有限扭转边界条件下的螺旋度模量与手征对称性破缺
Helicity modulus and chiral symmetry breaking for boundary conditions with finite twist
AI总结：
研究二维经典XY模型对有限扭转边界条件的响应，通过蒙特卡洛模拟发现自由能差与螺旋度模量偏离预期行为，揭示其源于手征态混合并提出改进计算方案，还讨论了相关应用。
摘要：
我们研究了二维经典XY模型对边界条件有限（非无穷小）扭转的响应。通过蒙特卡洛模拟计算周期与扭转周期边界条件间的自由能差，发现其与扭转角的依赖关系偏离预期的二次形式。因此，螺旋度模量（自旋刚度）对扭转角表现出非平庸的依赖关系。我们指出，这种偏离源于相反手征态的混合，在准长程序相中产生额外的熵贡献。我们提出了有限扭转下螺旋度模量数值计算的改进方案，并讨论了反周期边界条件下手征对称性的自发破缺，还探讨了其在离散自旋系统及需要有限扭转边界条件的实验场景中的应用。
英文摘要：
We study the response of a two-dimensional classical XY model to a finite (non-infinitesimal) twist of the boundary conditions. We use Monte Carlo simulations to evaluate the free energy difference between periodic and twisted-periodic boundary conditions and find deviations from the expected quadratic dependence on the twist angle. Consequently, the helicity modulus (spin-stiffness) shows a non-trivial dependence on the twist angle. We show that the deviation from the expected behavior arises because of the mixing of states with opposite chirality which leads to an additional entropy contribution in the quasi-long-range ordered phase. We give an improved prescription for the numerical evaluation of the helicity modulus for a finite twist, and we discuss the spontaneous breaking of the chiral symmetry for the anti-periodic boundary conditions. We also discuss applications to discrete spin systems and some experimental scenarios where boundary conditions with finite twist are necessary.
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