世界线量子蒙特卡洛方法中的符号问题与临界性
Sign problem and criticality in world-line quantum Monte Carlo methods
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中文总结 AI 辅助
本文研究世界线量子蒙特卡洛方法中符号问题随温度和尺寸的变化，发现其与硬核玻色子模型的Kosterlitz-Thouless相变相关，表明相变信息可编码于符号问题中。
中文摘要 AI 辅助
关于符号问题的讨论通常聚焦于其作为量子蒙特卡洛方法可靠求解量子多体模型的主要限制。在行列式量子蒙特卡洛算法中，符号问题随空间晶格尺寸、掺杂、温度和相互作用强度的变化行为已被仔细刻画。在此，我们考虑世界线量子蒙特卡洛方法中符号问题对温度和尺寸依赖这一较少探索的问题。我们回顾了在该算法中，即使对自由费米子的配分函数进行采样也会产生符号问题，并将其与相应参考模型——晶格上的硬核玻色子——中的非解析行为联系起来。后者在二维中表现出有限温度的Kosterlitz-Thouless相变，我们展示了这种非解析行为如何印刻在相应二维紧束缚自由费米子模型权重的平均符号上。因此，我们的结果表明，即使在直接符号采样变得不切实际之后，相变信息仍可编码在符号问题中。
英文摘要
Discussions of the sign problem usually focus on its role as the primary limitation of the applicability of quantum Monte Carlo methods for reliably solving quantum many-body models. Its behavior as a function of spatial lattice size, doping, temperature, and interaction strengths has been carefully characterized within the determinant quantum Monte Carlo algorithm. Here, we consider the much less well-explored question of the temperature- and size-dependence of the sign problem in the world-line quantum Monte Carlo method. We review how, in this algorithm, even sampling the partition function of free fermions yields a sign problem, which we connect to non-analytic behavior in the corresponding reference model, hard-core bosons on a lattice. The latter exhibits a finite-temperature Kosterlitz-Thouless phase transition in 2D, and we show how this non-analytic behavior is imprinted on the average sign of the weights for the corresponding free fermion 2D tight-binding model. Our results thus show how phase-transition information can remain encoded in the sign problem even after direct sign sampling becomes impractical.
发表机构
- University of Houston（休斯顿大学）
- Texas Center for Superconductivity, University of Houston（德克萨斯超导中心，休斯顿大学）
- University of California, Davis（加州大学戴维斯分校）
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