Symmetry-breaking Transition Research Articles

Variational tensor network renormalization in imaginary time: Two-dimensional quantum compass model at finite temperature

Progress in describing thermodynamic phase transitions in quantum systems is obtained by noticing that the Gibbs operator $e^{-\beta H}$ for a two-dimensional (2D) lattice system with a Hamiltonian $H$ can be represented by a three-dimensional tensor network, the third dimension being the imaginary time (inverse temperature) $\beta$. Coarse-graining the network along $\beta$ results in a 2D projected entangled-pair operator (PEPO) with a finite bond dimension $D$. The coarse-graining is performed by a tree tensor network of isometries. The isometries are optimized variationally --- taking into account full tensor environment --- to maximize the accuracy of the PEPO. The algorithm is applied to the isotropic quantum compass model on an infinite square lattice near a symmetry-breaking phase transition at finite temperature. From the linear susceptibility in the symmetric phase and the order parameter in the symmetry-broken phase the critical temperature is estimated at ${\cal T}_c=0.0606(4)J$, where $J$ is the isotropic coupling constant between $S=1/2$ pseudospins.

Stochastic precession of the polarization in a polariton laser

Microcavity polaritons in the lasing regime undergo a spontaneous symmetry breaking transition resulting in coherent emission with a well defined polarization. The order parameter is thus a vector describing both the laser global phase and polarization. Using an ultrafast single-shot detection technique we show that polariton lasing in GaAs-based microcavities presents a high degree of second order coherence ($g^{(2)}(\tau=0) \approx 1$) above threshold, and that the initial polarization is stochastic, taking any possible direction in the Poincar\'e sphere (linear, elliptical or circular). Once the polarization direction is established, subsequent oscillations of the emission probability witness the presence of an intrinsic polarization splitting. Our results show the negligible role of polariton interactions in the total emission statistics and in the establishment of the initial polarization.

Possibility of formation of a disoriented chiral condensate inppcollisions at energies available at the CERN Large Hadron Collider via the reaction-diffusion equation

There are indications of formation of a thermalized medium in high multiplicity pp collisions at LHC energy. It is possible that such a medium may reach high enough energy density/temperature so that a transient stage of quark-gluon plasma, where chiral symmetry is restored, may be achieved. Due to rapid 3-dimensional expansion, the system will quickly cool undergoing spontaneous chiral symmetry breaking transition. We study the dynamics of chiral field, after the symmetry breaking transition, for such an event using reaction-diffusion equation approach which we have recently applied for studying QCD transitions in relativistic heavy-ion collisions. We show that the interior of such a rapidly expanding system is likely to lead to the formation of a single large domain of disoriented chiral condensate (DCC) which has been a subject of intensive search in earlier experiments. We argue that large multiplicity pp collisions naturally give rise to required boundary conditions for the existence of slowly propagating front solutions of reaction-diffusion equation with resulting dynamics of chiral field leading to the formation of a large DCC domain.

A theoretical study of the stability of anionic defects in cubic ZrO2 at extreme conditions

Using first principles density functional theory calculations, we present a study of the structure, mobility, and the thermodynamic stability of anionic defects in the high-temperature cubic phase of ZrO2. Our results suggest that the local structure of an oxygen interstitial depends on the charge state and the cubic symmetry of the anionic sublattice is unstable at 0 K. In addition, the oxygen interstitials and the vacancies exhibit symmetry breaking transitions to low-energy structures with tetragonal distortion of the oxygen sublattice at 0 K. However, the vibrational entropy stabilizes the defect structures with cubic symmetry at 2600–2980 K. The formation free energies of the anionic defects and Gibbs free energy changes associated with different defect reactions are calculated by including the vibrational free energy contributions and the effect of pressure on these defect structures. By analyzing the defect chemistry, we obtain the defect concentrations at finite temperature and pressure conditions using the zero temperature ab initio results as input and find that at low oxygen partial pressures, neutral oxygen vacancies are most dominant and at high oxygen partial pressures, doubly charged anionic defects are dominant. The relevance of the results to the thermal protective coating capabilities of zirconium-based ceramic composites is elucidated.

