The Half-Filled One-Dimensional Extended Hubbard Model: Phase diagram and Thermodynamics

TL;DR

This study uses advanced numerical methods to map the phase diagram and thermodynamics of the half-filled one-dimensional extended Hubbard model, identifying phase transitions and confirming the existence of a long-range dimer order phase.

Contribution

It provides a detailed phase diagram and thermodynamic analysis using density-matrix renormalization group, clarifying the existence of a long-range dimer phase and estimating the tricritical point.

Findings

Universal crossing points in compressibility help locate charge gap closure.

Confirmed the long-range dimer (bond order) phase exists.

Estimated tricritical point at U=6.7±0.2, V=3.5±0.1.

Abstract

We study the thermodynamics of the one-dimensional extended Hubbard model at half-filling using a density-matrix renormalization group method applied to transfer matrices. We show that the various phase transitions in this system can be detected by measuring usual thermodynamic quantities like the isothermal compressibility and the uniform magnetic susceptibility. For the isothermal compressibility we show that universal crossing points exist which allow to accurately determine the line where the charge gap vanishes. By studying in addition several correlation functions, we confirm the existence of a phase with long-range dimer order (bond order) which has been a matter of debate for several years. According to our calculations this phase is located in a narrow region between the spin-density and charge-density wave phases up to a tricritical point which we estimate to be at $U_t=6.7\pm 0.2$, $V_t =3.5\pm 0.1$. Our results for the phase diagram are in good agreement with the most recent zero-temperature density-matrix renormalization group study, however, they disagree in some important aspects from the most recent Quantum-Monte-Carlo study.