Dynamical Quantum Phase Transitions in the Transverse Field Ising Model

Abstract

A phase transition indicates a sudden change in the properties of a large system. For temperature-driven phase transitions this is related to non-analytic behavior of the free energy density at the critical temperature: The knowledge of the free energy density in one phase is insufficient to predict the properties of the other phase. In this paper we show that a close analogue of this behavior can occur in the real time evolution of quantum systems, namely non-analytic behavior at a critical time. We denote such behavior a dynamical phase transition and explore its properties in the transverse field Ising model. Specifically, we show that the equilibrium quantum phase transition and the dynamical phase transition in this model are intimately related.

4+4 pages, 4 figures, Appendix added

References in corpus (5)

• The large deviation approach to statistical mechanics
• Quantum Quench in the Transverse Field Ising Chain
• Dynamical phase transition in correlated fermionic lattice systems
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Dynamics in the Ising field theory after a quantum quench

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• Exploring Dynamical Phase Transitions in the XY Chain through Linear Quench: Early and Long-term Perspectives
• Universal long-time behavior of stochastically driven interacting quantum systems
• Speeding up Pontus-Mpemba effects via dynamical phase transitions
• Entanglement in quenched extended Su-Schrieffer-Heeger model with anomalous dynamical quantum phase transitions
• Exact dynamical correlations of nonlocal operators in quadratic open Fermion systems: a characteristic function approach
• Thermally isolated Luttinger liquids with noisy Hamiltonians
• Limits to magnetic quantum criticality from nuclear spins
• Cumulative quantum work-deficit versus entanglement in the dynamics of an infinite spin chain
• Build-up of Vibron-Mediated Electron Correlations in Molecular Junctions
• Localization transition induced by programmable disorder
• Nonadiabatic Phase Transition with Broken Chiral Symmetry
• Dynamical symmetries and crossovers in a three-spin system with collective dissipation
• Fluctuations and Non-Hermiticity in the Stochastic Approach to Quantum Spins
• Decoherence and relaxation of topological states in extended quantum Ising models
• Analyticity constraints bound the decay of the spectral form factor
• Information Trapping by Topologically Protected Edge States: Scrambling and the Butterfly Velocity
• Unitary preparation of many body Chern insulators: Adiabatic bulk boundary correspondence
• Fermion-induced Dynamical Critical Point
• Indication of critical scaling in time during the relaxation of an open quantum system
• Singularities in large deviations of work in quantum quenches
• Fisher zeroes and dynamical quantum phase transitions for two- and three-dimensional models
• Signatures of quantum criticality in the complex inverse temperature plane
• Fermionic Magic Resources of Quantum Many-Body Systems
• Exact Fisher zeros and thermofield dynamics across a quantum critical point
• Spread complexity and dynamical transition in multimode Bose-Einstein condensates
• Meson content of entanglement spectra after integrable and nonintegrable quantum quenches
• Real-space effects of a quench in the Su-Schrieffer-Heeger model and elusive dynamical appearance of the topological edge states
• Probing the superfluid-insulator phase transition by a non-Hermitian external field
• Robustness and eventual slow decay of bound states of interacting microwave photons in the Google Quantum AI experiment
• Fibonacci-Modulation-Induced Multiple Topological Anderson Insulators
• Signature of Generalized Gibbs Ensemble Deviation from Equilibrium: Negative Absorption Induced by a Local Quench
• Work statistics and thermal phase transitions
• Disorder-induced dynamical Griffiths singularities after certain quantum quenches
• Dynamic phase transition theory
• Nonequilibrium dynamical renormalization group: Dynamical crossover from weak to infinite randomness in the transverse-field Ising chain
• Dynamical relaxation behavior of extended XY chain with gapless phase following a quantum quench
• Spin fluctuations after quantum quenches in the S=1 Haldane chain: numerical validation of the semi-semiclassical theory
• Lee-Yang theory of quantum phase transitions with neural network quantum states
