Symmetry-breaking Transition Research Articles

Entropic Analysis of Mirror Symmetry Breaking in Chiral Hypercycles.

Replicators are fundamental to the origin of life and evolvability. Biology exhibits homochirality: only one of two enantiomers is used in proteins and nucleic acids. Thermodynamic studies of chemical replicators able to lead to homochirality shed valuable light on the origin of homochirality and life in conformity with the underlying mechanisms and constraints. In line with this framework, enantioselective hypercyclic replicators may lead to spontaneous mirror symmetry breaking (SMSB) without the need for additional heterochiral inhibition reactions, which can be an obstacle for the emergence of evolutionary selection properties. We analyze the entropy production of a two-replicator system subject to homochiral cross-catalysis which can undergo SMSB in an open-flow reactor. The entropy exchange with the environment is provided by the input and output matter flows, and is essential for balancing the entropy production at the non-equilibrium stationary states. The partial entropy contributions, associated with the individual elementary flux modes, as defined by stoichiometric network analysis (SNA), describe how the system’s internal currents evolve, maintaining the balance between entropy production and exchange, while minimizing the entropy production after the symmetry breaking transition. We validate the General Evolution Criterion, stating that the change in the chemical affinities proceeds in a way as to lower the value of the entropy production.

Controlled symmetry breaking and vortex dynamics in intersecting flows

Vortices are a ubiquitous feature in complex flows and turbulence, but their dynamics are challenging to study due to their typically transient nature. Here, we perform a detailed study of the vortex dynamics and interactions associated with a symmetry-breaking flow instability at a 4-way intersection. By precisely controlling the flow rate (hence the Reynolds number, Re) of the flow about a critical value, we are able to induce the merging of two co-rotating vortices into a single structure and similarly to induce a single vortex to split into two. Using quantitative flow velocimetry, both processes are recorded with high spatial and temporal resolution. We find that both the merging and the splitting of vortices are exponential processes, with a rate that depends on the imposed Re. The vortex dynamics in our system are intimately connected with the symmetry-breaking transition and are affected by the degree of vortex confinement, which we control by varying the aspect ratio (α) of the flow geometry. We show how the confinement affects the fundamental nature of the flow transition, which varies from super through subcritical as α is increased. Our results are of direct relevance to understanding and predicting flow transitions and vortex dynamics in flow intersections, particularly in confined environments such as in microfluidic (lab-on-a-chip) devices and in the circulatory system, and may be relevant to the prediction of vortex interactions in general.

Path-Dependent Preparation of Complex Micelle Packings of a Hydrated Diblock Oligomer.

Small-angle X-ray scattering analyses reveal that the hydrated diblock oligomer n-C16H23(OCH2CH2)20-OH (C16E20 or Brij 58) forms lyotropic liquid crystals (LLCs) exhibiting face-centered cubic (FCC), body-centered cubic (BCC), Frank–Kasper (FK) A15, and cylindrical (HI) morphologies over the concentration range 30–65 wt % amphiphile. Heating LLCs comprising 54–59 wt % C16E20 drives the temperature-dependent phase transition sequence: A15 → BCC → HI. However, rapidly quenching the resulting HI phase from 70 to 25 °C initially forms a BCC phase that isothermally transforms into a complex, tetragonal FK σ phase comprising 30 quasispherical micelles. The metastability of this micellar σ phase is shown to depend on the sample cooling rate, thermal quench depth, and isothermal annealing temperature. We rationalize the preference for the A15 structure at 25 °C in terms of minimizing unfavorable water/hydrophobic contacts, while maximizing local particle sphericity. The symmetry breaking transition kinetics in these micellar LLCs apparently stem from the temperature-dependent activation barriers for phase nucleation and growth, which are intimately coupled to the time scales for micelle reconfiguration by amphiphile chain exchange and their spatial rearrangement. These findings highlight how thermal processing influences nucleation and growth of the self-assembled morphologies of intrinsically reconfigurable, soft spherical particles.

Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms

Open physical systems with balanced loss and gain, described by non-Hermitian parity-time left( {{cal P}{cal T}} right) reflection symmetric Hamiltonians, exhibit a transition which could engender modes that exponentially decay or grow with time, and thus spontaneously breaks the {cal P}{cal T}-symmetry. Such {cal P}{cal T}-symmetry-breaking transitions have attracted many interests because of their extraordinary behaviors and functionalities absent in closed systems. Here we report on the observation of {cal P}{cal T}-symmetry-breaking transitions by engineering time-periodic dissipation and coupling, which are realized through state-dependent atom loss in an optical dipole trap of ultracold 6Li atoms. Comparing with a single transition appearing for static dissipation, the time-periodic counterpart undergoes {cal P}{cal T}-symmetry breaking and restoring transitions at vanishingly small dissipation strength in both single and multiphoton transition domains, revealing rich phase structures associated to a Floquet open system. The results enable ultracold atoms to be a versatile tool for studying {cal P}{cal T}-symmetric quantum systems.

Critical flavor number in the 2+1D Thirring model

The Thirring model in 2+1 spacetime dimensions, in which $N$ flavors of relativistic fermion interact via a contact interaction between conserved fermion currents, is studied using lattice field theory simulations employing domain wall fermions, which furnish the correct U(2N) global symmetry in the limit that the wall separation $L_s\to\infty$. Attention is focussed on the issue of spontaneous symmetry breakdown via a non-vanishing fermion bilinear condensate $\langle\bar\psi\psi\rangle\not=0$. Results from quenched simulations are presented demonstrating that a non-zero condensate does indeed form over a range of couplings, provided simulation results are first extrapolated to the $L_s\to\infty$ limit. Next, results from simulations with $N=1$ using an RHMC algorithm demonstrate that U(2) symmetry is unbroken at weak coupling but plausibly broken at strong coupling. Correlators of mesons with spin zero are consistent with the Goldstone spectrum expected from U(2)$\to$U(1)$\otimes$U(1). We infer the existence of a symmetry-breaking phase transition at some finite coupling, and combine this with previous simulation results to deduce that the critical number of flavors for the existence of a quantum critical point in the Thirring model satisfies $0<N_c<2$, with strong evidence that in fact $N_c>1$.

Nonlinear symmetry breaking of Aharonov-Bohm cages

We study the influence of mean field cubic nonlinearity on Aharonov-Bohm caging in a diamond lattice with synthetic magnetic flux. For sufficiently weak nonlinearities the Aharonov-Bohm caging persists as periodic nonlinear breathing dynamics. Above a critical nonlinearity, symmetry breaking induces a sharp transition in the dynamics and enables stronger wavepacket spreading. This transition is distinct from other flatband networks, where continuous spreading is induced by effective nonlinear hopping or resonances with delocalized modes, and is in contrast to the quantum limit, where two-particle hopping enables arbitrarily large spreading. This nonlinear symmetry breaking transition is readily observable in femtosecond laser-written waveguide arrays.

High-order exceptional points in ultracold Bose gases

We show that arbitrarily high-order exceptional points (EPs) can be achieved in a repulsively interacting two-species Bose gas in one dimension. By exactly solving the non-Hermitian two-boson problem, we demonstrate the existence of third-order EPs when the system is driven across the parity-time symmetry breaking transition. We further address the fourth-order EPs with three bosons and generalize the results to $N$-body system, where the EP order can be as high as $N+1$. Physically, such high order originates from the intrinsic ferromagnetic correlation in spinor bosons, which renders the entire system collectively behave as a single huge spin. Moreover, we show how to create ultra-sensitive spectral response around EPs via an interaction anisotropy in different spin channels. Our work puts forward the possibility of atomic sensors made from highly controllable ultracold gases.

