## We study the resulting chiral symmetry breaking phase transition for models with $N_F=3$ and $N_F=4$ light flavors using the linear sigma model.

Dynamical Axions and Gravitational Waves.

## We also give signatures of the $\mathcal {PT}$-symmetric and the symmetry breaking phases for the interacting bosons in experiment.

Interaction effects on the PT -symmetry-breaking transition in atomic gases

## Our results show that although topological phase transitions do not follow a symmetry-breaking mechanism, it might be still possible to use concepts of symmetry-breaking phase transitions for topological ones by finding suitable mappings.

Ising order parameter and topological phase transitions: Toric code in uniform field

## We do this numerically by using the symmetry-breaking phase transition line of EQCD as a line of constant physics.

Full $\mathcal{O}(a)$ improvement of EQCD

10.1103/PhysRevB.100.125159

## Our results show that although topological phase transitions do not follow a symmetry-breaking mechanism, it might be still possible to use concepts of symmetry-breaking phase transitions for topological ones by finding suitable mappings.

Ising order parameter and topological phase transitions: Toric code in uniform field

10.1016/J.EUROMECHFLU.2018.03.012

## The simulation covers the initial development of the wind profile, the growth of the modulational instability, the breaking and post breaking phases.

Effects of the wind on the breaking of modulated wave trains

## We do this numerically by using the symmetry-breaking phase transition line of EQCD as a line of constant physics.

Full $\mathcal{O}(a)$ improvement of EQCD

10.1007/JHEP07(2019)146

## We study the resulting chiral symmetry breaking phase transition for models with $N_F=3$ and $N_F=4$ light flavors using the linear sigma model.

Dynamical Axions and Gravitational Waves.

10.1103/PhysRevB.99.184511

## In particular, critical sizes and shapes are identified, providing quantitative guidelines for sample fabrication in the experimental hunt for symmetry-breaking phases.

Spontaneous symmetry breaking at surfaces of d-wave superconductors: Influence of geometry and surface ruggedness

10.1103/PhysRevA.102.053510

## For unmodulated case with inhomogeneous inter- and intra- quadrimer coupling strength $\kappa_1\neq\kappa$, in addition to conventional global $PT$-symmetric phase and $PT$-symmetry-breaking phase, we find that there is exotic phase where global $PT$ symmetry is broken under open boundary condition, whereas it still is unbroken under periodical boundary condition.

Floquet control of global $PT$ symmetry in 2D arrays of quadrimer waveguides

10.1103/PhysRevB.99.165143

## Specifically, we investigate the quantum phase transition between Ising ferromagnetic and valence bond solid (VBS) symmetry-breaking phases.

Deconfined quantum critical point in one dimension.

10.1103/PhysRevA.99.043412

## We also give signatures of the $\mathcal {PT}$-symmetric and the symmetry breaking phases for the interacting bosons in experiment.

Interaction effects on the PT -symmetry-breaking transition in atomic gases

10.1103/PhysRevD.100.034510

## We do this numerically by using the symmetry-breaking phase transition point of the theory as a line of constant physics.

Full O(a) improvement in EQCD

10.1515/nanoph-2018-0207

## We theoretically and numerically demonstrate that the spontaneous parity-time (PT) symmetry breaking phase transition can be realized respectively by using two independent tuning ways in a tri-layered metamaterial that consists of periodic array of metal-semiconductor Schottky junctions.

Manifestation of the spontaneous parity-time symmetry breaking phase transition in hot-electron photodetection based on a tri-layered metamaterial

10.1103/PhysRevLett.122.147602

## By carefully examining active electronic degrees of freedom based on the lattice symmetry, we propose that two parity-breaking phases at ambient pressure are described by unconventional multipoles, electric toroidal quadrupoles (ETQs) with different components, x^{2}-y^{2} and 3z^{2}-r^{2}, in the pyrochlore tetrahedral unit.

Electric Toroidal Quadrupoles in the Spin-Orbit-Coupled Metal Cd_{2}Re_{2}O_{7}.

10.1038/S42254-019-0038-2

## Key pointsThe quantum spin liquid is an exotic state of matter in which interacting spins avoid symmetry-breaking phase transitions and form a ground state exhibiting long-range entanglement and topological order.

Concept and realization of Kitaev quantum spin liquids

10.1103/PhysRevB.100.125157

## Here we consider a parity-time ($\mathcal{PT}$) symmetric extension of the Aubry-Andre-Harper model, undergoing a topological metal-insulator phase transition, and provide rigorous analytical results of energy spectrum, symmetry breaking phase transition and localization length.

Metal-insulator phase transition in a non-Hermitian Aubry-André-Harper model

10.1007/978-1-4939-9084-9_10

## First of all, the symmetry can be spontaneously broken in the ground state leading to symmetry-breaking phases.

Symmetry-Protected Topological Phases

10.1088/1751-8121/ab40ec

## Resonances, spectral singularities and eigenvalues are analyzed in detail and discussed in the context of the associated laser-absorber modes and $\mathcal{PT}$-symmetry breaking phase transition.

