Dynamics of a Quantum Phase Transition

Abstract

We present two approaches to the dynamics of a quench-induced phase transition in quantum Ising model. The first one retraces steps of the standard approach to thermodynamic second order phase transitions in the quantum setting. The second one is purely quantum, based on the Landau-Zener formula for transition probabilities in avoided level crossings. We show that the two approaches yield compatible results for the scaling of the defect density with the quench rate. We exhibit similarities between them, and comment on the insights they give into dynamics of quantum phase transitions.

4 pages, 3 figures. Replaced by revised version

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• Dynamical Ginzburg criterion for the quantum-classical crossover of the Kibble-Zurek mechanism
• Bath engineering enhanced quantum critical engines
• Resolving chiral transitions in Rydberg arrays with quantum Kibble-Zurek mechanism and finite-time scaling
• Defect production in nonequilibrium phase transitions: Experimental investigation of the Kibble-Zurek mechanism in a two-qubit quantum simulator
• Exact results for the criticality of quench dynamics in quantum Ising models
• Mutual friction and diffusion of two-dimensional quantum vortices
• Exact one- and two-site reduced dynamics in a finite-size quantum Ising ring after a quench: A semi-analytical approach
• Dynamic scaling in the 2D Ising spin glass with Gaussian couplings
• Numerical investigation of quantum phases and phase transitions in a two-leg ladder of Rydberg atoms
• Observation of Near-Critical Kibble-Zurek Scaling in Rydberg Atom Arrays
• Semiclassical Approach to Survival Probability at Quantum Phase Transitions
• Equilibration of Topological Defects Near the Deconfined Quantum Multicritical Point
• Density of defects and the scaling law of the entanglement entropy in quantum phase transition of one dimensional spin systems induced by a quench
• Quantum Transport of Energy in Controlled Synthetic Quantum Magnets
• Out-of-equilibrium finite-size scaling in generalized Kibble-Zurek protocols crossing quantum phase transitions in the presence of symmetry-breaking perturbations
• Universal scaling in quenches across a discontinuity critical point
• Contour-time approach to the Bose-Hubbard model in the strong coupling regime: Studying two-point spatio-temporal correlations at the Hartree-Fock-Bogoliubov level
• Inhomogeneity induced shortcut to adiabaticity in Ising chains with long-range interactions
• Probing the Possibilities of Ergodicity in the 1D Spin-1/2 XY Chain with Quench Dynamics
• Non-Hermitian Quantum Annealing in the Ferromagnetic Ising Model
• Adiabatic dynamics in a spin-1 chain with uniaxial single-spin anisotropy
• Programmable adiabatic demagnetization for systems with trivial and topological excitations
• Dynamics of decoherence of an entangled pair of qubits locally connected to a one-dimensional disordered spin chain
• Quantum Formation of Topological Defects
• Numerical simulations of quantum clock for measuring tunneling times
• Achieving continuously tunable critical exponents for long-range spin systems simulated with trapped ions
• Slow quench dynamics in classical systems: kinetic Ising model and zero-range process
• Quantum adiabatic cycles and their breakdown
• Landau-Zener problem with waiting at the minimum gap and related quench dynamics of a many-body system
• Finite-time scaling beyond the Kibble-Zurek prerequisite in Dirac systems
• Cumulative quantum work-deficit versus entanglement in the dynamics of an infinite spin chain
• Cavity-assisted Dynamical Quantum Phase Transition at Bifurcation Points
• Controllable quantum spin glasses with magnetic impurities embedded in quantum solids
• Landau-Zener transition of a two-level system driven by spin chains near their critical points
• Work statistics across a quantum critical surface
• Driven one-dimensional noisy Kitaev chain
• Tricritical Kibble-Zurek scaling in Rydberg atom ladders
• Enhancement of quantum speed limit time due to cooperative effects in multilevel systems
• Non-Adiabatic Quantum Optimization for Crossing Quantum Phase Transitions
• Anti Kibble-Zurek behavior in the quantum XY spin-1/2 chain driven by correlated noisy magnetic field and anisotropy
• Experimental validation of the Kibble-Zurek Mechanism on a Digital Quantum Computer