Dynamical criticality in open systems: Nonperturbative physics, microscopic origin, and direct observation

Driven diffusive systems may undergo phase transitions to sustain atypical values of the current. This leads in some cases to symmetry-broken space-time trajectories which enhance the probability of such fluctuations. Here we shed light on both the macroscopic large deviation properties and the microscopic origin of such spontaneous symmetry breaking in the open weakly asymmetric exclusion process. By studying the joint fluctuations of the current and a collective order parameter, we uncover the full dynamical phase diagram for arbitrary boundary driving, which is reminiscent of a $\mathbb{Z}_2$ symmetry-breaking transition. The associated joint large deviation function becomes non-convex below the critical point, where a Maxwell-like violation of the additivity principle is observed. At the microscopic level, the dynamical phase transition is linked to an emerging degeneracy of the ground state of the microscopic generator, from which the optimal trajectories in the symmetry-broken phase follow. In addition, we observe this new symmetry-breaking phenomenon in extensive rare-event simulations, confirming our macroscopic and microscopic results.

Spontaneous symmetry breaking and discontinuous phase transition for spreading dynamics in multiplex networks

We propose a spreading model in multilayer networks and study the nature of nonequilibrium phase transition in the model. The model integrates the susceptible-infected-susceptible (or susceptible-infected-recovered) spreading dynamics with a biased diffusion process among different layers. A parameter α is introduced to control the bias of the diffusion process, such that each individual prefers to move to one layer with more infected (or recovered) neighbors for larger values of α. Using stochastic simulations and mean-field theory, we show that the type of phase transition from a disease-free phase to an endemic phase (EP) depends on the value of α. When α is small enough, the system undergoes a usual continuous phase transition as an effective spreading rate β increases, as in single-layer networks. Interestingly, when α exceeds a critical value the system shows either a hybrid two-step phase transition or a one-step discontinuous phase transition as β increases. The former contains a continuous transition between the disease-free phase and a low-prevalence EP, and a discontinuous transition between the low-prevalence EP and a high-prevalence EP. For the latter, only a discontinuous transition occurs from the disease-free phase directly to the high-prevalence EP. Moreover, we show that the discontinuous transition is always accompanied by a spontaneous symmetry breaking in occupation probabilities of individuals in each layer.

Observation of slowly decaying eigenmodes without exceptional points in Floquet dissipative synthetic circuits

AbstrctPassive parity-time symmetry breaking transitions, where long-lived eigenmodes emerge in a locally dissipative system, have been extensively studied in recent years. Conventional wisdom says that they occur at exceptional points. Here we report the observation of multiple transitions showing the emergence of slowly decaying eigenmodes in a dissipative, Floquet electronic system with synthetic components. Remarkably, in our system, the modes emerge without exceptional points. Our setup uses an electrical oscillator inductively coupled to a dissipative oscillator, where the time-periodic inductive coupling and resistive-heating losses are independently controlled. With a Floquet dissipation, slowly-decaying eigenmodes emerge at vanishingly small dissipation strength in the weak coupling limit. With a moderate Floquet coupling, multiple instances of their emergence and disappearance are observed. With an asymmetric dimer model, we show that these transitions, driven by avoided-level-crossing in purely dissipative systems, are generically present in static and Floquet domains.

Contact interactions and Kronig–Penney models in Hermitian and symmetric quantum mechanics

The delta function potential is a simple model of zero-range contact interaction in non-relativistic quantum mechanics in one dimension. The Kronig–Penney model is a one-dimensional periodic array of delta functions and provides a simple illustration of energy bands in a crystal. Here we investigate contact interactions that generalize the delta function potential and corresponding generalizations of the Kronig–Penney model within conventional and symmetric quantum mechanics. In conventional Hermitian quantum mechanics we determine the most general contact interaction compatible with self-adjointness and in quantum mechanics we consider interactions that respect symmetry under the transformation where denotes parity and denotes time reversal. In both cases we find that the most general interaction has four independent real parameters and depending on the values of those parameters the contact interaction can support zero, one or two bound states. By contrast the conventional delta function can only support zero or one bound state. In the symmetric case moreover the two bound state energies can be both real or a complex conjugate pair. The transition from real to complex bound state energies corresponds to the spontaneous breaking of symmetry. The scattering states for the symmetric case are also found to exhibit spontaneous breaking of symmetry wherein the eigenvalues of the non-unitary S-matrix depart the unit circle in the complex plane. We also investigate the energy bands when the generalized contact interactions are repeated periodically in space in one dimension. In the Hermitian case we find that the two bound states result in two narrow bands generically separated by a gap. These bands intersect at a single point in the Brillouin zone as the interaction parameters are varied. Near the intersection the bands form a massless Dirac cone. In the symmetric case we find that as the parameters of the contact interaction are varied the two bound state bands undergo a symmetry breaking transition wherein the two band energies go from being real to being a complex conjugate pair. The symmetric Kronig–Penney model provides a simple soluble example of the transition which has the same form as in other models of symmetric crystals.

