paper

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

arXiv:1905.05956

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 $I ¨ (T)$ 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 $J_{2} /∣ J_{1} ∣ \geq I^\pm_{c} = 1/4$ 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 $N$ .