Dynamics of quantum phase transition: exact solution in quantum Ising model

Abstract

Quantum Ising model is an exactly solvable model of quantum phase transition. This paper gives an exact solution when the system is driven through the critical point at finite rate. The evolution goes through a series of Landau-Zener level anticrossings when pairs of quasiparticles with opposite pseudomomenta get excited with probability depending on the transition rate. Average density of defects excited in this way scales like a square root of the transition rate. This scaling is the same as the scaling obtained when the standard Kibble-Zurek mechanism of thermodynamic second order phase transitions is applied to the quantum phase transition in the Ising model.

arXiv commentmisprints corrected; version to appear in Phys.Rev.Lett

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• Quantum critical engine at finite temperatures
• Quantum response to time-dependent external fields
• The Kibble Zurek Mechanism of Topological Defect Formation in Quantum Field Theory with Matrix Product States
• Nonadiabatic stationary behaviour in a driven low-dimensional gapped system
• Exact transition probabilities in the three-state Landau-Zener-Coulomb model
• The model of a level crossing with a Coulomb band: exact probabilities of nonadiabatic transitions
• Kibble-Zurek mechanism in quantum link model
• Protection of quantum information in a chain of Josephson junctions
• Propagation of quantum fluctuations in quantum Ising model
• Adiabatic transition from a BCS superconductor to a Fermi liquid and phase dynamics
• Loschmidt echo zeros in finite-size quantum systems with linear quench
• Reducing defect production in random transverse-field Ising chains by inhomogeneous driving fields
• Inhomogeneous adiabatic preparation of a quantum critical ground state in two dimensions
• Critical properties of Sudden Quench Dynamics in the anisotropic XY Model
• Exact bounds on the energy gap of transverse-field Ising chains by mapping to random walks
• Dynamical quantum phase transition of a two-component Bose-Einstein condensate in an optical lattice
• Unification of Finite Symmetries in Simulation of Many-body Systems on Quantum Computers
• Separation of the Kibble-Zurek Mechanism from Quantum Criticality
• Driven Critical Dynamics in Tricitical Point
• Defect production in quench from current-carrying non-equilibrium state
• Kibble-Zurek mechanism and errors of gapped quantum phases
• The geometric phase and the dynamics of quantum phase transition induced by a linear quench
• Universal Quench Dynamics of an Open Quantum System
• Kibble-Zurek scaling in the quantum Ising chain with a time-periodic perturbation
• Bang-bang preparation of quantum many-body ground states in two dimensions: optimization of the algorithm with a two-dimensional tensor network
• Exotic domain walls in Bose-Einstein condensates with double-well dispersion
• Quasiadiabatic dynamics of ultracold bosonic atoms in a one-dimensional optical superlattice
• Quantum annealing in the NISQ era: railway conflict management
• Microscopic dynamics and an effective Landau-Zener transition in the quasi-adiabatic preparation of spatially ordered states of Rydberg excitations
• Momentum space magic for the transverse field quantum Ising model
• Pattern formation in individual-based systems with time-varying parameters
• General theory for discrete symmetry-breaking equilibrium states
• Entanglement generation and scaling from noisy quenches across a quantum critical point
• Defect production due to quenching through a multicritical point and along a gapless line
• Kicked-Ising Quantum Battery
• Quantum criticality of geometric phase in coupled optical cavity arrays under linear quench
• Seeing spin dynamics in atomic gases
• Topological Defects from Quantum Reset Dynamics
• Probing universal critical scaling with scan-DMRG
• Nonequilibrium Dynamics of Ultracold Fermi Superfluids
• Half Landau-Zener ramp to a quantum phase transition in a dissipative single spin sodel
• Machine-learning-inspired quantum control in many-body dynamics
• Analytic approach to the Landau-Zener problem in bounded parameter space
• Is there Kibble-Zurek scaling of topological defects in first-order phase transitions?
• Dynamics of Topological Defects in a Rashba Spin-Orbit Coupled Bose-Einstein Condensate
• Interaction of a single mode field cavity with the 1D XY model: Energy spectrum