Majorana stripe order on the surface of a three-dimensional topological insulator

The issue on the effect of interactions in topological states concerns not only interacting topological phases but also novel symmetry-breaking phases and phase transitions. Here we study the interaction effect on Majorana zero modes (MZMs) bound to a square vortex lattice in two-dimensional topological superconductors. Under the neutrality condition, where single-body hybridization between MZMs is prohibited by an emergent symmetry, a minimal square-lattice model for MZMs can be faithfully mapped to a quantum spin model, which has no sign problem in the world-line quantum Monte Carlo simulation. Guided by an insight from a further duality mapping, we demonstrate that the interaction induces a Majorana stripe state, a gapped state spontaneously breaking lattice translational and rotational symmetries, as opposed to the previously conjectured topological quantum criticality. Away from neutrality, a mean-field theory suggests a quantum critical point induced by hybridization.

Multipartite Entanglement at Finite Temperature

The interplay of quantum and thermal fluctuations in the vicinity of a quantum critical point characterizes the physics of strongly correlated systems. Here we investigate this interplay from a quantum information perspective presenting the universal phase diagram of the quantum Fisher information at a quantum phase transition. Different regions in the diagram are identified by characteristic scaling laws of the quantum Fisher information with respect to temperature. This feature has immediate consequences on the thermal robustness of quantum coherence and multipartite entanglement. We support the theoretical predictions with the analysis of paradigmatic spin systems showing symmetry-breaking quantum phase transitions and free-fermion models characterized by topological phases. In particular we show that topological systems are characterized by the survival of large multipartite entanglement, reaching the Heisenberg limit at finite temperature.

Definite photon deflections of\xa0topological\xa0defects in metasurfaces and symmetry-breaking phase transitions with material loss

Combination of topology and general relativity can lead to some profound and farsighted predictions. It is well known that symmetry breaking of the Higgs vacuum field in the early universe possibly induced topological defects in space-time, whose nontrivial effects can provide some clues about the universe’s origin. Here, by using an artificial waveguide bounded with rotational metasurface, the nontrivial effects of a topological defect of spacetime are experimentally emulated. The photon deflection in the topological waveguide has a robust definite angle that does not depend on the location and momentum of incident photons. This is remarkably different from the random optical scattering in trivial space. By including material loss such a topological effect can be well understood from the symmetry breaking of photonic modes. Our technique provides a platform to investigate topological gravity in optical systems. This method can also be extended to obtain many other novel topological photonic devices.

What symmetry is actually broken in the Higgs phase of a gauge-Higgs theory?

In SU($N$) gauge-Higgs theories, with a single Higgs field in the fundamental representation, there exists in addition to the local gauge symmetry a global SU(2) symmetry, at $N=2$, and a global U(1) symmetry, for $N \ne 2$. We construct a gauge-invariant order parameter for the breaking of these global symmetries in the Higgs sector, and calculate numerically the transition lines, in coupling-constant space, for SU(2) and SU(3) gauge theories with unimodular Higgs fields. The order parameter is non-local, and therefore its non-analyticity does not violate the theorem proved by Osterwalder and Seiler. We then show that there exists a transition, in gauge-Higgs theories, between two types of confinement: ordinary color neutrality in the Higgs region, and a stronger condition, which we have called "separation-of-charge confinement," in the confinement region. We conjecture that the symmetry-breaking transition coincides with the transition between these two physically different types of confinement.

