We develop an analytical and numerical framework based on the disentanglement approach to study the ground states of many-body quantum spins systems. In this approach, observables are expressed as functional integrals over scalar fields, where the relevant measure is the Wiener measure. We identify the leading contribution to these integrals, given by the saddle point field configuration. Analytically, this can be used to develop an exact field-theoretical expansion of the functional integrals, performed by means of appropriate Feynman rules. The expansion can be truncated to the desired order to obtain approximate analytical results for ground state expectation values. Numerically, the saddle point configuration can be used to compute physical observables by means of an exact importance sampling scheme. We illustrate our methods by considering the quantum Ising model in 1, 2 and 3 spatial dimensions. Our analytical and numerical results are applicable to a broad class of many-body quantum spin systems, bridging concepts from quantum lattice models, continuum field theory, and classical stochastic processes.

中文翻译：

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量子自旋基态的解缠结方法：场论和随机模拟

我们开发了一个基于解缠结方法的分析和数值框架来研究多体量子自旋系统的基态。在这种方法中，可观察量表示为标量场上的函数积分，其中相关测度是维纳测度。我们确定了对这些积分的主要贡献，由鞍点场配置给出。从分析上讲，这可用于开发函数积分的精确场论扩展，通过适当的费曼规则执行。可以将展开截断为所需的阶数，以获得基态期望值的近似分析结果。在数值上，鞍点配置可用于通过精确的重要性采样方案来计算物理可观察量。我们通过考虑 1、2 和 3 个空间维度的量子 Ising 模型来说明我们的方法。我们的分析和数值结果适用于广泛的多体量子自旋系统，将量子晶格模型、连续场论和经典随机过程的概念桥接起来。