The Hubbard chain at finite temperatures: ab initio calculations of Tomonaga-Luttinger liquid properties

Abstract

We present a novel treatment of finite temperature properties of the onedimensional Hubbard model. Our approach is based on a Trotter-Suzuki mapping utilizing Shastry's classical model and a subsequent investigation of the quantum transfer matrix. We derive non-linear integral equations for three auxiliary functions which have a clear physical interpretation of elementary excitations of spin type and charge excitations in lower and upper Hubbard bands. This allows for a transparent analytical study of certain limiting cases as well as for precise numerical investigations. We present data for the specific heat, magnetic and charge susceptibilities for various particle densities and coupling strengths U . The structure exposed by these curves is discussed in terms of the elementary charge and spin excitations. Special emphasis is placed on the study of the low-temperature behavior within our ab initio approach confirming the scaling predictions by Tomonaga-Luttinger liquid theory. In addition we make contact with the "dressed energy" formalism established for the analysis of ground state properties. *

Magnetic susceptibility of alkali-tetracyanoquinodimethane salts and extended Hubbard models with bond order and charge density wave phases

“…Since g(TCNQ − ) ≈ 2.00236, the free-electron value, χ(x) is directly related to Avogadro's number N A and the Bohr magneton µ B . Jüttner et al [38] obtained quantitative χ(x) for the Hubbard We find similar χ(x) for the EHM with U = 5t, the EEHM with U = 8t, γ = 0.2 and the PCM with U = 8t. Small V is conveniently approximated as a Hubbard model with an effective U e = U − V .…”

High temperature expansion for a chain model

“…They are generically called chain models, some which having the property of integrability and to which the Bethe ansatz has been applied to solve them exactly at T = 0 and at finite T . Their thermodynamical properties are obtained through coupled integral equations which demand numerical analysis to be solved (as examples see references [10,11,12,13,14]). …”

Точный Расчет Термодинамики Одномерной Модели Хаббарда С Бесконечным Отталкиванием В Магнитном Поле

“…5. Как отмечается в работах [7], [8], для мо-дели Хаббарда с конечным значением энергии отталкивания U двух электронов на одном узле без магнитного поля зависимость теплоемкости от температуры также имеет две точки максимума. Низкотемпературный пик связан со спиновыми воз-буждениями и достигается при температуре T ≈ J/k B .…”