Symmetry-breaking Transition Research Articles

Passive parity-time-symmetry-breaking transitions without exceptional points in dissipative photonic systems [Invited

Over the past decade, parity-time ($\mathcal{PT}$)-symmetric Hamiltonians have been experimentally realized in classical, optical settings with balanced gain and loss, or in quantum systems with localized loss. In both realizations, the $\mathcal{PT}$-symmetry breaking transition occurs at the exceptional point of the non-Hermitian Hamiltonian, where its eigenvalues and the corresponding eigenvectors both coincide. Here, we show that in lossy systems, the $\mathcal{PT}$ transition is a phenomenon that broadly occurs without an attendant exceptional point, and is driven by the potential asymmetry between the neutral and the lossy regions. With experimentally realizable quantum models in mind, we investigate dimer and trimer waveguide configurations with one lossy waveguide. We validate the tight-binding model results by using the beam propagation method analysis. Our results pave a robust way toward studying the interplay between passive $\mathcal{PT}$ transitions and quantum effects in dissipative photonic configurations.

Material symmetry phase transitions in three-dimensional tensegrity metamaterials

Prestressing the cables of tensegrity-based metamaterials is a widespread practice for enhancing their stability and mechanical properties. We choose a recently developed three-dimensional tensegrity lattice (Rimoli and Pal, 2017) and investigate material symmetry phase transitions induced by varying cable prestresses. We study several combinations of prestress cases and a vast regime of prestress values for each case. In each prestress scenario, we compute the effective elasticity tensor through a homogenization scheme. We study the material symmetries of the lattice by examining the eigenspaces of the homogenized elasticity tensor. We demonstrate material symmetry breaking and phase transitions, occurring solely due to cable prestressing. We observe several phase transitions including cubic to tetragonal, tetragonal to orthotropic, and vice-versa. We also compare phase transitions in finite and infinite lattices, showing that while certain prestress conditions lead to orthotropic symmetry in the finite lattices, they result in tetragonal symmetry for the infinite case. This discrepancy in symmetries of the finite and infinite lattices is due to periodic boundary conditions and the non-symmorphic nature of the tensegrity lattice. Consequently, unlike many crystalline materials where increasing the size of the material is known to lead to symmetry reduction (Ayyub et al., 1995), we find a class of metamaterials where the infinite lattice exhibits a higher symmetry than the finite one.

Self-ordering induces multiple topological transitions for in-plane bulk waves in solid phononic crystals

Topological defects with symmetry-breaking phase transitions have captured much attention. Vortex generated by topological defects exhibits exotic properties and its flow direction can be switched by altering the spin configurations. Contrary to electromagnetic and acoustic domains, the topological transport of elastic waves in periodic structures with topological defects is not well explored due to the mode conversion between the longitudinal and transverse modes. Here, we propose an elastic topological insulator with spontaneously broken symmetry based on the topological theory of defects and homotopy theory. Multiple topological transitions for elastic waves are achieved by topologically modifying the ellipse orientation in a triangular lattice of elliptical cylinders. The solid system, independent of the number of molecules in order parameter space, breaks through the limit of the point-group symmetry to emulate elastic pseudospin-orbit coupling. The transport robustness of the edge states is experimentally demonstrated. Our approach provides new possibilities for controlling and transporting elastic waves.

Confinement transition of ℤ2 gauge theories coupled to massless fermions: Emergent quantum chromodynamics and SO(5) symmetry