• Synthetic topology and Floquet dynamic quantum phase transition in a periodically driven Raman lattice
• The Loschmidt Index
• Entanglement and dynamical phase transition in a spin-orbit-coupled Bose-Einstein condensate
• Two rate periodic protocol with dynamics driven through many cycles
• On model reduction for quantum dynamics: symmetries and invariant subspaces
• Universal cooling dynamics toward a quantum critical point
• Generation of concurrence between two qubits locally coupled to a one dimensional spin chain
• Infinite-range transverse field Ising models and quantum computation
• Photoexcitations in the Hubbard model -- generalized Loschmidt amplitude analysis of impact ionization in small clusters
• Effect of double local quenches on Loschmidt echo and entanglement entropy of a one-dimensional quantum system
• Slow and fast topological dynamical phase transitions in a Duffing resonator driven by two detuned tones
• Phase transition in complex-time Loschmidt echo of short and long range spin chain
• Reconstructing Thermal Quantum Quench Dynamics from Pure States
• Aperiodic dynamical quantum phase transitions in multi-band Bloch Hamiltonian and its origin
• Excited-State Phase Diagram of a Ferromagnetic Quantum Gas
• Lee-Yang theory of the superradiant phase transition in the open Dicke model
• Quenching the Kitaev honeycomb model
• Universal scaling of work statistics for quantum quenches
• Probing Confinement Through Dynamical Quantum Phase Transitions: From Quantum Spin Models to Lattice Gauge Theories
• Imaginary-Temperature Zeros for Quantum Phase Transitions
• Dynamical scaling laws in the quantum $q$-state clock chain
• Dynamical phase transitions of information flow in random quantum circuits
• Energy-filtered quantum states and the emergence of non-local correlations
• Vortex loop dynamics and dynamical quantum phase transitions in 3D fermion matter
• Exotic signature of dynamical quantum phase transition in the time evolution of engineered initial state
• Entanglement Dynamics between Ising Spins and a Central Ancilla
• Scaling and Universality at Noisy Quench Dynamical Quantum Phase Transitions
• Critical behavior at dynamical phase transition in the generalized Bose-Anderson model
• Beyond Fermi's golden rule with the statistical Jacobi approximation
• Quantum quench in a driven Ising chain
• Relaxation time as a control parameter for exploring dynamical phase diagrams
• Quantum quench thermodynamics at high temperatures
• Dynamical quantum phase transitions from quantum optics perspective
• Dynamical quantum phase transitions in Stark quantum spin chains
• Dynamical Phase Transitions in Open Quantum Walks
• Time-Evolving Weiss Fields in the Stochastic Approach to Quantum Spins
• Reduced fidelities for free fermions out of equilibrium: From dynamical quantum phase transitions to Mpemba effect
• Role of topology on the work distribution function of a quenched Haldane model of graphene
• Relation between equilibrium quantum phase transitions and dynamical quantum phase transitions in two-band systems
• Lee-Yang zeros in the Rydberg atoms
• Singularities in the Loschmidt echo of quenched topological superconductors
• Tunneling phase diagrams in anisotropic Multi-Weyl semimetals
• Propagation of quantum fluctuations in quantum Ising model
• Recognizing critical lines via entanglement in non-Hermitian systems
• Quantum coherence assisted dynamical phase transition
• Detecting Many-Body Scars from Fisher Zeros
• Loschmidt echo zeros in finite-size quantum systems with linear quench
• Dynamical quantum phase transitions from random matrix theory
• On the size of the space spanned by a nonequilibrium state in a quantum spin lattice system
• Cumulants of time-integrated observables of closed quantum systems and PT-symmetry, with an application to the quantum Ising chain
• From Complexification to Self-Similarity: New Aspects of Quantum Criticality
• Disentanglement Approach to Quantum Spin Ground States: Field Theory and Stochastic Simulation
• Geometric phases of Topological Systems under Quench Process
• Kibble-Zurek scaling in the quantum Ising chain with a time-periodic perturbation
• Signature of quantum phase transition manifested in quantum fidelity at finite temperature
• Fractonic Quantum Quench in Dipole-constrained Bosons
• Probing quantum phase transition via quantum speed limit
• Emerging topological characterization in non-equilibrium states of quenched Kitaev chains
• Coherent charge and spin oscillations induced by local quenches in nanowires with spin-orbit coupling