Universal Scaling of Spectral Fluctuation Transitions for Interacting Chaotic Systems.

The statistical properties of interacting strongly chaotic systems are investigated for varying interaction strength. In order to model tunable entangling interactions between such systems, we introduce a new class of random matrix transition ensembles. The nearest-neighbor-spacing distribution shows a very sensitive transition from Poisson statistics to those of random matrix theory as the interaction increases. The transition is universal and depends on a single scaling parameter only. We derive the analytic relationship between the model parameters and those of a bipartite system, with explicit results for coupled kicked rotors, a dynamical systems paradigm for interacting chaotic systems. With this relationship the spectral fluctuations for both are in perfect agreement. An accurate approximation of the nearest-neighbor-spacing distribution as a function of the transition parameter is derived using perturbation theory.

Sub-millimeter wave spectroscopy of CHD2OH: a-type and asymmetry induced c-type transitions in the lowest three torsional sub-levels

The sub-millimeter wave (SMMW) spectral measurements using a fast scan backward wave oscillator based spectrometer have been carried out for asymmetrically deuterated methanol CHD2OH (Methanol-D2). Transition frequencies have an estimated uncertainty of about ±50kHz. Albeit the complexity in the spectra, assignments were possible for a large number of a-type (ΔK=0) transitions. In the course of the assignment process a strong c-type (ΔK=1) Q-branch connecting two states of different symmetry species has been identified. This Q-branch assignment is significant because it is forbidden in the normal parent species CH3OH. It becomes allowed in the current species due to the effects of the asymmetry introduced by the off-axis deuterium in the hindering potential to the internal rotation in the molecule. The assignments are rigorously confirmed using combination relations which required the measurement of some other related lines. To our knowledge this is the first time such symmetry breaking transitions are reported in CHD2OH and in fact this is the first time the SMMW spectrum of CHD2OH is being reported. Detailed spectral study of this molecule in the IR and FIR regions is in progress and will be reported elsewhere. Detailed study of the identification optically pumped FIR laser line is underway.

Two-step electroweak baryogenesis

We analyze electroweak baryogenesis during a two-step electroweak symmetry breaking transition, wherein the baryon asymmetry is generated during the first step and preserved during the second. Focusing on the dynamics of CP-violation required for asymmetry generation, we discuss general considerations for successful two-step baryogenesis. Using a concrete model realization, we illustrate in detail the viability of this scenario and the implications for present and future electric dipole moment (EDM) searches. We find that CP-violation associated with a partially excluded sector may yield the observed baryon asymmetry while evading present and future EDM constraints.

Probing new physics of cubic Higgs boson interaction via Higgs pair production at hadron colliders

Despite the discovery of a Higgs boson $h$ (125 GeV) at the LHC run 1, its self-interaction has fully evaded direct experimental probe so far. Such self-interaction is vital for electroweak symmetry breaking, vacuum stability, and electroweak phase transition. It is a most likely place to encode new physics beyond the standard model. We parametrize such new physics by model-independent dimension-six effective operators and study their tests via Higgs pair production at hadron colliders. We analyze three major di-Higgs production channels at the parton level and compare the parameter dependence of total cross sections and kinematic distributions at the LHC (14 TeV) and $pp$ (100 TeV) hadron collider. We further perform full simulations for the di-Higgs production channel $gg\ensuremath{\rightarrow}hh\ensuremath{\rightarrow}b\overline{b}\ensuremath{\gamma}\ensuremath{\gamma}$ and its backgrounds at the $pp$ (100 TeV) hadron collider. We construct four kinds of benchmark points and study the sensitivities to probing different regions of the parameter space of cubic Higgs interactions. We find that for a one-parameter analysis and with a $3\text{ }\text{ }{\mathrm{ab}}^{\ensuremath{-}1}$ ($30\text{ }\text{ }{\mathrm{ab}}^{\ensuremath{-}1}$) integrated luminosity, the $gg\ensuremath{\rightarrow}hh\ensuremath{\rightarrow}b\overline{b}\ensuremath{\gamma}\ensuremath{\gamma}$ channel can measure the SM cubic Higgs coupling and the derivative cubic Higgs coupling to an accuracy of about 13% (4.2%) and 5% (1.6%), respectively.