We study a model of fermions on the square lattice at half-filling coupled to an Ising gauge theory that was recently shown in Monte Carlo simulations to exhibit [Formula: see text] topological order and massless Dirac fermion excitations. On tuning parameters, a confining phase with broken symmetry (an antiferromagnet in one choice of Hamiltonian) was also established, and the transition between these phases was found to be continuous, with coincident onset of symmetry breaking and confinement. While the confinement transition in pure gauge theories is well-understood in terms of condensing magnetic flux excitations, the same transition in the presence of gapless fermions is a challenging problem owing to the statistical interactions between fermions and the condensing flux excitations. The conventional scenario then proceeds via a two-step transition, involving a symmetry-breaking transition leading to gapped fermions followed by confinement. In contrast, here, using quantum Monte Carlo simulations, we provide further evidence for a direct, continuous transition and also find numerical evidence for an enlarged [Formula: see text] symmetry rotating between antiferromagnetism and valence bond solid orders proximate to criticality. Guided by our numerical finding, we develop a field theory description of the direct transition involving an emergent nonabelian [[Formula: see text]] gauge theory and a matrix Higgs field. We contrast our results with the conventional Gross-Neveu-Yukawa transition.

Linearly aligned single-chiral vortices in hexagonal manganites by insitu electric arc heating

Nanoscale topological defects, such as vortices and skyrmions in ferroic systems, have been intensively investigated due to their intriguing properties and behaviors. In addition to harnessing and tuning their functionalities, spatial manipulation and control of topological defects as functional elements are important for future nanotechnologies. Here, we report a linear alignment behavior of single-chiral vortices observed in thin transmission electron microscopy samples of multiferroic hexagonal manganites during an in situ heating experiment. In order to avoid chemical degradation during high-temperature heating in vacuum, we have utilized a rapid heating and quenching by $in$ situ electric arcing. Using atomic resolution electron microscopy and phase-field simulation, we found that vortices and antivortices formed near the phase transition temperature are pulled out in the opposite directions by mechanical strain to leave single-chiral vortices linearly aligned along an isothermal line formed during quenching. Our study provides important insight into spatial manipulation of the topological defects in oxide multiferroics by investigating far-equilibrium dynamics of symmetry-breaking continuous phase transitions.

A symmetry breaking transition in the edge/triangle network model

Our general subject is the emergence of phases, and phase transitions, in large networks subjected to a few variable constraints. Our main result is the analysis, in the model using edge and triangle subdensities for constraints, of a sharp transition between two phases with different symmetries, analogous to the transition between a fluid and a crystalline solid.

Parity-time symmetry breaking in spin chains

We investigate nonequilibrium phase transitions in classical Heisenberg spin chains associated with spontaneous breaking of parity-time ($\mathcal{PT}$) symmetry of the system under the action of Slonczewski spin-transfer torque (STT) modeled by an applied \textit{imaginary} magnetic field. We reveal the STT-driven $\mathcal{PT}$ symmetry-breaking phase transition between the regimes of precessional and exponentially damped spin dynamics and show that its several properties can be derived from the distribution of zeros of the system's partition function, the approach first introduced by Yang and Lee for studying equilibrium phase transitions in Ising spin chains. The physical interpretation of imaginary magnetic field as describing the action of non-conservative forces opens the possibility of direct observations of Lee-Yang zeros in nonequilibrium physical systems.

Giant magnetostriction effect near onset of spin reorientation in MnBi

In materials undergoing spontaneous symmetry breaking transitions, the emergence of multiple competing order parameters is pervasive. Employing in-field x-ray diffraction, we investigate the temperature and magnetic field dependence of the crystallographic structure of MnBi, elucidating the microscopic interplay between lattices and spin. The hexagonal phase of MnBi undergoes a spin reorientation transition (TSR), whereby the easy axis direction changes from the c axis to the basal plane. Across TSR, an abrupt symmetry change is accompanied by a clear sign change in the magnetostrictive coefficient, revealing that this transition corresponds to the onset of the spin reorientation. In the vicinity of TSR, a significantly larger in-plane magnetostrictive effect is observed, presenting the emergence of an intermediate phase that is highly susceptible to an applied magnetic field. X-ray linear dichroism shows that asymmetric Bi and Mn p orbitals do not play a role in the spin reorientation. This work suggests that the spin reorientation is caused by structural modification rather than changes in the local electronic configuration, providing a strategy for manipulating the magnetic anisotropy by external strain.