• Imaginary-time relaxation quantum critical dynamics in two-dimensional dimerized Heisenberg model
• Exact Spin Correlators of Integrable Quantum Circuits from Algebraic Geometry
• Dynamical quantum phase transition and thermal equilibrium in the lattice Thirring model
• Quantum purification spectroscopy
• Insights from the exact analytical solution of periodically driven transverse field Ising chain
• Geometry effect of the dynamical quantum phase transitions at finite temperatures
• Momentum space magic for the transverse field quantum Ising model
• Topological phases of spinless $p$-orbital fermions in zigzag optical lattices
• Dynamical quantum phase transition, metastable state, and dimensionality reduction: Krylov analysis of fully connected spin models
• Statistical complexity and the road to equilibrium in many-body chaotic quantum systems
• Time Evolution and Deterministic Optimisation of Correlator Product States
• Quantum memory and scrambling from the perspective of a classical neural network
• Purification Dynamics in a Continuous-time Hybrid Quantum Circuit Model
• Quantum Quench dynamics in XY spin chain with ferromagnetic and antiferromagnetic interactions
• Quantum dynamics of Gaudin magnets
• Importance Sampling Scheme for the Stochastic Simulation of Quantum Spin Dynamics
• Thermal-bath effects in quantum quenches within quantum critical regimes
• Amplifying quantum correlations with quench dynamics in a quantum spin chain: Steady-states versus ground-states
• From Chiral Topological Dynamics to Chiral Topological Amplification: Real vs Imaginary Parameters in a Hermitian Bosonic Chain
• Quench dynamics of quasi-periodic systems exhibiting Rabi oscillations of two-level integrals of motion
• Effect of long-range hopping on dynamic quantum phase transitions of an exactly solvable free-fermion model: Nonanalyticities at almost all times
• Order parameter dynamics of the non-linear sigma model in the large $N$ limit
• Scrambling and quantum feedback in a nanomechanical system
• Single-shot determination of quantum phases via continuous measurements
• Directional scrambling of quantum information in helical multiferroics
• Superconducting phase in the BCS model with imaginary magnetic field. III. Non-vanishing free dispersion relations
• Speedup of thermodynamic entropy production via quantum dynamical criticality
• Critical Exponent of Dynamical Quantum Phase Transition in One-Dimensional Bose-Hubbard Model in the Strong Interacting Limit
• Characterizing the Yang-Lee zeros of the classical Ising model through dynamic quantum phase transitions
• Critical behavior of order parameter at the nonequilibrium phase transition of the Ising model
• Partition function zeros of quantum many-body systems
• Dynamical dimerization phase in Jaynes-Cummings lattices
• Topology in the space-time scaling limit of quantum dynamics
• Sudden quench of harmonically trapped mass-imbalanced fermions
• Fidelity zeros and Lee-Yang theory of quantum phase transitions
• Non-equilibrium dynamics of superconductivity in the Hatsugai-Kohmoto model
• Exact zeros of fidelity in finite-size systems as a signature for probing quantum phase transitions
• The singularities of the rate function of quantum coherent work in one-dimensional transverse field Ising model
• Lee-Yang formalism for phase transitions of interacting fermions using tensor networks
• Feasibility of the ion-trap simulation of a class of non-equilibrium phase transitions
• Control of dynamical phase transitions and non-ergodic relaxation via spinor phases
• Markovian and Non-Markovian dynamics in the one-dimensional transverse-field XY model
• Clifford-Dressed Variational Principles for Precise Loschmidt Echoes
• Explicit Pfaffian Formula for Amplitudes of Fermionic Gaussian Pure States in Arbitrary Pauli Bases
• Quantum speed limit for the OTOC from an open systems perspective
• Universal Non-equilibrium I-V Curve Near Two-channel Kondo-Luttinger Quantum Critical Point
• Response of macroscopic and microscopic dynamical quantifiers to the quantum critical region
• Voltage Induced Dynamical Quantum Phase Transitions in Exciton Condensates
• Exploring dynamical quantum phase transition from pure states to mixed states through extended Su-Schrieffer-Heeger models
• Achieving the quantum field theory limit in far-from-equilibrium quantum link models
• Julia Set in Quantum Evolution: The case of Dynamical Quantum Phase Transitions