• Quantum annealing speedup of embedded problems via suppression of Griffiths singularities
• Out-of-equilibrium scaling behavior arising during round-trip protocols across a quantum first-order transition
• Decoherence and relaxation of topological states in extended quantum Ising models
• Time-optimal control fields for quantum systems with multiple avoided crossings
• Particle-Hole Pair Coherence in Mott Insulator Quench Dynamics
• Fermionic Magic Resources of Quantum Many-Body Systems
• Non-Hermitian Quantum Annealing in the Antiferromagnetic Ising Chain
• Nonadiabatic Phase Transition with Broken Chiral Symmetry
• Unitary preparation of many body Chern insulators: Adiabatic bulk boundary correspondence
• Spatial Kibble-Zurek mechanism through susceptibilities: the inhomogeneous quantum Ising model case
• Decoherence in a dynamical quantum phase transition
• Nonadiabatic multichannel dynamics of a spin-orbit coupled condensate
• Phase diagram and sweep dynamics of a one-dimensional generalized cluster model
• Dissociation dynamics of resonantly coupled bose-fermi mixtures in an optical lattice
• Speeding up quantum adiabatic processes with dynamical quantum geometric tensor
• Universal cooling dynamics toward a quantum critical point
• Dynamics of geometric phase in the adiabatic limit of quantum phase transition
• Kibble-Zurek mechanism from different angles: The transverse XY model and subleading scalings
• Quantum quench dynamics and population inversion in bilayer graphene
• A ring of BEC pools as a trap for persistent flow
• Adiabatic processes like isothermal processes
• Critical dynamics of classical systems under slow quench
• Quenching across quantum critical points in periodic systems: dependence of scaling laws on periodicity
• Holographic systems far from equilibrium: a review
• Fast generation of time-stationary spin-1 squeezed states by non-adiabatic control
• Universal spatiotemporal dynamics of spontaneous superfluidity breakdown in the presence of synthetic gauge fields
• Super-horizon cosmic string correlations
• Biased dynamics of the miscible-immiscible quantum phase transition in a binary Bose-Einstein condensate
• Driving a Quantum Phase Transition at Arbitrary Rate: Exact solution of the Transverse-Field Ising model
• Generation of concurrence between two qubits locally coupled to a one dimensional spin chain
• Low Temperature Domain Wall Freezing and Non-Equilibrium Dynamics in the Transverse-Field Ising Model Material CoNb${}_2$O${}_6$
• Universal Counterdiabatic Driving
• Dynamic trapping near a quantum critical point
• Dynamic scaling of the restoration of rotational symmetry in Heisenberg quantum antiferromagnets
• Linear-scale simulations of quench dynamics
• Pattern formation in charge density wave states after a quantum quench
• Quadrature interferometry for nonequilibrium ultracold bosons in optical lattices
• Kibble-Zurek scaling of the superfluid-supersolid transition in an elongated dipolar gas
• Kibble-Zurek scaling immune to anti-Kibble-Zurek behavior in driven open systems at the limit of loss difference
• Navigating the noise-depth tradeoff in adiabatic quantum circuits
• Adiabatic-impulse approximation in non-Hermitian Landau-Zener Model
• Proximity effect and spatial Kibble-Zurek mechanism in atomic Fermi gases with inhomogeneous pairing interactions
• Aperiodic dynamical quantum phase transitions in multi-band Bloch Hamiltonian and its origin
• Universal defects statistics with strong long-range interactions
• Out-of-equilibrium dynamics across the first-order quantum transitions of one-dimensional quantum Ising models
• Adiabatic time evolution of highly excited states
• Hidden Sector Monopole Dark Matter with Matter Domination
• Finite temperature ferromagnetic transition in coherently coupled Bose gases
• Resonant spin-changing collisions in spinor Fermi gases
• Kibble-Zurek behavior in a topological phase transition with a quadratic band crossing
• Universal scaling of work statistics for quantum quenches
• Critical slowing down and entanglement protection
• Nonadiabatic stationary behaviour in a driven low-dimensional gapped system
• The Kibble Zurek Mechanism of Topological Defect Formation in Quantum Field Theory with Matrix Product States
• Errors in quantum optimal control and strategy for the search of easily implementable control pulses