• Phase diagram of Rydberg atoms in a two-leg rectangular ladder
• Input-Output Optics as a Causal Time Series Mapping: A Generative Machine Learning Solution
• Fighting Exponentially Small Gaps by Counterdiabatic Driving
• Asymmetry Amplification by a Nonadiabatic Passage through a Critical Point
• Kibble-Zurek Mechanism and Beyond: Lessons from a Holographic Superfluid Disk
• Exploring the Nexus between Thermodynamic Phase Transitions and Geometric Fractals through Systematic Lattice Point Classification
• A scalable 2-local architecture for quantum annealing of Ising models with arbitrary dimensions
• The singularities of the rate function of quantum coherent work in one-dimensional transverse field Ising model
• Squeezing generation crossing a mean-field critical point: Work statistics, irreversibility and critical fingerprints
• Deconstructing symmetry breaking dynamics
• Assessing the performance of quantum annealing with nonlinear driving
• Digitized counterdiabatic quantum critical dynamics
• Finite-time scaling with two characteristic time scales: Driven critical dynamics with emergent symmetry
• Dynamics of the Mott Insulator to Superfluid quantum phase transition in the truncated Wigner approximation
• A map between time-dependent and time-independent quantum many-body Hamiltonians
• Analytical shortcuts to adiabaticity of weakly driven processes
• 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
• Scaling corrections in driven critical dynamics: Application to a two-dimensional dimerized quantum Heisenberg model
• Learning topological defects formation with neural networks in a quantum phase transition
• Optimized adiabatic-impulse protocol preserving Kibble-Zurek scaling with attenuated anti-Kibble-Zurek behavior
• Persistent oscillation of a Cooper-pair condensate of topological defects in a nonintegrable quantum Ising chain
• Dynamics of the order parameter in symmetry breaking phase transitions
• Simulating the Kibble-Zurek mechanism of the Ising model with a superconducting qubit system
• Universality in Non-Equilibrium Quantum Systems
• Structure and scaling of Kitaev chain across a quantum critical point in real space
• Multiple-time-scale Landau-Zener transitions in many-body systems
• Defects in Quantum Computers
• Benchmarking Embedded Chain Breaking in Quantum Annealing
• Echoes and defects in the Calogero model
• Time-dependent Real-space Renormalization-Group Approach: application to an adiabatic random quantum Ising model
• Excitation and Entanglement Transfer Near Quantum Critical Points
• Quantum cluster kink and ring frustration
• Multipartite Entanglement in Crossing the Quantum Critical Point
• Algebraic law of local correlations in a driven Rydberg atomic system
• Anomalous universal adiabatic dynamics: The case of the Fredkin model
• Kibble-Zurek scaling from linear response theory
• Probing universal imaginary-time relaxation critical dynamics with infinite projected entangled pair states
• Quantum fingerprints of self-organization in spin chains coupled to a Kuramoto model
• A quantum phase transition in a quantum external field: Superposing two magnetic phases
• Anomalous parametric resonance in a spin-1/2 chain: dynamical effects of nontrivial topology
• Momentum space topology and quantum phase transitions
• Quantum Transition Rates in Arbitrary Physical Processes
• Finite-rate quench in disordered Chern and $Z_2$ topological insulators
• Rate Function Modelling of Quantum Many-Body Adiabaticity
• Shortcuts to Analog Preparation of Non-Equilibrium Quantum Lakes
• Quasi-adiabatic thermal ensemble preparation in the thermodynamic limit
• Controlling Symmetries and Quantum Criticality in the Anisotropic Coupled-Top Model
• Nonequilibrium Dynamics in a Quantum Spin Chain with Pump-Probe Resonant Inelastic X-ray Scattering
• Elementary asymptotic approach to the Landau-Zener problem
• Integrability in the multistate Landau-Zener model with time-quadratic commuting operators
• Detecting quantumness with generalized Loschmidt echoes
• Adiabaticity enhancement in the classical transverse field Ising chain, and its effective non-Hermitian description
• Dissipation-Induced Deviations from Kibble-Zurek Scaling in Non-Hermitian Quantum Annealing
• Mechanism of defect formation in the quantum annealing of the random transverse-field Ising chain
• Anomalous Dynamical Scaling at Topological Quantum Criticality