符号问题、PT对称性与阿贝尔格对偶
The Sign Problem, PT Symmetry and Abelian Lattice Duality
摘要：
具有复杂作用的格点场论不容易用传统的解析或模拟方法来研究。然而，这些模型中的一大类在CT下是不变的，其中C是电荷共轭，T是时间反演，包括具有非零化学势的模型。对于这类阿贝尔模型，格对偶将具有复杂动作的模型映射到具有真实动作的对偶模型。对于扩展区域的参数空间，可计算的每个模型，对偶解决了符号问题的分析方法和计算机模拟。给出了基于Z（N）和U（1）对称群的自旋模型和规范模型的显式对偶关系。对偶形式分别是Z（N）手征钟模型和格点Frenkel-Kontorova模型的推广。从这些等价，丰富的空间调制相位集被发现在强耦合区域的原始模型。
英文摘要：
Lattice field theories with complex actions are not easily studied using conventional analytic or simulation methods. However, a large class of these models are invariant under CT, where C is charge conjugation and T is time reversal, including models with non-zero chemical potential. For Abelian models in this class, lattice duality maps models with complex actions into dual models with real actions. For extended regions of parameter space, calculable for each model, duality resolves the sign problem for both analytic methods and computer simulations. Explicit duality relations are given for models for spin and gauge models based on Z(N) and U(1) symmetry groups. The dual forms are generalizations of the Z(N) chiral clock model and the lattice Frenkel-Kontorova model, respectively. From these equivalences, rich sets of spatially-modulated phases are found in the strong-coupling region of the original models.
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