Effective field theory of chiral spin liquid between ordered phases in a kagome antiferromagnet

We propose in this work an effective field theory description of the chiral spin liquid state in a Heisenberg spin system on a kagome lattice. To this end, we derive the low-energy effective theory of a kagome (isotropic) Heisenberg antiferromagnet around its ordered ground states found numerically and show that quantum fluctuations induced by further neighbor spin exchanges are equally strong as those from the first neighbor. We use a chiral order parameter theory to argue for the occurrence of finite temperature chiral symmetry breaking transition into a chiral ordered state in a kagome antiferromagnet with further neighbor spin exchange interactions. We compute the chiral symmetry breaking term in the effective ground state energy and show that chiral spin liquid necessarily occurs in the ground state of a kagome antiferromagnet with the first three nearest-neighbor spin exchange interactions. Finally, we consider the quantum criticality of the kagome antiferromagnet and show that a Chern–Simons term emerges naturally at the transition between the two ordered states that satisfy an appropriate ‘matching condition’ that we derive, providing an explanation for why chiral spin liquid could occur at the transition between appropriate ordered states. This emergent Chern–Simons term is the low energy effective theory of the chiral spin liquid state, where the chirality is the immediate consequence of the breaking of discrete symmetries by this topological field theory.

Dissipation-Induced Anomalous Multicritical Phenomena.

We explore the influence of dissipation on a paradigmatic driven-dissipative model where a collection of two level atoms interact with both quadratures of a quantum cavity mode. The closed system exhibits multiple phase transitions involving discrete and continuous symmetries breaking and all phases culminate in a multicritical point. In the open system, we show that infinitesimal dissipation erases the phase with broken continuous symmetry and radically alters the model's phase diagram. The multicritical point now becomes brittle and splits into two tricritical points where first- and second-order symmetry-breaking transitions meet. A quantum fluctuations analysis shows that, surprisingly, the tricritical points exhibit anomalous finite fluctuations, as opposed to standard tricritical points arising in ^{3}He-^{4}He mixtures. Our work has direct implications for a variety of fields, including cold atoms and ions in optical cavities, circuit-quantum electrodynamics as well as optomechanical systems.

Atomic and electronic structure of doped Si(111)(23×23)R30∘ -Sn interfaces

The hole doped Si(111)(2root3x2root3)R30(degrees)-Sn interface exhibits a symmetry-breaking insulator-insulator transition below 100 K that appears to be triggered by electron tunneling into the empty surface-state bands. No such transition is seen in electron-doped systems. To elucidate the nature and driving force of this phenomenon, the structure of the interface must be resolved. Here we report on an extensive experimental and theoretical study, including scanning tunneling microscopy and spectroscopy (STM/STS), dynamical low-energy electron diffraction (LEED) analysis, and density functional theory (DFT) calculations, to elucidate the structure of this interface. We consider six different structure models, three of which have been proposed before, and conclude that only two of them can account for the majority of experimental data. One of them is the model according to Tornevik et al. [C. Tornevik et al., Phys. Rev. B 44, 13144 (1991)] with a total Sn coverage of 14/12 monolayers (ML). The other is the 'revised trimer model' with a total Sn coverage of 13/12 ML, introduced in this work. These two models are very difficult to discriminate on the basis of DFT or LEED alone, but STS data clearly point toward the T\"ornevik model as the most viable candidate among the models considered here. The STS data also provide additional insights regarding the electron-injection-driven phase transformation as well as the critical role of valence band holes in this process. Similar processes may occur at other metal/semiconductor interfaces, provided they are non-metallic and can be doped. This could open up a new pathway toward the creation of novel surface phases with potentially very interesting and desirable electronic properties.

Spontaneous motion of localized structures induced by parity symmetry breaking transition.

