Some exact results for the zero-bandwidth extended Hubbard model with intersite charge and magnetic interactions

TL;DR

This paper provides exact analytical results for the zero-bandwidth extended Hubbard model with intersite interactions, revealing temperature-dependent thermodynamic properties and ground state transitions in specific cases.

Contribution

It presents rigorous transfer-matrix solutions for the 1D extended Hubbard model in two particular cases, offering explicit formulas for thermodynamic quantities.

Findings

Temperature dependence of specific heat with a two-peak structure

No finite-temperature phase transitions, only ground state transitions

Exact formulas for partition functions and thermodynamic properties

Abstract

The extended Hubbard model in the zero-bandwidth limit is studied. The effective Hamiltonian consists of (i) on-site $U$ interaction and intersite (ii) density-density interaction $W$ and (iii) Ising-like magnetic exchange interaction $J$ (between the nearest-neighbors). We present rigorous (and analytical) results obtained within the transfer-matrix method for 1D-chain in two particular cases: (a) $W=0$ and $n=1$; (b) $U\rightarrow+\infty$ and $n=1/2$ ($W\neq 0$, $J\neq 0$). We obtain the exact formulas for the partition functions which enables to calculate thermodynamic properties such as entropy, specific heat ($c$), and double occupancy per site. In both cases the system exhibits an interesting temperature dependence of $c$ involving a characteristic two-peak structure. There are no phase transitions at finite temperatures and the only transitions occur in the ground state.