Abdelshafy Mahmoud, Rigol Marcos
Department of Physics, <a href="https://ror.org/04p491231">The Pennsylvania State University</a>, University Park, Pennsylvania 16802, USA.
Phys Rev E. 2024 May;109(5-1):054127. doi: 10.1103/PhysRevE.109.054127.
We show that numerical linked cluster expansions (NLCEs) based on sufficiently large building blocks allow one to obtain accurate low-temperature results for the thermodynamic properties of spin lattice models with continuous disorder distributions. Specifically, we show that such results can be obtained computing the disorder averages in the NLCE clusters before calculating their weights. We provide a proof of concept using three different NLCEs based on L, square, and rectangle building blocks. We consider both classical (Ising) and quantum (Heisenberg) spin-1/2 models and show that convergence can be achieved down to temperatures that are up to two orders of magnitude lower than the relevant energy scale in the model. Additionally, we provide evidence that in one dimension one can obtain accurate results for observables such as the energy down to their ground-state values.
我们表明，基于足够大构建块的数值关联簇展开（NLCEs）能够使人们获得具有连续无序分布的自旋晶格模型热力学性质的精确低温结果。具体而言，我们表明通过在计算NLCE簇的权重之前计算其无序平均值，就可以获得此类结果。我们基于L形、方形和矩形构建块使用三种不同的NLCE提供了一个概念验证。我们考虑了经典（伊辛）和量子（海森堡）自旋 - 1/2模型，并表明可以实现收敛，直至温度比模型中的相关能量尺度低两个数量级。此外，我们提供证据表明，在一维中，对于诸如能量等可观测量，人们可以获得精确到其基态值的结果。
