Quantum quench in the transverse-field Ising chain.

We consider the time evolution of observables in the transverse-field Ising chain after a sudden quench of the magnetic field. We provide exact analytical results for the asymptotic time and distance dependence of one- and two-point correlation functions of the order parameter. We employ two complementary approaches based on asymptotic evaluations of determinants and form-factor sums. We prove that the stationary value of the two-point correlation function is not thermal, but can be described by a generalized Gibbs ensemble (GGE). The approach to the stationary state can also be understood in terms of a GGE. We present a conjecture on how these results generalize to particular quenches in other integrable models.

[1]  G. Roux.  Finite size effects in global quantum quenches: examples from free bosons in an harmonic trap and the one-dimensional Bose-Hubbard model , 2009, 0909.4620.

[2]  R. Konik,et al.  Finite-temperature lineshapes in gapped quantum spin chains , 2007, 0711.2524.

[3]  E. Demler,et al.  Exact methods in the analysis of the non-equilibrium dynamics of integrable models: application to the study of correlation functions for non-equilibrium 1D Bose gas , 2009, 0904.3221.

[4]  Eytan Barouch,et al.  Statistical Mechanics of the XY Model. III , 1970 .

[5]  Bruno Sciolla,et al.  Quantum quenches and off-equilibrium dynamical transition in the infinite-dimensional Bose-Hubbard model. , 2010, Physical review letters.

[6]  E. Demler,et al.  Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench. , 2008, Physical review letters.

[7]  G. Santoro,et al.  Effective thermal dynamics following a quantum quench in a spin chain. , 2008, Physical review letters.

[8]  Marcos Rigol,et al.  Relaxation in a completely integrable many-body quantum system: an ab initio study of the dynamics of the highly excited states of 1D lattice hard-core bosons. , 2007, Physical review letters.

[9]  Guillaume Roux,et al.  Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined , 2008, 0810.3720.

[10]  J. Cardy,et al.  Quantum quenches in extended systems , 2007, 0704.1880.

[11]  Oscillating superfluidity of bosons in optical lattices. , 2002, Physical review letters.

[12]  F. Smirnov.  Form Factors in Completely Integrable Models of Quantum Field Theory , 1992 .

[13]  Quench dynamics across quantum critical points , 2003, cond-mat/0311355.

[14]  J. Cardy,et al.  Evolution of entanglement entropy in one-dimensional systems , 2005, cond-mat/0503393.

[15]  Immanuel Bloch,et al.  Collapse and revival of the matter wave field of a Bose–Einstein condensate , 2002, Nature.

[16]  M. Rigol,et al.  Thermalization and its mechanism for generic isolated quantum systems , 2007, Nature.

[17]  J. Cirac,et al.  Strong and weak thermalization of infinite nonintegrable quantum systems. , 2010, Physical review letters.

[18]  E. Demler,et al.  Quantum quenches in the anisotropic spin- Heisenberg chain: different approaches to many-body dynamics far from equilibrium , 2009, 0911.1927.

[19]  H. Rieger,et al.  Quantum relaxation after a quench in systems with boundaries. , 2010, Physical review letters.

[20]  J Eisert,et al.  Exact relaxation in a class of nonequilibrium quantum lattice systems. , 2008, Physical review letters.

[21]  R. Konik,et al.  Finite-temperature dynamical correlations in massive integrable quantum field theories , 2009, 0907.0779.

[22]  Jens Eisert,et al.  Absence of thermalization in nonintegrable systems. , 2010, Physical review letters.

[23]  U. Schollwock,et al.  Dephasing and the steady state in quantum many-particle systems. , 2007, Physical review letters.

[24]  Giuseppe Mussardo,et al.  Quantum quenches in integrable field theories , 2009, 0911.3345.

[25]  G. Santoro,et al.  Long time dynamics following a quench in an integrable quantum spin chain: local versus non-local operators and effective thermal behavior , 2010, 1002.2842.

[26]  J. Cardy,et al.  Quantum quench from a thermal initial state , 2009, 0903.0895.

[27]  Martin Eckstein,et al.  Thermalization after an interaction quench in the Hubbard model. , 2009, Physical review letters.

[28]  P. Calabrese,et al.  Quantum quenches from integrability: the fermionic pairing model , 2008, 0812.1928.

[29]  J. Schmiedmayer,et al.  Non-equilibrium coherence dynamics in one-dimensional Bose gases. , 2007, Nature.

[30]  Eytan Barouch,et al.  Statistical Mechanics of the X Y Model. II. Spin-Correlation Functions , 1971 .

[31]  G. Takács,et al.  Form factor expansion for thermal correlators , 2010, 1008.3810.

[32]  E. Yuzbashyan,et al.  Dynamical vanishing of the order parameter in a fermionic condensate. , 2006, Physical review letters.

[33]  Michele Fabrizio,et al.  Time-dependent mean field theory for quench dynamics in correlated electron systems. , 2010, Physical review letters.

[34]  Ehud Altman,et al.  Quench dynamics and nonequilibrium phase diagram of the bose-hubbard model. , 2007, Physical review letters.

[35]  Rosario Fazio,et al.  Quantum quenches, thermalization, and many-body localization , 2010, 1006.1634.

[36]  P. Calabrese,et al.  Evolution of entanglement entropy following a quantum quench : Analytic results for the XY chain in a transverse magnetic field , 2008, 0804.3559.

[37]  S. Pakuliak,et al.  Form-factors in the Baxter–Bazhanov–Stroganov model II: Ising model on the finite lattice , 2007, 0711.0457.

[38]  D. Weiss,et al.  A quantum Newton's cradle , 2006, Nature.

[39]  J. Cardy,et al.  Time dependence of correlation functions following a quantum quench. , 2006, Physical review letters.

[40]  M. Cazalilla.  Effect of suddenly turning on interactions in the Luttinger model. , 2006, Physical review letters.

[41]  Strongly correlated fermions after a quantum quench. , 2006, Physical review letters.