We consider a paradigmatic nonvariational scalar Swift-Hohenberg equation that describes short wavenumber or large wavelength pattern forming systems. This work unveils evidence of the transition from stable stationary to moving localized structures in one spatial dimension as a result of a parity breaking instability. This behavior is attributed to the nonvariational character of the model. We show that the nature of this transition is supercritical. We characterize analytically and numerically this bifurcation scenario from which emerges asymmetric moving localized structures. A generalization for two-dimensional settings is discussed.

Simulations of cold electroweak baryogenesis: dependence on the source of CP-violation

We compute the baryon asymmetry created in a tachyonic electroweak symmetry breaking transition, focusing on the dependence on the source of effective CP-violation. Earlier simulations of Cold Electroweak Baryogenesis have almost exclusively considered a very specific CP-violating term explicitly biasing Chern-Simons number. We compare four different dimension six, scalar-gauge CP-violating terms, involving both the Higgs field and another dynamical scalar coupled to SU(2) or U(1) gauge fields. We find that for sensible values of parameters, all implementations can generate a baryon asymmetry consistent with observations, showing that baryogenesis is a generic outcome of a fast tachyonic electroweak transition.

Transition from homogeneous to inhomogeneous limit cycles: Effect of local filtering in coupled oscillators.

We report an interesting symmetry-breaking transition in coupled identical oscillators, namely, the continuous transition from homogeneous to inhomogeneous limit cycle oscillations. The observed transition is the oscillatory analog of the Turing-type symmetry-breaking transition from amplitude death (i.e., stable homogeneous steady state) to oscillation death (i.e., stable inhomogeneous steady state). This novel transition occurs in the parametric zone of occurrence of rhythmogenesis and oscillation death as a consequence of the presence of local filtering in the coupling path. We consider paradigmatic oscillators, such as Stuart-Landau and van der Pol oscillators, under mean-field coupling with low-pass or all-pass filtered self-feedback and through a rigorous bifurcation analysis we explore the genesis of this transition. Further, we experimentally demonstrate the observed transition, which establishes its robustness in the presence of parameter fluctuations and noise.

Dynamical phase transitions in the current distribution of driven diffusive channels

We study singularities in the large deviation function of the time-averaged current of diffusive systems connected to two reservoirs. A set of conditions for the occurrence of phase transitions, both first and second order, are obtained by deriving Landau theories. First-order transitions occur in the absence of a particle-hole symmetry, while second-order occur in its presence and are associated with a symmetry breaking. The analysis is done in two distinct statistical ensembles, shedding light on previous results. In addition, we also provide an exact solution of a model exhibiting a second-order symmetry-breaking transition.

Synthesis and Self-Assembly of Chiral Cylindrical Molecular Complexes: Functional Heterogeneous Liquid-Solid Materials Formed by Helicene Oligomers.

Chiral cylindrical molecular complexes of homo- and hetero-double-helices derived from helicene oligomers self-assemble in solution, providing functional heterogeneous liquid-solid materials. Gels and liotropic liquid crystals are formed by fibril self-assembly in solution; molecular monolayers and fibril films are formed by self-assembly on solid surfaces; gels containing gold nanoparticles emit light; silica nanoparticles aggregate and adsorb double-helices. Notable dynamics appears during self-assembly, including multistep self-assembly, solid surface catalyzed double-helix formation, sigmoidal and stairwise kinetics, molecular recognition of nanoparticles, discontinuous self-assembly, materials clocking, chiral symmetry breaking and homogeneous-heterogeneous transitions. These phenomena are derived from strong intercomplex interactions of chiral cylindrical molecular complexes.

Charge response of the Majorana toric code

At zero temperature, a two dimensional lattice of Majorana zero modes on mesoscopic superconducting islands has a topologically ordered toric code phase. Recently, a Landau field theory has been proposed for the system that captures its different phases and the associated phase-transitions. It was shown that with the increase of Josephson tunneling between the islands, a continuous symmetry-breaking 3D-XY transition gets transformed into a discrete symmetry-breaking 3D-Ising transition through a couple of tricritical points and first order transitions. Using the proposed field theory, we analyze the charge-response of the system at the different continuous phase-transitions. We calculate the universal conductivity at the 3D-XY transitions and the change in the superconducting density at the Ising transition using 1/N expansion. Furthermore, by computing a one-loop correction to the field theory, we show that an additional tricritical point is likely to be present in the phase-diagram. Finally, we provide a mean-field calculation that supports the earlier proposed field theory.

