Return amplitude after a quantum quench in the XY chain

被引:12
作者
Najafi, Khadijeh [1 ]
Rajabpour, M. A. [2 ]
Viti, Jacopo [3 ,4 ]
机构
[1] Virginia Tech, Dept Phys, Blacksburg, VA 24061 USA
[2] Univ Fed Fluminense, Inst Fis, Av Gal Milton Tavares de Souza S-N, BR-24210346 Niteroi, RJ, Brazil
[3] Univ Fed Rio Grande do Norte, Int Inst Phys, Campos Univ, BR-59078970 Natal, RN, Brazil
[4] Univ Fed Rio Grande do Norte, ECT, Campos Univ, BR-59078970 Natal, RN, Brazil
来源
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT | 2019年
基金
美国国家科学基金会;
关键词
quantum quenches; SPIN CHAINS; THERMALIZATION;
D O I
10.1088/1742-5468/ab3413
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
We determine an exact formula for the transition amplitude between any two arbitrary eigenstates of the local z-magnetization operators in the quantum XY chain. We further use this formula to obtain an analytical expression for the return amplitude of fully polarized states and the Neel state on a ring of length L. Then, we investigate finite-size effects in the return amplitude: in particular quasi-particle interference halfway along the ring, a phenomenon that has been dubbed traversal (Essler and Fagotti 2016 J. Stat. Mech. 064002). We show that the traversal time and the features of the return amplitude at the traversal time depend on the initial state and on the parity of L. Finally, we briefly discuss non-analyticities in time of the decay rates in the thermodynamic limit L -> infinity, which are known as dynamical phase transitions.
引用
收藏
页数:23
相关论文
共 103 条
[11]   Time dependence of correlation functions following a quantum quench [J].
Calabrese, P ;
Cardy, J .
PHYSICAL REVIEW LETTERS, 2006, 96 (13)
[12]   Quantum quenches in extended systems [J].
Calabrese, Pasquale ;
Cardy, John .
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2007,
[13]   Introduction to 'Quantum Integrability in Out of Equilibrium Systems' [J].
Calabrese, Pasquale ;
Essler, Fabian H. L. ;
Mussardo, Giuseppe .
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2016,
[14]   Quantum quench in the transverse field Ising chain: I. Time evolution of order parameter correlators [J].
Calabrese, Pasquale ;
Essler, Fabian H. L. ;
Fagotti, Maurizio .
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2012,
[15]   Quantum quenches in the transverse field Ising chain: II. Stationary state properties [J].
Calabrese, Pasquale ;
Essler, Fabian H. L. ;
Fagotti, Maurizio .
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2012,
[16]   Quantum Quench in the Transverse-Field Ising Chain [J].
Calabrese, Pasquale ;
Essler, Fabian H. L. ;
Fagotti, Maurizio .
PHYSICAL REVIEW LETTERS, 2011, 106 (22)
[17]   Thermalization and Revivals after a Quantum Quench in Conformal Field Theory [J].
Cardy, John .
PHYSICAL REVIEW LETTERS, 2014, 112 (22)
[18]   Time Evolution of Local Observables After Quenching to an Integrable Model [J].
Caux, Jean-Sebastien ;
Essler, Fabian H. L. .
PHYSICAL REVIEW LETTERS, 2013, 110 (25)
[19]   From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics [J].
D'Alessio, Luca ;
Kafri, Yariv ;
Polkovnikov, Anatoli ;
Rigol, Marcos .
ADVANCES IN PHYSICS, 2016, 65 (03) :239-362
[20]   Exact results for fidelity susceptibility of the quantum Ising model: the interplay between parity, system size, and magnetic field [J].
Damski, Bogdan ;
Rams, Marek M. .
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2014, 47 (02)