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Quantum quench in the transverse-field Ising chain.
Pasquale Calabrese1, Fabian H L Essler, Maurizio Fagotti
1Dipartimento di Fisica dell'Università di Pisa and INFN, Pisa, Italy.
Physical Review Letters
|June 28, 2011
Summary
We studied the transverse-field Ising chain after a magnetic field quench, finding its steady state is described by a generalized Gibbs ensemble (GGE), not a thermal state. This provides insights into quantum quenches in integrable models.
Area of Science:
- Condensed Matter Physics
- Quantum Many-Body Systems
- Statistical Mechanics
Background:
- The transverse-field Ising chain is a fundamental model in condensed matter physics.
- Understanding the dynamics after a quantum quench is crucial for non-equilibrium statistical mechanics.
Purpose of the Study:
- To investigate the time evolution of observables in the transverse-field Ising chain after a sudden magnetic field quench.
- To determine the nature of the stationary state and the approach to it.
Main Methods:
- Exact analytical calculations using asymptotic evaluations of determinants.
- Analysis of form-factor sums for correlation functions.
- Comparison with generalized Gibbs ensemble (GGE) predictions.
Main Results:
- Exact results for the asymptotic time and distance dependence of order parameter correlation functions.
- Proof that the stationary state is non-thermal and described by a GGE.
- Demonstration that the approach to the stationary state is also governed by a GGE.
Conclusions:
- The stationary state of the transverse-field Ising chain after a magnetic field quench is non-thermal and accurately described by a GGE.
- The GGE framework successfully captures the dynamics towards the stationary state.
- A conjecture is proposed for generalizing these findings to other integrable models.
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