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Anisotropic XY chain with DM interaction quantum phase transitions , quantum entanglement and thermal entanglement

Author: XuHui
Tutor: TongPeiQing
School: Nanjing Normal University
Course: Theoretical Physics
Keywords: XY model DM interaction Quantum phase transitions Quantum entanglement Thermal Entanglement
CLC: O413
Type: Master's thesis
Year: 2011
Downloads: 34
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Abstract


The system phase transitions and critical phenomena has been an important topic in condensed matter physics. Among them, the most studied and most simple model is one-dimensional quantum the Heisenberg (?) Model. In recent years, the DM interaction has many potential applications, and the phase transition behavior of the one-dimensional spin chains also have a certain impact, causing a wide range of research. So we study the anisotropic XY chain with DM interaction quantum phase transitions. Taking into account the recent application of the amount to be entangled study quantum phase transition behavior also become a new and very effective method, we study the behavior of quantum entanglement. Zero temperature in the experiment is difficult to achieve, the end of this article the thermal entanglement behavior of the system carried out a preliminary study. This paper studies the amount of anisotropic XY chain in a transverse field with Dzyaloshinskii-Moriya (DM) interaction to the phase transition and quantum entanglement. We first use Lee - Yang zero theory has been the model critical point, followed, by the ground state energy, average magnetic pitch, the correlation function and spiral virtual parameters understanding of the phase change type and the respective phase nature, to obtain a model phase diagram. Anisotropic XY chain in transverse field without DM interaction is addition to the paramagnetic phase of the ferromagnetic phase, the model is also more of a new phase, which we call the spiral phase. In order to verify the correctness of the phase diagram, we also studied the behavior of the model of quantum entanglement - collaboration parameters and the von Neumann entropy behavior can be found in the behavior of of two quantum entanglement amount of phase diagram meet well . And we also found that when 0 lt; D lt; 0.5 when, Ising phase transition still occurs at h = 1, and the phase transition line, the von Neumann Man entropy SL ∞ Alog2L A ≈ 1 / 6, its behavior in anisotropic XY chain without DM interaction Ising phase transition line. In a spiral phase, the von Neumann entropy SL and ∞ Alog2L, wherein A ≈ 1 /, which with its no DM interaction anisotropic XY chain anisotropic behavior of phase change line can be determined this spiral phase is a critical region. When D ≥ 0.5, the ferromagnetic phase will disappear. Next, we study the behavior of the system at finite temperature thermal entanglement, the physical quantity of our research is a collaboration parameters and the von Neumann entropy. We found that a low temperature in the region 7 ≥ 2D, with the increase of the field h collaboration parameters by the nonzero value is reduced to zero, but in 0 LT; gamma LT; γc (γc = 0.3875) within collaborative parameter in nonzero value is reduced to zero, it will rise again to a nonzero value, later reduced to zero, which we call the three critical phenomena, the same the cryogenic situation with no DM interaction anisotropic XY chain, but it is interesting when 7 gt; 0.3875, supposed to be three critical phenomena, but again with the increase in the value of D, three critical phenomena. We also study the thermal entanglement entropy of the system at finite temperatures. We are given the behavior of sub-chain part of the entropy change with temperature, outside the field as well as to the chain length.

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CLC: > Mathematical sciences and chemical > Physics > Theoretical Physics > Quantum theory
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