温度增量 Monte Carlo 方法中的残余熵
Residual entropy from temperature incremental Monte Carlo method
AI总结：
本文提出温度增量 Monte Carlo（TIMC）方法，通过相邻温度配分函数比的增量计算，在阻挫、玻璃态和量子 Ising 等系统中实现全温区精确熵及残余熵测量。
摘要：
残余熵反映系统在绝对零度下的自由度，对于理解量子和经典基态至关重要。尽管它在解释低温现象和基态简并方面具有关键作用，但由于计算限制，准确测量残余熵仍是一项困难任务。在这篇 Letter 中，我们提出温度增量 Monte Carlo（TIMC）方法，作为克服这些挑战的途径。TIMC 方法在 Monte Carlo 模拟中增量计算相邻温度之间的配分函数比，从而实现精确的熵计算，并在一次温度扫描计算中揭示其他依赖于温度的性质。我们已在若干复杂系统上严格测试 TIMC，包括 C60 和二维三角晶格上的阻挫反铁磁 Ising 模型、Newman-Moore 玻璃态模型，以及二维量子横场 Ising 模型。值得注意的是，我们的方法克服了将 d 维量子模型映射到 d+1 维经典对应模型时在配分函数测量中遇到的困难。这些挑战源于量子到经典映射过程中在小 Δ_τ 极限下出现的奇异相互作用。正如我们对阻挫自旋模型、玻璃相以及表现出自发对称性破缺的相的研究所展示的，TIMC 方法能够在整个温度范围内进行精确的熵计算。该方法计算残余熵的能力在应用于缺乏解析解的系统时，有望提供新的认识。
英文摘要：
Residual entropy, which reflects the degrees of freedom in a system at absolute zero temperature, is crucial for understanding quantum and classical ground states. Despite its key role in explaining low-temperature phenomena and ground state degeneracy, accurately measuring residual entropy remains a difficult task owing to computational limitations. In this Letter, we introduce the temperature incremental Monte Carlo (TIMC) method, our approach to overcoming these challenges. The TIMC method incrementally calculates the partition function ratio of neighboring temperatures within Monte Carlo simulations, enabling precise entropy calculations and revealing other temperature-dependent properties in a single computational sweep of temperatures. We have rogorously tested TIMC on several complex systems, including the frustrated antiferromagnetic Ising model on both C60 and 2D triangular lattices, the Newman-Moore glassy model, and a 2D quantum transverse field Ising model. Notably, our method overcomes the difficulties encountered in partition function measurements when mapping $d$-dimensional quantum models to $d+1$-dimensional classical counterparts. These challenges arise from singular interactions that emerge in the small $Δ_τ$ limit during the quantum-to-classical mapping procedure. The TIMC method enables precise entropy calculations across the entire temperature range, as demonstrated in our studies of frustrated spin models, glassy phases, and phases exhibiting spontaneous symmetry breaking. This method's capability to calculate residual entropy could provide insights when applied to systems lacking analytical solutions.
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