Geometric phases and quantum phase transitions in inhomogeneous XY spin-chains: Effect of the Dzyaloshinski–Moriya interaction

2010 ◽  
Vol 19 (4) ◽  
pp. 040512 ◽  
Author(s):  
Wang Lin-Cheng ◽  
Yan Jun-Yan ◽  
Yi Xue-Xi
Keyword(s):  
Phase Transitions ◽  
Quantum Phase Transitions ◽  
Spin Chains ◽  
Quantum Phase ◽  
Geometric Phases ◽  
Moriya Interaction

scholarly journals GEOMETRIC PHASES AND QUANTUM PHASE TRANSITIONS

2008 ◽  
Vol 22 (06) ◽  
pp. 561-581 ◽  
Author(s):  
SHI-LIANG ZHU
Keyword(s):  
Phase Transitions ◽  
Geometric Phase ◽  
Quantum Phase Transitions ◽  
Condensed Matter ◽  
Quantum Phase ◽  
Many Body ◽  
Scientific Communities ◽  
Geometric Phases ◽  
Many Body Systems ◽  
The Many

Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant relation was recognized before recent work. In this paper, we present a review of the connection recently established between these two interesting fields: investigations in the geometric phase of the many-body systems have revealed the so-called "criticality of geometric phase", in which the geometric phase associated with the many-body ground state exhibits universality, or scaling behavior in the vicinity of the critical point. In addition, we address the recent advances on the connection of some other geometric quantities and quantum phase transitions. The closed relation recently recognized between quantum phase transitions and some of the geometric quantities may open attractive avenues and fruitful dialogue between different scientific communities.

Dynamical quantum phase transition in XY chains with the Dzyaloshinskii-Moriya and XZY-YZX three-site interactions

2022 ◽  
Author(s):  
Kaiyuan Cao ◽  
Ming Zhong ◽  
Peiqing Tong
Keyword(s):  
Phase Transitions ◽  
Quantum Phase Transitions ◽  
Quantum Spin ◽  
Quantum Phase ◽  
Quantum Spin Chains ◽  
Excitation Spectra ◽  
Quasiparticle Excitation ◽  
Loschmidt Echo ◽  
Bogoliubov Transformations ◽  
Moriya Interaction

Abstract We study the dynamical quantum phase transitions (DQPTs) in the XY chains with the Dzyaloshinskii-Moriya interaction and the XZY-YZX type of three-site interaction after a sudden quench. Both the models can be mapped to the spinless free fermion models by the Jordan-Wigner and Bogoliubov transformations with the form $H=\sum_{k}\varepsilon_{k}(\eta^†_{k}\eta_{k}-\frac{1}{2})$, where the quasiparticle excitation spectra $\varepsilon_{k}$ may be smaller than 0 for some $k$ and are asymmetrical ($\varepsilon_{k}\neq\varepsilon_{-k}$). It's found that the factors of Loschmidt echo equal 1 for some $k$ corresponding to the quasiparticle excitation spectra of the pre-quench Hamiltonian satisfying $\varepsilon_{k}\cdot\varepsilon_{-k}<0$, when the quench is from the gapless phase. By considering the quench from different ground states, we obtain the conditions for the occurrence of DQPTs for the general XY chains with gapless phase, and find that the DQPTs may not occur in the quench across the quantum phase transitions regardless of whether the quench is from the gapless phase to gapped phase or from the gapped phase to gapless phase. This is different from the DQPTs in the case of quench from the gapped phase to gapped phase, in which the DQPTs will always appear. Besides, we also analyze the different reasons for the absence of DQPTs in the quench from the gapless phase and the gapped phase. The conclusion can also be extended to the general quantum spin chains.

Sign in / Sign up

Export Citation Format

Share Document