Phase transitions and critical behaviors of XXZ ladders
Phase transitions and critical behaviors of XXZ ladders
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XXZ 梯子的相变和关键行为
DOI：
10.1088/1742-5468/ab5705
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Chengxiang Ding
中科院分区：
文献类型：
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作者：
Chengxiang Ding
我们通过广泛的蒙特卡罗模拟和有限尺寸尺度分析研究了两腿二聚XXZ梯子的相变和临界行为。对于交错阶梯上的Heisenberg模型，我们验证了两个拓扑相之间的相变属于四态Potts普适类；对于XY情况（），相图与Heisenberg情况相似，但临界行为属于一个新的普适性类；对于Ising情况（），我们发现了三个拓扑相，其中一个既有拓扑序又有局部磁序；与这些相相关的两个相变也属于伊辛普适类。在柱状阶梯上，我们没有发现所有三种情况的任何相变。此外，我们发现磁场还可以诱导交错和柱状模型的相变，并且拓扑相处于一定的磁平台中。对于交错模型，我们研究了与零磁化平台相关的相变；我们发现弦序参数的临界行为属于二维经典Ising模型，而均匀磁化的标度行为不同于Dzhaparidze-Nersesyan-Pokrovsky-Talapov普适性类。对于柱状模型，我们研究了磁化强度为饱和值一半的平台的相变，该平台具有分数阶量化的Berry相；在这种情况下，常规的弦序参数不适用作为序参数，我们通过均匀磁化的标度行为来确定该相变的临界点，这也不同于Dzhaparidze-Nersesyan-Pokrovsky-Talapov普适性类。
We study the phase transitions and critical behaviors of the two-leg dimerized XXZ ladders by extensive Monte Carlo simulations and finite-size scaling analysis. For the Heisenberg model on the staggered ladder, we verify that the phase transition between the two topological phases belongs to the four-state Potts universality class; for the XY case (), the phase diagram is similar to the Heisenberg case, but the critical behavior belongs to a new universality class; for the Ising case (), we find three topological phases, in which one of them has both the topological orders and the local magnetic order; the two phase transitions associated with these phases also belong to the Ising universality class. On the columnar ladder, we have not found any phase transition for all the three cases. Furthermore, we find that the magnetic field can also induce phase transitions for both the staggered and columnar models, and the topological phases are in certain magnetic plateaux. For the staggered model, we study the phase transition associated with the plateau of zero magnetization; we find that the critical behavior of the string order parameter belongs to the 2D classical Ising model, and the scaling behavior of the uniform magnetization is different from the Dzhaparidze–Nersesyan–Pokrovsky–Talapov universality class. For the columnar model, we study the phase transition associated with the plateau whose magnetization is half of the saturation value, which has fractional quantized Berry phase; in this case, the conventional string order parameters are not applicable as order parameters, we determine the critical point of this phase transition by the scaling behavior of the uniform magnetization which is also different from the Dzhaparidze–Nersesyan–Pokrovsky–Talapov universality class.