scholarly journals Dynamical Quantum Phase Transitions in the Transverse-Field Ising Model

2013 ◽  
Vol 110 (13) ◽  
Author(s):  
M. Heyl ◽  
A. Polkovnikov ◽  
S. Kehrein
Keyword(s):  
Phase Transitions ◽  
Ising Model ◽  
Quantum Phase Transitions ◽  
Transverse Field ◽  
Quantum Phase ◽  
Transverse Field Ising Model

scholarly journals FIDELITY APPROACH TO QUANTUM PHASE TRANSITIONS

2010 ◽  
Vol 24 (23) ◽  
pp. 4371-4458 ◽  
Author(s):  
SHI-JIAN GU
Keyword(s):  
Phase Transitions ◽  
Thermal State ◽  
Quantum Phase Transitions ◽  
Transverse Field ◽  
Quantum Phase ◽  
Leading Term ◽  
Many Body Systems ◽  
The One ◽  
Definition Of ◽  
Transverse Field Ising Model

We review the quantum fidelity approach to quantum phase transitions in a pedagogical manner. We try to relate all established but scattered results on the leading term of the fidelity into a systematic theoretical framework, which might provide an alternative paradigm for understanding quantum critical phenomena. The definition of the fidelity and the scaling behavior of its leading term, as well as their explicit applications to the one-dimensional transverse-field Ising model and the Lipkin–Meshkov–Glick model, are introduced at the graduate-student level. Besides, we survey also other types of fidelity approach, such as the fidelity per site, reduced fidelity, thermal-state fidelity, operator fidelity, etc; as well as relevant works on the fidelity approach to quantum phase transitions occurring in various many-body systems.

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