Vortex and half-vortex dynamics in a nonlinear spinor quantum fluid.

Vortices are archetypal objects that recur in the universe across the scale of complexity, from subatomic particles to galaxies and black holes. Their appearance is connected with spontaneous symmetry breaking and phase transitions. In Bose-Einstein condensates and superfluids, vortices are both point-like and quantized quasiparticles. We use a two-dimensional (2D) fluid of polaritons, bosonic particles constituted by hybrid photonic and electronic oscillations, to study quantum vortex dynamics. Polaritons benefit from easiness of wave function phase detection, a spinor nature sustaining half-integer vorticity, strong nonlinearity, and tuning of the background disorder. We can directly generate by resonant pulsed excitations a polariton condensate carrying either a full or half-integer vortex as initial condition and follow their coherent evolution using ultrafast imaging on the picosecond scale. The observations highlight a rich phenomenology, such as the spiraling of the half-vortex and the joint path of the twin charges of a full vortex, until the moment of their splitting. Furthermore, we observe the ordered branching into newly generated secondary couples, associated with the breaking of radial and azimuthal symmetries. This allows us to devise the interplay of nonlinearity and sample disorder in shaping the fluid and driving the vortex dynamics. In addition, our observations suggest that phase singularities may be seen as fundamental particles whose quantized events span from pair creation and recombination to 2D+t topological vortex strings.

Quantum Sensors Assisted by Spontaneous Symmetry Breaking for Detecting Very Small Forces

We propose a quantum sensing scheme for measuring weak forces based on a symmetry-breaking adiabatic transition in the quantum Rabi model. We show that the system described by the Rabi Hamiltonian can serve as a sensor for extremely weak forces with sensitivity beyond the yN $/\sqrt{\text{Hz}}$ range. We propose an implementation of this sensing protocol using a single trapped ion. A major advantage of our scheme is that the force detection is performed by projective measurement of the population of the spin states at the end of the transition, instead of the far slower phonon number measurement used hitherto.

Chirality-driven intrinsic spin-glass ordering and field-induced ferromagnetism in Ni3Al nanoparticle aggregates

Weak itinerant-electron ferromagnet Ni3Al is driven to magnetic instability (quantum critical point, QCP, where the long-range ferromagnetic order of the bulk ceases to exist) by reducing the average crystallite size to d=50nm. ‘Zero-field’ (H=0) linear and nonlinear ac-susceptibilities, measured on Ni3Al nanoparticle aggregates, with d=50nm (S1) and d=5nm (S2), provide strong evidence for two spin glass (SG)-like thermodynamic phase transitions: one at Ti(H=0)≃30K (Ti†(H=0)≃230K) and the other at a lower temperature Tp(H=0)≃8K (Th(H=0)≃52K) in S1 (S2). ‘In-field’ (H≠0) linear ac-susceptibility and dc magnetization demonstrate that the thermodynamic nature of these transitions is preserved in finite fields. The presently determined H–T phase diagrams for the samples S1 and S2 are compared with those predicted by the Kotliar–Sompolinsky and Gabay–Toulouse mean-field models and Monte Carlo simulations, based on the chirality-driven spin glass (SG) ordering scenario, for a three-dimensional nearest-neighbor Heisenberg SG system with or without weak random anisotropy. Such a detailed comparison permits us to unambiguously identify various ‘zero-field’ and ‘in-field’ SG phase transitions as: (i) the simultaneous paramagnetic (PM)-chiral glass (CG) and PM-SG phase transitions at Ti(H), (ii) the PM-CG transition at Ti†(H), (iii) the replica symmetry-breaking SG transition at Tp(H), and (iv) the continuous spin-rotation symmetry-breaking SG transition at Th(H). In the presence of random anisotropy, magnetization fails to saturate even at 90kOe in S1 whereas negligibly small anisotropy allows even fields as weak as 1kOe to saturate magnetization and induce ferromagnetism in S2. Due to the proximity to CG/SG-QCP, magnetization and susceptibility both exhibit non-Fermi liquid behavior over a wide range at low temperatures.

