Dynamical quantum phase transitions: a review

Abstract

Quantum theory provides an extensive framework for the description of the equilibrium properties of quantum matter. Yet experiments in quantum simulators have now opened up a route towards generating quantum states beyond this equilibrium paradigm. While these states promise to show properties not constrained by equilibrium principles such as the equal a priori probability of the microcanonical ensemble, identifying general properties of nonequilibrium quantum dynamics remains a major challenge especially in view of the lack of conventional concepts such as free energies. The theory of dynamical quantum phase transitions attempts to identify such general principles by lifting the concept of phase transitions to coherent quantum real-time evolution. This review provides a pedagogical introduction to this field. Starting from the general setting of nonequilibrium dynamics in closed quantum many-body systems, we give the definition of dynamical quantum phase transitions as phase transitions in time with physical quantities becoming nonanalytic at critical times. We summarize the achieved theoretical advances as well as the first experimental observations, and furthermore provide an outlook onto major open questions as well as future directions of research.

arXiv commentAny comments or suggestions are highly welcome, extended presentation

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• Relation between equilibrium quantum phase transitions and dynamical quantum phase transitions in two-band systems
• Universal work statistics in long-range interacting quantum systems
• Disentanglement Approach to Quantum Spin Ground States: Field Theory and Stochastic Simulation
• Symmetry shapes thermodynamics of macroscopic quantum systems
• Numerical Simulations Unveil Superradiant Coherence in a Lattice of Charged Quantum Oscillators
• From Complexification to Self-Similarity: New Aspects of Quantum Criticality
• Tunneling phase diagrams in anisotropic Multi-Weyl semimetals
• Time-Evolving Weiss Fields in the Stochastic Approach to Quantum Spins
• Role of topology on the work distribution function of a quenched Haldane model of graphene
• Spectroscopic evidence for engineered hadron formation in repulsive fermionic $\text{SU}(N)$ Hubbard Models
• Dynamical quantum phase transitions from random matrix theory
• Dynamical quantum phase transitions in Stark quantum spin chains
• Reduced fidelities for free fermions out of equilibrium: From dynamical quantum phase transitions to Mpemba effect
• Dynamical Phase Transitions in Open Quantum Walks
• Phonon-assisted tunnelling in a double quantum dot molecule immersed in a cavity
• Loschmidt echo zeros in finite-size quantum systems with linear quench
• Geometric phases of Topological Systems under Quench Process
• Relaxation time as a control parameter for exploring dynamical phase diagrams
• Quantum coherence assisted dynamical phase transition
• Recognizing critical lines via entanglement in non-Hermitian systems
• Periodic quantum Rabi model with cold atoms at deep strong coupling
• Dissipative preparation of a Floquet topological insulator in an optical lattice via bath engineering
• Detecting Many-Body Scars from Fisher Zeros
• Full counting statistics and first-passage times in quantum Markovian processes: Ensemble relations, metastability, and fluctuation theorems
• Importance Sampling Scheme for the Stochastic Simulation of Quantum Spin Dynamics
• Statistical complexity and the road to equilibrium in many-body chaotic quantum systems
• Dynamical detection of mean-field topological phases in an interacting Chern insulator
• Correlation functions of the Bjorken flow in the holographic Schwinger-Keldysh approach
• Stable many-body resonances in open quantum systems
• Signature of quantum phase transition manifested in quantum fidelity at finite temperature
• Conformal symmetry in quasi-free Markovian open quantum systems
• Thermal-bath effects in quantum quenches within quantum critical regimes
• Topological phases of spinless $p$-orbital fermions in zigzag optical lattices
• Purification Dynamics in a Continuous-time Hybrid Quantum Circuit Model
• Probing quantum phase transition via quantum speed limit
• Emerging topological characterization in non-equilibrium states of quenched Kitaev chains
• Fidelity decay and error accumulation in random quantum circuits
• Exact Spin Correlators of Integrable Quantum Circuits from Algebraic Geometry
