Uhlmann phase of a thermal spin-1 system with zero field splitting

IF 3 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY
F. Nieto-Guadarrama , F. Rojas , E. Cota , Jesús A. Maytorena , J. Villavicencio , D. Morachis-Galindo
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引用次数: 0

Abstract

We study the Uhlmann geometric phase of a spin-1 particle subjected to zero-field splitting (ZFS) interaction, modulated by a dimensionless parameter α, under the effect of an external magnetic field with a tilting angle θ. We show that the ZFS term induces a transition in the geometrical phase behavior, characterized by a critical parameter value, α=αc. For α<αc, this phase displays two critical temperatures at θ=π/2, similar to spin-1 systems without ZFS, but with a separation that varies with α. In contrast, for α>αc, the phase exhibits two singularities at a single critical temperature but at different field orientations θπ/2. The phase disappears for significantly large |α|, regardless of the values of the Hamiltonian parameters. This behavior clearly departs from the usual thermal Uhlmann phase observed in SU(2) systems. In addition, we analytically calculate the heat capacity, which, for θ=π/2 and nearby values, displays two different regimes according to the sign of α. For α<0, it develops two peaks associated to the multilevel nature of the system, while for α>0 only a single Schottky-anomaly like peak appears as in two level systems. Interestingly, when θ=π/2, the temperature centroids of the Uhlmann phase and the heat capacity coincide in the region between critical temperatures for a given value of α<αc. Furthermore, we demonstrate that when α=0, the Uhlmann phase, a global topological property of the system, can be expressed as a function of the thermal component of the Bures metric, a local geometric property related to the heat capacity.

具有零场分裂的热自旋-1 系统的乌尔曼相
我们研究了在倾斜角为θ的外磁场作用下,受零场分裂(ZFS)相互作用、由无量纲参数α调制的自旋-1粒子的乌尔曼几何相。 我们发现,ZFS项引起了几何相行为的转变,其特征是临界参数值α=αc。对于 α<αc,该相在θ=π/2 时显示出两个临界温度,类似于没有 ZFS 的自旋-1 系统,但其分离程度随 α 而变化。相反,对于 α>αc,该相在单一临界温度下显示出两个奇点,但在不同的场方向 θ≠π/2。无论哈密顿参数的值如何,当|α| 显著增大时,该相就会消失。这种行为明显不同于在 SU(2) 系统中观察到的通常的热乌尔曼相。此外,我们还分析计算了热容量,对于 θ=π/2 及其附近的值,热容量会根据 α 的符号显示出两种不同的状态。当 α<0 时,会出现两个峰值,这与系统的多级性质有关,而当α>0 时,则只出现一个肖特基反常峰值,这与两级系统的情况相同。有趣的是,当 θ=π/2 时,乌尔曼相的温度中心点和热容量在临界温度之间的区域重合,而临界温度为 α<αc 给定值。此外,我们还证明,当 α=0 时,乌尔曼相(系统的一种全局拓扑特性)可以用布雷斯度量的热分量函数来表示,而布雷斯度量是一种与热容量相关的局部几何特性。
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来源期刊
Annals of Physics
Annals of Physics 物理-物理:综合
CiteScore
5.30
自引率
3.30%
发文量
211
审稿时长
47 days
期刊介绍: Annals of Physics presents original work in all areas of basic theoretic physics research. Ideas are developed and fully explored, and thorough treatment is given to first principles and ultimate applications. Annals of Physics emphasizes clarity and intelligibility in the articles it publishes, thus making them as accessible as possible. Readers familiar with recent developments in the field are provided with sufficient detail and background to follow the arguments and understand their significance. The Editors of the journal cover all fields of theoretical physics. Articles published in the journal are typically longer than 20 pages.
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