New Superconductivity Dome in LaFeAsO1−xFx Accompanied by Structural Transition**Supported by the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No XDB07020200, the National Basic Research Program of China under Grant Nos 2012CB821402, 2011CBA00109 and 2011CBA00101, and the National Natural Science Foundation of China under Grant No 11204362.

High-temperature superconductivity is often found in the vicinity of antiferromagnetism. This is also true in LaFeAsO1−xFx (x ≤ 0.2) and many other iron-based superconductors, which leads to proposals that superconductivity is mediated by fluctuations associated with the nearby magnetism. Here we report the discovery of a new superconductivity dome without low-energy magnetic fluctuations in LaFeAsO1−xFx with 0.25 ≤ x ≤ 0.75, where the maximal critical temperature Tc at xopt = 0.5−0.55 is even higher than that at x ≤ 0.2. By nuclear magnetic resonance and transmission electron microscopy, we show that a C4 rotation symmetry-breaking structural transition takes place for x > 0.5 above Tc. Our results point to a new paradigm of high temperature superconductivity.

Reaction-diffusion equation for quark-hadron transition in heavy-ion collisions

Reaction-diffusion equations with suitable boundary conditions have special propagating solutions which very closely resemble the moving interfaces in a first order transition. We show that the dynamics of chiral order parameter for chiral symmetry breaking transition in heavy-ion collisions, with dissipative dynamics, is governed by one such equation, specifically, the Newell-Whitehead equation. Further, required boundary conditions are automatically satisfied due to the geometry of the collision. The chiral transition is, therefore, completed by a propagating interface, exactly as for a first order transition, even though the transition actually is a crossover for relativistic heavy-ion collisions. Same thing also happens when we consider the initial confinement-deconfinement transition with Polyakov loop order parameter. The resulting equation, again with dissipative dynamics, can then be identified with the reaction-diffusion equation known as the Fitzhugh-Nagumo equation which is used in population genetics. We discuss the implications of these results for heavy-ion collisions. We also discuss possible extensions for the case of early universe.

Electroweak baryogenesis from exotic electroweak symmetry breaking

We investigate scenarios in which electroweak baryogenesis can occur during an exotic stage of electroweak symmetry breaking in the early Universe. This transition is driven by the expectation value of a new electroweak scalar instead of the standard Higgs field. A later, second transition then takes the system to the usual electroweak minimum, dominated by the Higgs, while preserving the baryon asymmetry created in the first transition. We discuss the general requirements for such a two-stage electroweak transition to be suitable for electroweak baryogenesis and present a toy model that illustrates the necessary ingredients. We then apply these results to construct an explicit realization of this scenario within the inert two Higgs doublet model. Despite decoupling the Higgs from the symmetry-breaking transition required for electroweak baryogenesis, we find that this picture generically predicts new light states that are accessible experimentally.

SpontaneousPT-symmetry breaking in non-Hermitian Kitaev and extended Kitaev models

The spontaneous parity-time $(\mathcal{PT})$ symmetry breaking is discussed in non-Hermitian $\mathcal{PT}$-symmetric Kitaev and extended Kitaev models whose Hermiticity is broken by the presence of two conjugated imaginary potentials $\ifmmode\pm\else\textpm\fi{}i\ensuremath{\gamma}$ at two end sites. In the case of the non-Hermitian Kitaev model, a spontaneous $\mathcal{PT}$-symmetry breaking transition $(S\mathcal{PT}BT)$ occurs at a certain ${\ensuremath{\gamma}}_{c}$ in the topologically trivial phase (TTP) region, similar to that of the Su-Schrieffer-Heeger (SSH) model. However, unlike the SSH model, the system also undergoes such a transition in the topologically nontrivial phase (TNP) region. We study an extended Kitaev model by combining the superconducting pairing in the Kitaev model and the staggered hopping in the SSH model. This model contains three different topological phases: the TTP, the Kitaev-like TNP, and the SSH-like TNP. For the non-Hermitian extended Kitaev model, a $S\mathcal{PT}BT$ occurs in the Kitaev-like TNP region, as well as in part of the TTP and SSH-like TNP regions, whereas the $\mathcal{PT}$ symmetry is broken for an arbitrary nonzero $\ensuremath{\gamma}$ in the rest of the TTP and SSH-like TNP regions. Therefore, we can conclude that there is no universal correlation between topological properties and the $S\mathcal{PT}BT$.

