# Hybrid ED/DMRG approach to the thermodynamics of 1D quantum models

## TL;DR

This paper introduces a hybrid ED/DMRG method to accurately compute the thermodynamics of 1D quantum spin models at low temperatures, extending the range of reliable results for frustrated chains.

## Contribution

The paper develops and validates a hybrid ED/DMRG approach that improves low-temperature thermodynamic calculations for 1D quantum spin chains, especially the frustrated J1-J2 model.

## Key findings

- Extends thermodynamic calculations down to T ~ 0.01|J1| for certain parameters.
- Validates the hybrid approach against known HAF results.
- Provides bounds for the thermodynamic limit based on cutoff criteria.

## Abstract

Exact diagonalization (ED) of small model systems gives the thermodynamics of spin chains or quantum cell models at high temperature $T$. Density matrix renormalization group (DMRG) calculations of progressively larger systems are used to obtain excitations up to a cutoff $W_C$ and the low-$T$ thermodynamics. The hybrid approach is applied to the magnetic susceptibility $\chi(T)$ and specific heat $C(T)$ of spin-$1/2$ chains with isotropic exchange such as the linear Heisenberg antiferromagnet (HAF) and the frustrated $J_1-J_2$ model with ferromagnetic (F) $J_1 < 0$ and antiferromagnetic (AF) $J_2 > 0$. The hybrid approach is fully validated by comparison with HAF results. It extends $J_1-J_2$ thermodynamics down to $T \sim 0.01|J_1|$ for $J_2/|J_1| \geq \alpha_c = 1/4$ and is consistent with other methods. The criterion for the cutoff $W_C(N)$ in systems of $N$ spins is discussed. The cutoff leads to bounds for the thermodynamic limit that are best satisfied at a specific $T(N)$ at system size $N$.