Density matrix renormalization group approach to the low temperature thermodynamics of correlated 1D fermionic models

TL;DR

This paper develops a combined ED and DMRG approach to accurately study the low-temperature thermodynamics of 1D correlated fermionic models, including Hubbard models, by explicitly accounting for size dependence and spectrum scaling.

Contribution

It introduces a novel ED/DMRG method that targets low-energy states for larger systems, enabling precise thermodynamic calculations at very low temperatures in 1D fermionic models.

Findings

Validated against exact results for susceptibility and entropy.

Extended the temperature range of accurate thermodynamics calculations.

Analyzed the bond-order-wave phase with small gaps.

Abstract

The low temperature thermodynamics of correlated 1D fermionic models with spin and charge degrees of freedom is obtained by exact diagonalization (ED) of small systems and followed by density matrix renormalization group (DMRG) calculations that target the lowest hundreds of states $\{E(N)\}$ at system size $N$ instead of the ground state. Progressively larger $N$ reaches $T < 0.05t$ in correlated models with electron transfer $t$ between first neighbors and bandwidth $4t$. The size dependence of the many-fermion basis is explicitly included for arbitrary interactions by scaling the partition function. The remaining size dependence is then entirely due to the energy spectrum $\{E(N)\}$ of the model. The ED/DMRG method is applied to Hubbard and extended Hubbard models, both gapped and gapless, with $N_e = N$ or $N/2$ electrons and is validated against exact results for the magnetic susceptibility $\chi(T)$ and entropy $S(T)$ per site. Some limitations of the method are noted. Special attention is given to the bond-order-wave phase of the extended Hubbard model with competing interactions and low $T$ thermodynamics sensitive to small gaps.