Quantum Critical Elasticity.

We discuss elastic instabilities of the atomic crystal lattice at zero temperature. Because of long-range shear forces of the solid, at such transitions the phonon velocities vanish, if at all, only along certain crystallographic directions, and, consequently, the critical phonon fluctuations are suppressed to a lower dimensional manifold and governed by a Gaussian fixed point. In the case of symmetry-breaking elastic transitions, a characteristic critical phonon thermodynamics arises that is found, e.g., to violate Debye's T(3) law for the specific heat. We point out that quantum critical elasticity is triggered whenever a critical soft mode couples linearly to the strain tensor. In particular, this is relevant for the electronic Ising-nematic quantum phase transition in a tetragonal crystal as discussed in the context of certain cuprates, ruthenates, and iron-based superconductors.

Critical elasticity at zero and finite temperature

Elastic phase transitions of crystals and phase transitions whose order parameter couples linearly to elastic degrees of freedom are reviewed with particular focus on instabilities at zero temperature. A characteristic feature of these transitions is the suppression of critical fluctuations by long-range shear forces. As a consequence, at an elastic crystal symmetry-breaking quantum phase transition the phonon velocity vanishes only along certain crystallographic directions giving rise to critical phonon thermodynamics described by a stable Gaussian fixed point. At an isostructural solid-solid quantum critical end point, on the other hand, the complete suppression of critical fluctuations results in true mean-field critical behavior without a diverging correlation length. Whenever an order parameter couples bilinearly to the strain tensor, the critical properties are eventually governed by critical crystal elasticity. This is, for example, the case for quantum critical metamagnetism but also for the classical critical Mott end point at finite T. We discuss and compare the solid-solid end points expected close to the Mott transition in V2O3 and κ-(BEDT-TTF)2 X.

Self-organization and transition to turbulence in isotropic fluid motion driven by negative damping at low wavenumbers

We observe a symmetry-breaking transition from a turbulent to a self-organized state in direct numerical simulation of the Navier–Stokes equation at very low Reynolds number. In this self-organized state the kinetic energy is contained only in modes at the lowest resolved wavenumber, the skewness vanishes, and visualization of the flows shows a lack of small-scale structure, with the vorticity and velocity vectors becoming aligned (a Beltrami flow).

Chimeras in globally coupled oscillatory systems: From ensembles of oscillators to spatially continuous media.

We study an oscillatory medium with a nonlinear global coupling that gives rise to a harmonic mean-field oscillation with constant amplitude and frequency. Two types of cluster states are found, each undergoing a symmetry-breaking transition towards a related chimera state. We demonstrate that the diffusional coupling is non-essential for these complex dynamics. Furthermore, we investigate localized turbulence and discuss whether it can be categorized as a chimera state.

Curvature-induced symmetry breaking determines elastic surface patterns.

Symmetry-breaking transitions associated with the buckling and folding of curved multilayered surfaces-which are common to a wide range of systems and processes such as embryogenesis, tissue differentiation and structure formation in heterogeneous thin films or on planetary surfaces-have been characterized experimentally. Yet owing to the nonlinearity of the underlying stretching and bending forces, the transitions cannot be reliably predicted by current theoretical models. Here, we report a generalized Swift-Hohenberg theory that describes wrinkling morphology and pattern selection in curved elastic bilayer materials. By testing the theory against experiments on spherically shaped surfaces, we find quantitative agreement with analytical predictions for the critical curves separating labyrinth, hybrid and hexagonal phases. Furthermore, a comparison to earlier experiments suggests that the theory is universally applicable to macroscopic and microscopic systems. Our approach builds on general differential-geometry principles and can thus be extended to arbitrarily shaped surfaces.