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arXiv 2406.02677cond-mat.str-elcond-mat.quant-gasquant-ph
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强关联物质的量子输运理论

Quantum Transport Theory of Strongly Correlated Matter

Assa Auerbach, Sauri Bhattacharyya

AI总结:

本文回顾了强散射区域中计算相互作用体系磁电导率的三种量子输运方法,即简并投影极化公式、连分数表示和Hall系数求和公式,并展示了它们在晶格电子与玻色子模型中的应用及对Mott绝缘体附近金属输运的揭示。

摘要:

本报告回顾了在计算一般相互作用哈密顿量的Kubo公式方面的最新进展。其目标是在Boltzmann方程和Hall电导率代理量超出其适用范围的强散射区域中计算电和热磁电导率。文中解释了三种主要方法。1. 用于Hall型电导率的简并投影极化公式,该公式大幅减少了所需计算的电流矩阵元数量。这些表达式将Berry曲率积分公式推广到了非完美晶格。2. 动力学纵向电导率的连分数表示。计算产生一组热力学平均值,可以利用它们与低频和高频电导率渐近行为之间的数学关系对其进行可控外推。3. Hall型系数的求和公式,该公式由热力学平均值构造而成。这些热力学公式是在算子Hilbert空间形式体系中推导出来的,该形式体系避免了哈密顿量本征谱的不透明性和高昂的计算成本。这些系数可以通过成熟的虚时Monte Carlo采样、高温展开、算子乘积的迹以及低温下的变分波函数来获得。我们通过将这些方法1至3应用于著名的晶格电子和玻色子模型来展示其威力。这些计算阐明了强局域相互作用对Mott绝缘体附近金属输运的深远影响。文中还讨论了这些方法的未来发展方向。

英文摘要:

This report reviews recent progress in computing Kubo formulas for general interacting Hamiltonians. The aim is to calculate electric and thermal magneto-conductivities in strong scattering regimes where Boltzmann equation and Hall conductivity proxies exceed their validity. Three primary approaches are explained. 1. Degeneracy-projected polarization formulas for Hall-type conductivities, which substantially reduce the number of calculated current matrix elements. These expressions generalize the Berry curvature integral formulas to imperfect lattices. 2. Continued fraction representation of dynamical longitudinal conductivities. The calculations produce a set of thermodynamic averages, which can be controllably extrapolated using their mathematical relations to low and high frequency conductivity asymptotics. 3. Hall-type coefficients summation formulas, which are constructed from thermodynamic averages. The thermodynamic formulas are derived in the operator Hilbert space formalism, which avoids the opacity and high computational cost of the Hamiltonian eigenspectrum. The coefficients can be obtained by well established imaginary-time Monte Carlo sampling, high temperature expansion, traces of operator products, and variational wavefunctions at low temperatures. We demonstrate the power of approaches 1--3 by their application to well known models of lattice electrons and bosons. The calculations clarify the far-reaching influence of strong local interactions on the metallic transport near Mott insulators. Future directions for these approaches are discussed.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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