couples the otherwise dark modes to free space. Transmission and eigenmode analyses reveal five sharp resonance dips in the 0.8–1.0 THz band. We harness the quasi-BIC resonances excited under TE polarization for refractometric sensing by placing an analyte layer above the metasurface and quantify performance vs. analyte refractive index (1.4–1.5) and thickness (0–150 μm). The device attains a maximum sensitivity of 169.6 GHz RIU⁻¹ and a figure of merit (FOM) of 3.818 × 10 3 RIU −1 and a Q-factor of 3.42 × 10 4 owing to strong near-field confinement in the slit-perturbed element. The straightforward geometry, multi-resonant operation, and compatibility with dielectric microfabrication provide a practical route to multi-channel THz sensors. Our results establish design guidelines for engineering quasi-BICs at THz frequencies and for tailoring their spectral response to maximize sensing performance.

The quest for simpler structures that do not require the use of nanofabrication techniques and exhibit high Q Fano resonances has attracted growing interest in the past decade. Here, we study an arrangement of coupled resonator waveguides that can excite Fano resonances. The results show that an odd mode, except for the usual even mode, is excited due to the symmetry breaking of the position stub intersection. The superposition of the even and odd modes generates a Fano-shaped spectrum with a very narrow linewidth. Coupled mode theory is used to analyze these waveguide-based Fano resonances. Experimental results obtained using VNA and VDI show good agreement with theory and simulations. Such waveguide-based Fano resonances can be tailored and are simple in structure and have potential applications in narrowband filtering, sensing, lasing, and nonlinearity enhancement.

Abstract The thermodynamic properties of an ideal bosonic system composed of particles and antiparticles at finite temperatures are examined within the framework of a scalar field model. It is assumed that particle–antiparticle pair creation occurs; however, the system is simultaneously subject to exact charge (isospin) conservation. To implement this constraint, we first consider the system within the Grand Canonical Ensemble and then transform to the Canonical Ensemble using a Legendre transformation. This procedure provides a formally consistent scheme for incorporating the chemical potential at the microscopic level into the Canonical Ensemble framework. To enforce exact conservation of charge (isospin, N I ), we further analyze the thermodynamic properties of the system within the extended Canonical Ensemble , in which the chemical potential becomes a thermodynamic function of the temperature and conserved charge. It is shown that as the temperature decreases, the system undergoes a second-order phase transition to a Bose–Einstein condensate at the critical temperature T c , but only when the conserved charge is finite, N I = const ≠ 0. In a particle–antiparticle system, the condensate forms exclusively in the component with the dominant particle number density, which determines the excess charge. We demonstrate that the symmetry breaking of the ground state at T = 0 results from a first-order phase transition associated with the formation of a Bose–Einstein condensate . Although the transition involves symmetry breaking, it is not spontaneous in the strict field-theoretic sense, but is instead induced by the external injection of particles. Potential experimental signals of Bose–Einstein condensation of pions produced in high-energy nuclear collisions are briefly discussed.

Strain engineering presents a promising pathway for modulating the physical properties of two-dimensional (2D) transition metal dichalcogenides materials. In this study, we investigate the strain-induced magnetic behavior of diamagnetic MoS2 films prepared by the DC magnetron sputtering technique. By applying +1% tensile strain to few-layered MoS2 films (∼3.5 nm), we observe the emergence of room-temperature ferromagnetism with a magnetization saturation of about ∼130 emu/cm3, in stark contrast to bulk films (∼40 nm), which remain diamagnetic under similar conditions. Raman spectroscopy reveals a pronounced reduction in the intensity and the splitting of the E′ mode in 1% strained few-layered films, indicating a possible bond elongation and symmetry breaking under tensile stress. Additionally, x-ray absorption spectroscopy at the Mo M3 edge further confirms a strain-induced electronic structure modification in few-layered films, with no corresponding shift observed in bulk counterparts. Moreover, the strain-induced magnetic and structural changes are largely reversible upon strain release. We attribute the origin of ferromagnetism in few-layered films to the combined influence of tensile strain and defect-assisted bond weakening, which facilitates crystal field transitions within the Mo 4d orbitals. These findings demonstrate that strain engineering can effectively induce and modulate magnetism in 2D materials, providing opportunities for developing strain-controlled spintronic applications.