Dynamical scaling laws in the quantum q-state clock chain

被引:3
作者
Tang, Jia-Chen [1 ,2 ]
You, Wen-Long [1 ,2 ]
Hwang, Myung-Joong [3 ,4 ]
Sun, Gaoyong [1 ,2 ]
机构
[1] Nanjing Univ Aeronaut & Astronaut, Coll Phys, Nanjing 211106, Peoples R China
[2] Nanjing Univ Aeronaut & Astronaut, Key Lab Aerosp Informat Mat & Phys, MIIT, Nanjing 211106, Peoples R China
[3] Duke Kunshan Univ, Div Nat & Appl Sci, Kunshan 215300, Jiangsu, Peoples R China
[4] Duke Kunshan Univ, Zu Chongzhi Ctr Math & Computat Sci, Kunshan 215300, Jiangsu, Peoples R China
关键词
RENORMALIZATION-GROUP;
D O I
10.1103/PhysRevB.107.134303
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
We show that phase transitions in the quantum q-state clock model for q 4 can be characterized by an enhanced decay behavior of the Loschmidt echo via a small quench. The quantum criticality of the quantum q-state clock model is numerically investigated by the finite-size scaling of the first minimum of the Loschmidt echo and the short-time average of the rate function. The equilibrium correlation-length critical exponents are obtained from the scaling laws which are consistent with previous results. Furthermore, we study dynamical quantum phase transitions by analyzing the Loschmidt echo and the order parameter for any q upon a big quench. For q 4, we show that dynamical quantum phase transitions can be described by the Loschmidt echo and the zeros of the order parameter. In particular, we find the rate function increases logarithmically with q at the first critical time. However, for q > 4, we find that the correspondence between the singularities of the Loschmidt echo and the zeros of the order parameter no longer exists. Instead, we find that the Loschmidt echo near its first minimum converges, while the order parameter at its first zero increases linearly with q.
引用
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页数:12
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