• Dynamics of a Nonequilibrium Discontinuous Quantum Phase Transition in a Spinor Bose-Einstein Condensate
• Exploring the topological sector optimization on quantum computers
• Observation of quantum superposition of topological defects in a trapped ion quantum simulator
• Nonequilibrium Critical Dynamics with Emergent Supersymmetry
• Efficient quantum-enhanced classical simulation for patches of quantum landscapes
• Restoration of a Spontaneously Broken Symmetry in an Euclidean Quantum $\lambda {\phi }_{d+1}^4$ model with Quenched Disorder
• Critical quantum geometric tensors of parametrically-driven nonlinear resonators
• Adiabatic transition from a BCS superconductor to a Fermi liquid and phase dynamics
• Loschmidt echo zeros in finite-size quantum systems with linear quench
• Dynamics of a quantum quench in an ultra-cold atomic BCS superfluid
• Quantum Ising chain with time-averaged work in linear response theory
• Search for optimal driving in finite quantum systems with precursors of criticality
• Kibble-Zurek mechanism in quantum link model
• Reducing defect production in random transverse-field Ising chains by inhomogeneous driving fields
• Propagation of quantum fluctuations in quantum Ising model
• Critical properties of Sudden Quench Dynamics in the anisotropic XY Model
• Inhomogeneous adiabatic preparation of a quantum critical ground state in two dimensions
• Exact transition probabilities in the three-state Landau-Zener-Coulomb model
• Bang-bang preparation of quantum many-body ground states in two dimensions: optimization of the algorithm with a two-dimensional tensor network
• Defect production in quench from current-carrying non-equilibrium state
• Suppression of Quantum Correlations in a Clean-Disordered Atom-Nanophotonic Interface
• Entanglement generation and scaling from noisy quenches across a quantum critical point
• Quasiadiabatic dynamics of ultracold bosonic atoms in a one-dimensional optical superlattice
• Driven Critical Dynamics in Tricitical Point
• Universal Quench Dynamics of an Open Quantum System
• Separation of the Kibble-Zurek Mechanism from Quantum Criticality
• Fidelity, Rosen-Zener Dynamics, Entropy and Decoherence in one dimensional hard-core bosonic systems
• Periodic dynamics of fermionic superfluids in the BCS regime
• Kibble-Zurek mechanism and errors of gapped quantum phases
• Kibble-Zurek scaling in the quantum Ising chain with a time-periodic perturbation
• Microscopic dynamics and an effective Landau-Zener transition in the quasi-adiabatic preparation of spatially ordered states of Rydberg excitations
• Defect Formation Preempts Dynamical Symmetry Breaking in Closed Quantum Systems
• Observation of heat scaling across a first-order quantum phase transition in a spinor condensate
• Critical slowing down of multi-atom entanglement by Rydberg blockade
• The geometric phase and the dynamics of quantum phase transition induced by a linear quench
• Thermal-bath effects in quantum quenches within quantum critical regimes
• Decoherence-assisted quantum driving
• Exotic domain walls in Bose-Einstein condensates with double-well dispersion
• Dynamical quantum phase transition of a two-component Bose-Einstein condensate in an optical lattice
• Coarsening of Disordered Quantum Rotors under a Bias Voltage
• Probing universal critical scaling with scan-DMRG
• Seeing spin dynamics in atomic gases
• Quench dynamics in spin crossover induced by high pressure
• Generation of quantum phases of matter and finding a maximum-weight independent set of unit-disk graphs using Rydberg atoms
• Topological Defects from Quantum Reset Dynamics
• Zero Curvature Condition for Quantum Criticality
• Dynamics of Topological Defects in a Rashba Spin-Orbit Coupled Bose-Einstein Condensate
• Defect production due to quenching through a multicritical point and along a gapless line
• Shortcuts to adiabaticity in open quantum critical systems
• Fighting Exponentially Small Gaps by Counterdiabatic Driving
• Quantum criticality of geometric phase in coupled optical cavity arrays under linear quench
• Quadratic fermionic interactions yield effective Hamiltonians for adiabatic quantum computing
• Phase diagram of Rydberg atoms in a two-leg rectangular ladder
• Is there Kibble-Zurek scaling of topological defects in first-order phase transitions?