Veiled symmetry of disordered Parity-Time lattices: protected PT-threshold and the fate of localization

Open, non-equilibrium systems with balanced gain and loss, known as parity-time ({mathscr{P}}{mathscr{T}})-symmetric systems, exhibit properties that are absent in closed, isolated systems. A key property is the {mathscr{P}}{mathscr{T}}-symmetry breaking transition, which occurs when the gain-loss strength, a measure of the openness of the system, exceeds the intrinsic energy-scale of the system. We analyze the fate of this transition in disordered lattices with non-Hermitian gain and loss potentials ±iγ at reflection-symmetric sites. Contrary to the popular belief, we show that the {mathscr{P}}{mathscr{T}}-symmetric phase is protected in the presence of a periodic disorder which leads to a positive {mathscr{P}}{mathscr{T}}-symmetry breaking threshold. We uncover a veiled symmetry of such disordered systems that is instrumental for the said protection, and show that this symmetry leads to new localization behavior across the {mathscr{P}}{mathscr{T}}-symmetry breaking transition. We elucidate the interplay between such localization and the {mathscr{P}}{mathscr{T}}-symmetry breaking phenomena in disordered {mathscr{P}}{mathscr{T}}-symmetric lattices, with Hermitian disorder or gain-loss disorder, and support our conclusions with a beampropagation- method analysis. Our theoretical predictions provide avenues for experimental realizations of -symmetric systems with engineered disorder.

Extra thermo- and water-stable one-dimensional organic-inorganic hybrid perovskite [N-methyldabconium]PbI3 showing switchable dielectric behaviour, conductivity and bright yellow-green emission.

Haloplumbate-based perovskites display promising functionalities for advanced photovoltaic, optoelectronic and other applications with high performances and low costs. Herein, we present a study of variable-temperature crystal structures, dielectrics and conductance at 153-513 K, and luminescence at ambient temperature for a one-dimensional organic-inorganic perovskite, [N-methyldabconium]PbI3 (1). Hybrid 1 shows extra thermo- and water-stability (thermal decomposition at ca. 653 K), switchable dielectric behaviour and conductance at around 348 K, owing to symmetry-breaking structure phase transition from the hexagonal space group P63/mmc in the high-temperature phase to the orthogonal space group Pcba in the low-temperature phase, and bright yellow-green emission at room temperature, originating from the electron transition within the semiconducting {PbI3}∞ chains. This study will broaden the scope of lead halide-based hybrid materials for practical application in optical and electrical devices.

Instanton-dyon ensembles reproduce deconfinement and chiral restoration phase transitions

Paradigm shift in gauge topology at finite temperatures, from the instantons to their constituents – instanton-dyons – has recently lead to studies of their ensembles and very significant advances. Like instantons, they have fermionic zero modes, and their collectivization at suffciently high density explains the chiral symmetry breaking transition. Unlike instantons, these objects have electric and magnetic charges. Simulations of the instanton-dyon ensembles have demonstrated that their back reaction on the Polyakov line modifies its potential and generates the deconfinement phase transition. For the Nc = 2 gauge theory the transition is second order, for QCD-like theory with Nc = 2 and two light quark flavors Nf = 2 both transitions are weak crossovers at happening at about the same condition. Introduction of quark-flavor-dependent periodicity phases (imaginary chemical potentials) leads to drastic changes in both transitions. In particulaly, in the so called Z(Nc) – QCD model the deconfinement transforms to strong first order transition, while the chiral condensate does not disappear at all. The talk will also cover more detailed studies of correlations between the dyons, effective eta’ mass and other screening masses.