Dynamic critical properties of non-equilibrium Potts models with absorbing states

We present extensive numerical simulations of a family of non-equilibrium Potts models with absorbing states that allows for a variety of scenarios, depending on the number of spin states and the range of the spin–spin interactions. These scenarios encompass a voter critical point, a discontinuous transition as well as the presence of both a symmetry-breaking phase transition and an absorbing phase transition. While we also investigate standard steady-state quantities, our emphasis is on time-dependent quantities that provide insights into the transient properties of the models.

Effects of non-Hermiticity on Su-Schrieffer-Heeger defect states

We study the emergence and disappearance of defect states in the complex Su-Schrieffer-Heeger (cSSH) model, a non-Hermitian one-dimensional lattice model containing gain and loss on alternating sites. Previous studies of this model have focused on the existence of a non-Hermitian defect state that is localized to the interface between two cSSH domains, and is continuable to the topologically protected defect state of the Hermitian Su-Schrieffer-Heeger (SSH) model. For large gain/loss magnitudes, we find that these defect states can disappear into the continuum, or undergo pairwise spontaneous breaking of a composite sublattice/time-reversal symmetry. The symmetry-breaking transition gives rise to a pair of defect states continuable to nontopologically protected defect states of the SSH model. We discuss the phase diagram for the defect states, and its implications for non-Hermitian defect states.

Icosahedral (H2)13 supermolecule

We investigate a range of possible materials containing the supermolecular form of hydrogen comprising 13 hydrogen molecules arranged in an icosahedral arrangement. This supermolecule consists of freely rotating 12 hydrogen molecules in an icosahedral arrangement, enclosing another freely rotating molecule. To date, this supermolecule has only been observed in a compound with Iodane (HI). The extremely high hydrogen content suggests possible application in hydrogen storage so we examine the possibility of supermolecule formation at ambient pressures. We show that ab initio molecular dynamics calculations give a good description of the known properties of the HI(H2)13 material, and make predictions of the existence of related compounds Xe(H2)1, HBr(H2)13 and HCl(H2)13, including a symmetry-breaking phase transition at low temperature. The icosahedral (H2)13 supermolecule, remains stable in all these compounds. This suggests (H2)13 is a widespread feature in hydrogen compounds, and that appropriately-sized cavities could hold hydrogen supermolecules even at low pressure. The structure of the supermolecule network is shown to be independent of the compound at equivalent density.

Topological origin of phase transitions in the absence of critical points of the energy landscape

Different arguments led us to surmise that the deep origin of phase transitions has to be identified with suitable topological changes of potential-related submanifolds of configuration space of a physical system. An important step forward for this approach was achieved with two theorems stating that, for a wide class of physical systems, phase transitions should necessarily stem from topological changes of equipotential energy submanifolds of configuration space. However, it has been recently shown that the 2D lattice -model provides a counterexample that falsifies the mentioned theorems. On the basis of a numerical investigation, the present work indicates the way to overcome this difficulty: in spite of the absence of critical points of the potential in correspondence of the transition energy, also the phase transition of this model stems from a change of topology of both the energy and potential level sets. But in this case the topology changes are asymptotic (). This fact is not obvious since the symmetry-breaking transition could be given measure-based explanations in presence of trivial topology.

Critical mode and band-gap-controlled bipolar thermoelectric properties of SnSe

The reliable calculation of electronic structures and understanding of electrical properties depends on an accurate model of the crystal structure. Here, we have reinvestigated the crystal structure of the high-zT thermoelectric material tin selenide, SnSe, between 4 and 1000 K using high-resolution neutron powder diffraction. Symmetry analysis reveals the presence of four active structural distortion modes, one of which is found to be active over a relatively wide range of more than +/-200 K around the symmetry-breaking Pnma-Cmcm transition at 800 K. Density functional theory calculations on the basis of the experimental structure parameters show that the unusual, step-like temperature dependencies of the electrical transport properties of SnSe are caused by the onset of intrinsic bipolar conductivity, amplified and shifted to lower temperatures by a rapid reduction of the band gap between 700 and 800 K. The calculated band gap is highly sensitive to small out-of-plane Sn displacements observed in the diffraction experiments. SnSe with a sufficiently controlled acceptor concentration is predicted to produce simultaneously a large positive and a large negative Seebeck effect along different crystal directions.