• Nonadiabatic transitions during a passage near a critical point
• Kibble-Zurek dynamics in the anisotropic Ising model of the Si(001) surface
• Half Landau-Zener ramp to a quantum phase transition in a dissipative single spin sodel
• Time-dependent Real-space Renormalization-Group Approach: application to an adiabatic random quantum Ising model
• Exact bounds for dynamical critical exponents of transverse-field Ising chains with a correlated disorder
• Multiple-time-scale Landau-Zener transitions in many-body systems
• Finite-temperature phase diagram and collective modes of coherently coupled Bose mixtures
• Dynamics for the Haldane phase in the Bilinear-Biquadratic Model
• Dynamics of the Mott Insulator to Superfluid quantum phase transition in the truncated Wigner approximation
• Entanglement in a fermionic spin chain containing a single mobile boson under decoherence
• Structure and scaling of Kitaev chain across a quantum critical point in real space
• Squeezing generation crossing a mean-field critical point: Work statistics, irreversibility and critical fingerprints
• Defects in Quantum Computers
• Scaling corrections in driven critical dynamics: Application to a two-dimensional dimerized quantum Heisenberg model
• Dynamics of the order parameter in symmetry breaking phase transitions
• Scaling of Loschmidt echo in boundary driven critical Z-3 Potts model
• Assessing the performance of quantum annealing with nonlinear driving
• Finite-time scaling with two characteristic time scales: Driven critical dynamics with emergent symmetry
• Non-equilibrium dynamics of an ultracold Bose gas under a multi-pulsed quantum quench in interaction
• Loschmidt echo and Momentum Distribution in a Kitaev Spin Chain
• Quantum quenches across continuous and first-order quantum transitions in one-dimensional quantum Ising models
• Simulating the Kibble-Zurek mechanism of the Ising model with a superconducting qubit system
• Exploring dynamical quantum phase transition from pure states to mixed states through extended Su-Schrieffer-Heeger models
• Discrete time crystals in the presence of non-Markovian dynamics
• Entanglement and Quantum Phase Transitions via Adiabatic Quantum Computation
• Universality in Non-Equilibrium Quantum Systems
• Digitized counterdiabatic quantum critical dynamics
• Deconstructing symmetry breaking dynamics
• Optimized adiabatic-impulse protocol preserving Kibble-Zurek scaling with attenuated anti-Kibble-Zurek behavior
• Quantum phases and dynamics of geometric phase in a quantum spin chain system under linear quench
• Dynamics of quantum Fisher and Wigner-Yanase skew information following a noisy quench
• Analytical shortcuts to adiabaticity of weakly driven processes
• Simulating dynamics of the two-dimensional transverse-field Ising model: a comparative study of large-scale classical numerics
• Learning topological defects formation with neural networks in a quantum phase transition
• Persistent oscillation of a Cooper-pair condensate of topological defects in a nonintegrable quantum Ising chain
• Divergence of thermalization rates driven by the competition between finite temperature and quantum coherence
• Multipartite entanglement in quantum phase transitions
• Dynamic scaling near the Kasteleyn transition in spin ice: critical relaxation of monopoles and strings following a field quench
• Adiabaticity enhancement in the classical transverse field Ising chain, and its effective non-Hermitian description
• Anomalous Dynamical Scaling at Topological Quantum Criticality
• Dynamical Phase Transitions in Periodically Driving 1D Ising Model
• Quantum phase transition in an effective three-mode model of interacting bosons
• Quantum Chaos and Universal Trotterisation Behaviours in Digital Quantum Simulations
• Quasi-adiabatic thermal ensemble preparation in the thermodynamic limit
• Shortcuts to Analog Preparation of Non-Equilibrium Quantum Lakes
• Experimental observation of multimode quantum phase transitions in a superconducting Bose-Hubbard simulator
• Kibble-Zurek scaling from linear response theory
• Multipartite Entanglement in Crossing the Quantum Critical Point
• Quantum Transition Rates in Arbitrary Physical Processes
• Anomalous universal adiabatic dynamics: The case of the Fredkin model
• Quantum collapses and revivals of a matter wave in the dynamics of symmetry breaking
• Algebraic law of local correlations in a driven Rydberg atomic system
• Quantum cluster kink and ring frustration
• Finite-rate quench in disordered Chern and $Z_2$ topological insulators
• Mechanism of defect formation in the quantum annealing of the random transverse-field Ising chain
• Excitation and Entanglement Transfer Near Quantum Critical Points
• Ultrafast light-induced long range antiferromagnetic correlations in paramagnets
• Momentum space topology and quantum phase transitions
• Critical Scaling of the Quantum Wasserstein Distance
• Anomalous isothermal compressibility in spin-orbit coupled degenerate Fermi gases