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Studies in computational intelligence

Spectral Density of 1D Ising Model in n-Vicinity Method

Leonid B. Litinskii, Inna M. Kaganova

Published Oct 5, 2018• 1 citation
Publisher
DOI
10.1007/978-3-030-01328-8_6

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Изучена плотность состояний для 1D модели Изинга. Установлено, что гауссова аппроксимация спектральной плотности делает метод n-окрестностей непригодным для описания 1D модели Изинга. Найдено точное комбинаторное выражение для распределения энергий в n-окрестности. На этой основе получено распределение намагниченности для произвольной температуры Normal approximation of a spectral density for 1D Ising Model
We extend to initial ground states with zero spin density m = 0 the expressions provided by the pseudofermion dynamical theory (PDT) for the finite-energy one- and two-electron spectral-weight distributions of a one-dimensional (1D) correlated metal with on-site particle-particle repulsion. The spectral-function expressions derived in this paper were used in recent successful and detailed theoretical studies of the finite-energy singular features in photoemission of the organic compound tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) metallic phase. Our studies take into account spectral contributions from types of microscopic processes that do not occur for finite values of the spin density. Expressions for the spectral functions in the vicinity of the singular border lines which also appear in the TTF- TCNQ spectral-weight distribution are derived. In addition, the PDT expressions are generalized for electronic densities in the vicinity of half filling. Further details on the processes involved in the applications to TTF-TCNQ are reported. Our results are useful for the further understanding of the unusual spectral properties observed in low-dimensional organic metals and also provide expressions for the one- and two-atom spectral functions of a correlated quantum system of ultracold fermionic atoms in a 1D optical lattice with on-site two-atom repulsion.