• The ITransverse.jl library for transverse tensor network contractions
• Emergent dynamical quantum phase transition in a $Z_3$ symmetric chiral clock model
• Loschmidt echo and Momentum Distribution in a Kitaev Spin Chain
• Su-Schrieffer-Heeger model driven by sequences of two unitaries: periodic, quasiperiodic, aperiodic, and random protocols
• Finite time path field theory perturbative methods for local quantum spin chain quenches
• Topological Classification of Dynamical Quantum Phase Transitions in the 1D XY model via Critical Mode Analysis
• Phase structure and real-time dynamics of the massive Thirring model in 1+1 dimensions using the tensor-network method
• Finite time path field theory and a new type of universal quantum spin chain quench behavior
• Slow decay rate of correlations induced by long-range extended Dzyaloshinskii-Moriya interactions
• Quantum fluctuation theorem for initial near-equilibrium system
• Distinguishing dynamical quantum criticality through local fidelity distances
• Dynamical Phase Transitions, Caustics, and Quantum Dark Bands
• Dynamics for the Haldane phase in the Bilinear-Biquadratic Model
• Irreversible Work Reduction by Disorder in Many-Body Quantum Systems
• Relaxation dynamics in the alternating XY chain following a quantum quench
• Universality in Non-Equilibrium Quantum Systems
• Non-equilibrium critical scaling and universality in a quantum simulator
• Exact solutions and Dynamical phase transitions in the Lipkin-Meshkov-Glick model with Dual nonlinear interactions
• Zeros of partition function for Continuous Phase Transitions using cumulants
• Nonequilibrium Critical Scaling of a Squeezing Phase Transition
• $\mathcal{P}\mathcal{T}$-symmetric two-photon quantum Rabi models
• A Universal Quantum Computing Virtual Machine
• Enhanced quantum metrology by criticality-assisted noncommutative preparation
• Nutation dynamics and multifrequency resonance in a many-body seesaw
• Ladder of Loschmidt anomalies in the deep strong-coupling regime of a qubit-oscillator system
• Rate Function Modelling of Quantum Many-Body Adiabaticity
• Time evolution of effective central charge and signatures of RG irreversibility after a quantum quench
• Detecting the purely imaginary Fisher zeros of an Ising spin system on a quantum computer
• A Dynamical Bulk-Boundary Correspondence in Two Dimensional Topological Matter
• Asymmetry and dynamical criticality
• Dynamical Quantum Phase Transitions in Interacting Atomic Interferometers
• Padé Approximation and Partition Function Zeros
• Dynamical quantum phase transitions in strongly correlated two-dimensional spin lattices following a quench
• Quantum Supercritical Crossover with Dynamical Singularity
• Anatomy of Non-Hermitian Dynamical Quantum Phase Transitions
• Dynamical Phase Transitions in Periodically Driving 1D Ising Model
• Observing Algebraic Variety of Lee-Yang Zeros in Asymmetrical Systems via a Quantum Probe
• Floquet Recurrences in the Double Kicked Top
• Characterizing dynamical phase transitions in a spinor Bose-Einstein condensate via quantum and semiclassical analyses
• Out-of-time-order correlation and detection of phase structure in Floquet transverse Ising spin system
• Designing non-equilibrium states of quantum matter through stochastic resetting
• Anomalous parametric resonance in a spin-1/2 chain: dynamical effects of nontrivial topology
• Dynamical quantum phase transitions on random networks
• Controlling Symmetries and Quantum Criticality in the Anisotropic Coupled-Top Model
• Effective metal-insulator non-equilibrium quantum phase transition
• Krylov Complexity Under Hamiltonian Deformations and Toda Flows
• Dynamical Quantum Phase Transitions and Many-Body Backflow in Open Quantum Systems
• Nonlocal pseudospin dynamics in a quantum Ising chain
• Interaction quenches in Bose gases studied with a time-dependent hypernetted-chain Euler-Lagrange method
• From orthogonal link to phase vortex in generalized dynamical Hopf insulators
• Stabilizing confined quasiparticle dynamics in one-dimensional polar lattice gases
• Nonequilibrium Dynamics in a Quantum Spin Chain with Pump-Probe Resonant Inelastic X-ray Scattering
• Universal features of non-analytical energy storage in quantum critical quantum batteries
• Quantum Chaos and Universal Trotterisation Behaviours in Digital Quantum Simulations
• Floquet dynamical quantum phase transitions in periodically flux-quenched systems
• Numerically efficient unitary evolution for Hamiltonians beyond nearest-neighbors