Spacing gain and absorption in a simple $\mathcal{PT}$-symmetric model: spectral singularities and ladders of eigenvalues and resonances

10.21468/SciPostPhys.7.3.029

## Coarsening dynamics, the canonical theory of phase ordering following a quench across a symmetry breaking phase transition, is thought to be driven by the annihilation of topological defects.

Anomalous phase ordering of a quenched ferromagnetic superfluid

## For this model, the dissipative phase transition (DPT), accompanying a parity-time (PT) symmetry-breaking phase transition, occurs when the imaginary field changes through the YLES.

Scaling of the Berry Phase in the Yang-Lee Edge Singularity

10.1103/PhysRevE.99.022132

## A replica-symmetry-breaking phase transition is predicted in a host of disordered media.

Morphology of renormalization-group flow for the de Almeida-Thouless-Gardner universality class.

10.1103/PhysRevE.100.012124

## Our purpose is discovering, if any, the relation between the second-order Z_{2}-symmetry-breaking phase transition and the geometric entities mentioned above.

Topology of configuration space of the mean-field ϕ^{4} model by Morse theory.

10.1109/JPHOT.2018.2889145

## We consider the properties of the small-signal modulation response of symmetry-breaking phase-locked states of twin coupled semiconductor lasers.

Antiresonances and Ultrafast Resonances in a Twin Photonic Oscillator

10.1103/PhysRevB.100.125137

## The deconfined quantum critical point (DQCP) was originally proposed as a continuous transition between two spontaneous symmetry breaking phases in 2D spin-1/2 systems.

Emergent symmetry and conserved current at a one-dimensional incarnation of deconfined quantum critical point

10.7566/JPSJ.88.063703

## Across the Lifshitz transition point, the sign of the relative phase between the Cooper-pair components drastically changes, leading to the emergence of the time-reversal breaking phase with complex gap functions.

Time-reversal symmetry breaking superconductivity in hole-doped monolayer MoS$_{2}$.

10.1103/PhysRevResearch.1.023013

## In non-Hermitian crystals showing the non-Hermitian skin effect, ordinary Bloch band theory and Bloch topological invariants fail to correctly predict energy spectra, topological boundary states, and symmetry breaking phase transitions in systems with open boundaries.

Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions

10.1109/ICEMPE.2019.8727374

## Influences of breaking phase angels, velocity and gas pressure were discussed at the same time.

Study on Dielectric Recovery Characteristics of High Voltage SF6Circuit Breaker

10.1007/s13233-019-7173-6

## In this paper, we report distinct symmetry-breaking phase transitions in molecules based on oligo-para-phenylene rods and a poly(ethylene oxide) coil depending on the length of the aromatic rod block The observed phase transitions were characterized by differential scanning calorimetry (DSC) and X-ray scattering methods.

Sequential Symmetry-Breaking Intercolumnar Transformations of a Conjugated Rod Molecule with a Flexible Coil

## Here, we unveil that non-unitary discrete-time quantum walks of photons in systems involving gain and loss show rather generally non-Bloch parity-time symmetry-breaking phase transitions and suggest a bulk probing method to detect such boundary-driven phase transitions.

Non-Bloch ${\cal P}{\cal T}$PT symmetry breaking in non-Hermitian photonic quantum walks.

10.1103/PhysRevD.99.034504

## 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 $0 1$.

Critical flavor number in the 2+1D Thirring model

10.1103/PHYSREVD.100.034510

## We do this numerically by using the symmetry-breaking phase transition point of the theory as a line of constant physics.

Full O(a) improvement in electrostatic QCD

10.1038/s41567-020-0983-9

## In most unconventional and high-temperature superconductors, superconductivity emerges as a nearby symmetry-breaking phase is suppressed by chemical doping or pressure 1 – 7.

Suppression of superconductivity by anisotropic strain near a nematic quantum critical point

## The origin of the symmetry-breaking phase transition is associated with the motion or reorientation of the DMEA cations, accompanied by the crystal structures from orthorhombic Pnma to monoclinic P21/c with the temperature decreases.

Ultrahigh phase transition temperature in a metal-halide perovskite-type material containing unprecedented hydrogen bonding interactions.

10.1109/PHOSST.2019.8794865

## In this talk we will cover the properties of the small-signal modulation response of symmetry-breaking phase-locked states of twin coupled semiconductor lasers.

WC1.3 - Antiresonances, Ultrafast Resonances and Exeptional Points in Twin Photonic Oscillators (Invited)

10.1007/978-1-4939-9084-9_9

## In this chapter, we first introduce the basic properties of tensor product states and then proceed to discuss how it represents symmetry-breaking phases and topological phases with explicit examples.

Tensor Product States and 2D Gapped Phases

## We start by showing that any contest that satisfies our assumptions decomposes into two phases, a principal phase (in which states cannot be revisited) and a concluding tie-breaking phase (in which all non-terminal states can be revisited).

Multi-Battle Contests, Finite Automata, and the Tug-of-War

10.1103/PhysRevResearch.2.023225

## Our RG analysis leads to the qualitative conclusion that the emergent interaction-induced symmetry-breaking phases in this model system, and perhaps therefore by extension in twisted bilayer graphene, are generically unstable and fragile, and may thus manifest strong sample dependence.

Spontaneous symmetry breaking in a honeycomb lattice subject to a periodic potential