Semi-classical theory for quantum quenches in the O(3) non-linear sigma model

Abstract

We use the semi-classical approach to study the non-equilibrium dynamics of the O(3) non-linear sigma model. For a class of quenches defined in the text, we obtain the order parameter dynamical correlator in the thermodynamic limit. In particular we predict quench-dependent relaxation times and correlation lengths. The approach developed for the O(3) non-linear sigma model can also be applied to the transverse field Ising chain, where the semi-classical results can be directly compared to both the exact and the numerical ones, revealing the limits of the method.

v1: 26 pages, 10 figures; v2: References added; v3: Comments added, notation clarified

References in corpus (24)

• Thermalization and its mechanism for generic isolated quantum systems
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Quantum Quench in the Transverse Field Ising Chain
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• The Luttinger model following a sudden interaction switch-on
• Dephasing and the steady state in quantum many-particle systems
• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• Strong and weak thermalization of infinite non-integrable quantum systems
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Quench dynamics across quantum critical points
• Quantum quench dynamics of the Luttinger model
• Absence of Thermalization in Nonintegrable Systems
• Effective thermal dynamics following a quantum quench in a spin chain
• Dynamical Correlations after a Quantum Quench
• Long time dynamics following a quench in an integrable quantum spin chain: local versus non-local operators and effective thermal behavior
• Form factors in finite volume II:disconnected terms and finite temperature correlators
• Form factors in finite volume I: form factor bootstrap and truncated conformal space
• Time evolution of correlations in strongly interacting fermions after a quantum quench
• Generalized TBA and generalized Gibbs
• Dynamics in the Ising field theory after a quantum quench
• Quantum relaxation after a quench in systems with boundaries
• Exact infinite-time statistics of the Loschmidt echo for a quantum quench
• Entanglement in spin chains with gradients
• Universal diffusive decay of correlations in gapped one-dimensional systems

Cited by in corpus (26)

• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Quantum quenches in 1+1 dimensional conformal field theories
• Quench dynamics of a Tonks-Girardeau gas released from a harmonic trap
• Hamiltonian truncation approach to quenches in the Ising field theory
• Hybrid semiclassical theory of quantum quenches in one dimensional systems
• Transport in the sine-Gordon field theory: from generalized hydrodynamics to semiclassics
• Quantum quenches in the sine--Gordon model: a semiclassical approach
• Finite-size corrections vs. relaxation after a sudden quench
• Quench dynamics of the Ising field theory in a magnetic field
• Quantum quench in long-range field theories
• Exactly solvable deterministic lattice model of crossover between ballistic and diffusive transport
• Non-equilibrium quantum relaxation across a localization-delocalization transition
• Overlap singularity and time evolution in integrable quantum field theory
• Non-equilibrium quantum transport in presence of a defect: the non-interacting case
• Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions
• Quantum quench in the attractive regime of the sine-Gordon model
• Semiclassical theory of front propagation and front equilibration following an inhomogeneous quantum quench
• Finite temperature dynamics in gapped 1D models in the sine-Gordon family
• Systematic strong coupling expansion for out-of-equilibrium dynamics in the Lieb-Liniger model
• Quantum quenches in integrable systems: Constraints from factorisation
• Nonequilibrium dynamics of the Ising chain in a fluctuating transverse field
• Divergent nonlinear response from quasiparticle interactions
• Evolution of the magnetization after a local quench in the critical transverse-field Ising chain
• Spin fluctuations after quantum quenches in the S=1 Haldane chain: numerical validation of the semi-semiclassical theory
• Critical quench dynamics of random quantum spin chains: Ultra-slow relaxation from initial order and delayed ordering from initial disorder
• Probing Klein tunneling through quantum quenches