• Dynamical quantum phase transition and thermal equilibrium in the lattice Thirring model
• Insights from the exact analytical solution of periodically driven transverse field Ising chain
• Geometry effect of the dynamical quantum phase transitions at finite temperatures
• Quantum error mitigation in optimized circuits for particle-density correlations in real-time dynamics of the Schwinger model
• Bosons condensed in two modes with flavour-changing interaction
• Dynamical quantum phase transition, metastable state, and dimensionality reduction: Krylov analysis of fully connected spin models
• The eigenstate distribution fluctuation from thermal to localized transitions
• Quantum memory and scrambling from the perspective of a classical neural network
• Spectral Analysis of Proton Eigenfunctions in Crystalline Environments
• Quantum purification spectroscopy
• Fidelity zeros and Lee-Yang theory of quantum phase transitions
• Multipartite Greenberger-Horne-Zeilinger Entanglement in Monitored Random Clifford Circuits
• Thermalization and non-monotonic entanglement growth in an exactly solvable model
• The singularities of the rate function of quantum coherent work in one-dimensional transverse field Ising model
• Classical Theory of Quantum Work Distribution in Chaotic Fermion Systems
• Directional scrambling of quantum information in helical multiferroics
• Universal Anomaly of Dynamics at Phase Transition Points Induced by Pancharatnam-Berry Phase
• From Chiral Topological Dynamics to Chiral Topological Amplification: Real vs Imaginary Parameters in a Hermitian Bosonic Chain
• Digital Quantum Simulation of Scalar Yukawa Coupling
• Investigating the quench dynamics of the bound states in a spin-orbital coupling system using a trapped ion
• Non-equilibrium dynamics of superconductivity in the Hatsugai-Kohmoto model
• Disorder Enhanced Thermalization in Interacting Many-Particle System
• Pseudochaotic Many-Body Dynamics as a Pseudorandom State Generator
• Amplifying quantum correlations with quench dynamics in a quantum spin chain: Steady-states versus ground-states
• Ab-Initio Approach to Many-Body Quantum Spin Dynamics
• Exact zeros of fidelity in finite-size systems as a signature for probing quantum phase transitions
• Non-stationarity and Dissipative Time Crystals: Spectral Properties and Finite-Size Effects
• Dynamical signatures of symmetry protected topology following symmetry breaking
• Speedup of thermodynamic entropy production via quantum dynamical criticality
• Characterizing the Yang-Lee zeros of the classical Ising model through dynamic quantum phase transitions
• Infinite Grassmann time-evolving matrix product operators for quantum impurity problems after a quench
• Nonadiabatic transition at a band-touching point
• Effects of geometry on spin-orbit Kramers states in semiconducting nanorings
• Superconducting phase in the BCS model with imaginary magnetic field. III. Non-vanishing free dispersion relations
• Response of macroscopic and microscopic dynamical quantifiers to the quantum critical region
• A recipe for local simulation of strongly-correlated fermionic matter on quantum computers: the 2D Fermi-Hubbard model
• Effect of long-range hopping on dynamic quantum phase transitions of an exactly solvable free-fermion model: Nonanalyticities at almost all times
• Scrambling and quantum feedback in a nanomechanical system
• Superfluidity vs prethermalisation in a nonlinear Floquet system
• Quench dynamics of quasi-periodic systems exhibiting Rabi oscillations of two-level integrals of motion
• Markovian and Non-Markovian dynamics in the one-dimensional transverse-field XY model
• Dynamical phase transition of light in time-varying nonlinear dispersive media
• Explicit Pfaffian Formula for Amplitudes of Fermionic Gaussian Pure States in Arbitrary Pauli Bases
• Control of dynamical phase transitions and non-ergodic relaxation via spinor phases
• Dynamical dimerization phase in Jaynes-Cummings lattices
• Clifford-Dressed Variational Principles for Precise Loschmidt Echoes
• Critical Exponent of Dynamical Quantum Phase Transition in One-Dimensional Bose-Hubbard Model in the Strong Interacting Limit
• Extended edge modes and disorder preservation of a symmetry-protected topological phase out of equilibrium
• Topological Classification of Dynamical Quantum Phase Transitions in the 1D XY model via Critical Mode Analysis
• Achieving the quantum field theory limit in far-from-equilibrium quantum link models
• Emergent dynamical quantum phase transition in a $Z_3$ symmetric chiral clock model
