| Issue |
EPL
Volume 106, Number 6, June 2014
|
|
|---|---|---|
| Article Number | 67003 | |
| Number of page(s) | 6 | |
| Section | Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties | |
| DOI | https://doi.org/10.1209/0295-5075/106/67003 | |
| Published online | 18 June 2014 | |
Loschmidt echo and dynamical fidelity in periodically driven quantum systems
1 Department of Physics, Indian Institute of Technology Kanpur - Kanpur 208016, India
2 SISSA - Via Bonomea 265, I-34136 Trieste, Italy
3 CNR-IOM Democritos National Simulation Center - Via Bonomea 265, I-34136 Trieste, Italy
4 International Centre for Theoretical Physics (ICTP) - P.O. Box 586, I-34014 Trieste, Italy
Received: 27 February 2014
Accepted: 26 May 2014
We study the dynamical fidelity 
and the Loschmidt echo 
, following a periodic driving of the transverse magnetic field of a quantum Ising chain (back and forth across the quantum critical point) by calculating the overlap between the initial ground state and the state reached after n periods τ. We show that ![$[\log{\mathcal F}(n\tau)]/L$](/articles/epl/abs/2014/12/epl16328/epl16328_tex_eq3.png)
(the logarithm of the fidelity per site) reaches a steady value in the asymptotic limit 
, and we derive an exact analytical expression for this quantity. Remarkably, the steady-state value of ![$[\log{\mathcal F}(n\tau\to \infty)]/L$](/articles/epl/abs/2014/12/epl16328/epl16328_tex_eq5.png)
shows memory of non-trivial phase information which is instead hidden in the case of thermodynamic quantities; this conclusion, moreover, is not restricted to 1-dimensional models.
PACS: 75.10.Pq – Spin chain models / 05.30.Rt – Quantum phase transitions / 03.65.-w – Quantum mechanics
© EPLA, 2014
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