scholarly journals Dynamical quantum phase transitions of quantum spin chains with a Loschmidt-rate critical exponent equal to 12

2020 ◽  
Vol 101 (6) ◽  
Author(s):  
Yantao Wu
Keyword(s):  
Phase Transitions ◽  
Critical Exponent ◽  
Quantum Phase Transitions ◽  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Phase ◽  
Quantum Spin Chains

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.

LEE-YANG ZEROS AND QUANTUM PHASE TRANSITIONS OF NONUNIFORM ANISOTROPIC CHAINS IN A TRANSVERSE FIELD

2007 ◽  
Vol 21 (23n24) ◽  
pp. 4225-4229
Author(s):  
MING ZHONG ◽  
XIAOXIAN LIU ◽  
PEIQING TONG
Keyword(s):  
Phase Transitions ◽  
Quantum Phase Transitions ◽  
Transverse Field ◽  
Quantum Spin ◽  
Quantum Phase ◽  
Quantum Spin Chains ◽  
Positive Real ◽  
Partition Function Zeros ◽  
Closed Curves ◽  
Transition Points

The quantum phase transitions of four kinds of nonuniform anisotropic XY quantum spin chains in a transverse field are studied by the Lee-Yang zeros method. It is found that the closed curves of the partition function zeros cut the positive real axis at the quantum phase transition points. The results are checked by the explicit calculations of the magnetization.

Quantum phase transitions in 1/3 plateau of the quantum spin tube

2013 ◽  
Vol 63 (3) ◽  
pp. 596-600
Author(s):  
Kouichi Okunishi ◽  
Masahiro Sato ◽  
Tôru Sakai ◽  
Kiyomi Okamoto ◽  
Chigaku Itoi
Keyword(s):  
Phase Transitions ◽  
Quantum Phase Transitions ◽  
Quantum Spin ◽  
Quantum Phase ◽  
Spin Tube
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