Dynamics of a quantum phase transition and relaxation to a steady state

2009/12/31 by Jacek Dziarmaga · 35 citations
Physics and Astronomy · #Adiabatic process #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Excitation #Excited state #Gapless playback #Hamiltonian (control theory) #Open quantum system #Physics #Quantum #Quantum dissipation #Quantum dynamics #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Quantum phases #Quantum simulator #Quantum system #Relaxation (psychology) #Statistical physics #Strong Light-Matter Interactions #cond-mat.mes-hall #cond-mat.quant-gas #cond-mat.stat-mech #cond-mat.str-el #cond-mat.supr-con #quant-ph

paper · pdf · doi:10.1080/00018732.2010.514702

published as Advances in Physics, vol. 59, issue 6, pp. 1063-1189 (2010) · 117 pages; review accepted in Advances in Physics

arxiv created 2010/08/09 · openalex publication_date 2010/09/22 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We review recent theoretical work on two closely related issues: excitation of an isolated quantum condensed matter system driven adiabatically across a continuous quantum phase transition or a gapless phase, and apparent relaxation of an excited system after a sudden quench of a parameter in its Hamiltonian. Accordingly, the review is divided into two parts. The first part revolves around a quantum version of the Kibble–Zurek mechanism including also phenomena that go beyond this simple paradigm. What they have in common is that excitation of a gapless many-body system scales with a power of the driving rate. The second part attempts a systematic presentation of recent results and conjectures on apparent relaxation of a pure state of an isolated quantum many-body system after its excitation by a sudden quench. This research is motivated in part by recent experimental developments in the physics of ultracold atoms with potential applications in the adiabatic quantum state preparation and quantum computation.

Citations

• Validity of many-body approximation methods for a solvable model
• Simulating the Quantum Magnet
• Scaling of Entanglement Entropy in the Random Singlet Phase
• Nonequilibrium Gross-Pitaevskii dynamics of boson lattice models
• Oscillating Superfluidity of Bosons in Optical Lattices
• Quench dynamics near a quantum critical point
• Effect of Suddenly Turning on Interactions in the Luttinger Model
• Exact Coherent States of a Harmonically Confined Tonks-Girardeau Gas
• Experimental demonstration of painting arbitrary and dynamic potentials for Bose–Einstein condensates
• Exact Results for Quench Dynamics and Defect Production in a Two-Dimensional Model
• Classification of topological insulators and superconductors in three spatial dimensions
• Spreading of correlations and entanglement after a quench in the one-dimensional Bose–Hubbard model
• Quantum mechanical computers
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons
• Entanglement in theXYspin chain
• Time-dependent tunneling of Bose-Einstein condensates
• Adiabatic-impulse approximation for avoided level crossings: From phase-transition dynamics to Landau-Zener evolutions and back again
• Sweeping from the Superfluid to the Mott Phase in the Bose-Hubbard Model
• Is domain formation decided before or after the transition?
• Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
• Entropy of entanglement and correlations induced by a quench: Dynamics of a quantum phase transition in the quantum Ising model
• Quantum Many Particle Systems in Ring-Shaped Optical Lattices
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Relaxation of a one-dimensional Mott insulator after an interaction quench
• Vortex Quantum Creation and Winding Number Scaling in a Quenched Spinor Bose Gas
• Decoherence in a dynamical quantum phase transition of the transverse Ising chain
• An Exactly Soluble Model of a Many-Fermion System
• Nonappearance of Vortices in Fast Mechanical Expansions of Liquid4Hethrough the Lambda Transition
• Defect Production in Nonlinear Quench across a Quantum Critical Point
• Optimal Nonlinear Passage Through a Quantum Critical Point
• Spontaneous vortices in the formation of Bose–Einstein condensates
• Quantum Critical Scaling of the Geometric Tensors
• Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Quantum statistical mechanics in a closed system
• Entropy and correlation functions of a driven quantum spin chain
• Quench dynamics across quantum critical points
• Statistical properties of many particle eigenfunctions
• Fault-tolerant quantum computation by anyons
• Two soluble models of an antiferromagnetic chain
• Anyons in an exactly solved model and beyond
• Topology of cosmic domains and strings
• Bosonizing one-dimensional cold atomic gases
• Unpaired Majorana fermions in quantum wires
• Quantum Decay of Dark Solitons

Cited by

• Kibble-Zurek mechanism in a topological phase transition
• Quench dynamics of edge states in 2-D topological insulator ribbons
• Transverse Ising chain under periodic instantaneous quenches: Dynamical many-body freezing and emergence of slow solitary oscillations
• Difference in Bose-Einstein condensation of conserved and unconserved particles
• Optimal suppression of defect generation during a passage across a quantum critical point
• Shortcuts to Adiabaticity in the Infinite-Range Ising Model by Mean-Field Counter-Diabatic Driving
• Bose-Hubbard ladder subject to effective magnetic field: Quench dynamics in a harmonic trap
• Quantum quenches and many-body localization in the thermodynamic limit
• Universal finite-time thermodynamics of many-body quantum machines from Kibble-Zurek scaling
• Exploring Symmetry Breaking at the Dicke Quantum Phase Transition
• Quantum adiabatic cycles and their breakdown
• Interaction quenches in the one-dimensional Bose gas
• On quantum mean-field models and their quantum annealing
• Engineering non-equilibrium quantum phase transitions via causally gapped Hamiltonians
• Asymptotic work statistics of periodically driven Ising chains
• Experimental Trapped-ion Quantum Simulation of the Kibble-Zurek dynamics in momentum space
• Kilohertz-Driven Bose–Einstein Condensates in Optical Lattices
• Quenches and dynamical phase transitions in a nonintegrable quantum Ising model
• Bosonic quantum dynamics following a linear interaction quench in finite optical lattices of unit filling
• Dual dynamic scaling in deconfined quantum criticality
• Entanglement entropy of theQ<mml:mspace width="0.16em"/>≥<mml:mspace width="0.16em"/>4quantum Potts chain
• Causality and non-equilibrium second-order phase transitions in inhomogeneous systems
• Exact entanglement growth of a one-dimensional hard-core quantum gas during a free expansion
• Matter-wave propagation in optical lattices: geometrical and flat-band effects
• Scaling of ground-state fidelity in the thermodynamic limit:XYmodel and beyond
• Expansion of Bose-Hubbard Mott insulators in optical lattices
• Order parameter dynamics of the non-linear sigma model in the large N limit
• Dynamical quantum phase transitions in systems with broken continuous time and space translation symmetries
• Quantum quench and scaling of entanglement entropy
• Universality of miscible–immiscible phase separation dynamics in two-component Bose–Einstein condensates
• Slow quench dynamics of Mott-insulating regions in a trapped Bose gas
• Finite-time interaction quench in a Luttinger liquid
• Scaling properties of the dynamics at first-order quantum transitions when boundary conditions favor one of the two phases
• Exact one- and two-site reduced dynamics in a finite-size quantum Ising ring after a quench: A semianalytical approach
• Quench-induced entanglement and relaxation dynamics in Luttinger liquids

Related

• Dynamics of non-equilibrium steady state quantum phase transitions
• Nonequilibrium dynamics of closed interacting quantum systems
• Coherent and dissipative dynamics at quantum phase transitions
• Universal Quench Dynamics of an Open Quantum System
• Dynamical quantum phase transitions: a review