• Critical properties in the non-Hermitian Aubry-Andre-Stark model
• Distinguishing dynamical quantum criticality through local fidelity distances
• Exploring dynamical quantum phase transition from pure states to mixed states through extended Su-Schrieffer-Heeger models
• Memory-Critical Dynamical Buildup of Phonon-Dressed Majorana Fermions
• Nonequilibrium Critical Scaling of a Squeezing Phase Transition
• Exact analysis of AC sensors based on Floquet time crystals
• Julia Set in Quantum Evolution: The case of Dynamical Quantum Phase Transitions
• The ITransverse.jl library for transverse tensor network contractions
• Su-Schrieffer-Heeger model driven by sequences of two unitaries: periodic, quasiperiodic, aperiodic, and random protocols
• Quantum quenches across continuous and first-order quantum transitions in one-dimensional quantum Ising models
• Loschmidt echo and Momentum Distribution in a Kitaev Spin Chain
• Quantum fluctuation theorem for initial near-equilibrium system
• On computing non-equilibrium dynamics following a quench
• Slow decay rate of correlations induced by long-range extended Dzyaloshinskii-Moriya interactions
• Relaxation dynamics in the alternating XY chain following a quantum quench
• Realizing Topological Quantum Walks on NISQ Digital Quantum Computer
• Dynamical Quantum Phase Transitions in Interacting Atomic Interferometers
• Non-equilibrium dynamics of the open quantum $O(n)$-model with non-Markovian noise: exact results
• Dynamical Quantum Phase Transitions and Many-Body Backflow in Open Quantum Systems
• Krylov Complexity Under Hamiltonian Deformations and Toda Flows
• Comparing quantum complexity and quantum fidelity
• Work and heat exchanged during sudden quenches of strongly coupled quantum systems
• Dynamical Phase Transitions in Periodically Driving 1D Ising Model
• Hierarchy of percolation patterns in a kinetic replication model
• Chaos, thermalization and breakdown of quantum-classical correspondence in a collective many-body system
• Evolution of quantum geometric tensor of 1D periodic systems after a quench
• Characterizing dynamical phase transitions in a spinor Bose-Einstein condensate via quantum and semiclassical analyses
• Asymmetry and dynamical criticality
• Reaching Quantum Critical Point by Adding Non-magnetic Disorder in Single Crystals of Superconductor $({\text{Ca}}_x{\text{Sr}}_{1-x}{)}_3{\text{Rh}}_4{\text{Sn}}_{13}$
• Floquet dynamical quantum phase transitions in periodically flux-quenched systems
• Toward nonthermal control of excited quantum materials: framework and investigations by ultrafast electron scattering and imaging
• Non-Markovian Noise in Symmetry-Preserving Quantum Dynamics
• Universal features of non-analytical energy storage in quantum critical quantum batteries
• Nonequilibrium Dynamics in a Quantum Spin Chain with Pump-Probe Resonant Inelastic X-ray Scattering
• Algebraic law of local correlations in a driven Rydberg atomic system
• Nanomechanically-induced nonequilibrium quantum phase transition to a self-organized density wave of a Bose-Einstein condensate
• Designing non-equilibrium states of quantum matter through stochastic resetting
• Superradiant Quantum Phase Transition in Open Systems: System-Bath Interaction at the Critical Point
• Distinct many-body scars and emergent quantum phases driven by competing interactions in two-species Rydberg arrays
• Entanglement entropy dynamics of non-Gaussian states in free boson systems: Random sampling approach
• Scaling laws for the sensitivity enhancement of non-Gaussian spin states
• Entanglement dynamics and ergodicity breaking in a quantum cellular automaton
• Linear differential equation approach to the Loschmidt amplitude
• Numerically efficient unitary evolution for Hamiltonians beyond nearest-neighbors
• Dynamical quantum phase transitions in strongly correlated two-dimensional spin lattices following a quench
• Hierarchies among genuine multipartite entangling capabilities of quantum gates
• Entanglement dynamics in minimal Kitaev chains
• A digital Rydberg simulation of dynamical quantum phase transitions in the Schwinger model
• Orthogonalization speed-up from quantum coherence after a sudden quench
• Anatomy of Non-Hermitian Dynamical Quantum Phase Transitions
• A Dynamical Bulk-Boundary Correspondence in Two Dimensional Topological Matter
• Trajectory-Resolved Weiss Fields for Quantum Spin Dynamics
• Adaptive quantum dynamics with the time-dependent variational Monte Carlo method
• Dynamical quantum phase transitions on random networks