Hybrid exact diagonalization and density matrix renormalization group approach to the thermodynamics of one-dimensional quantum models

Abstract

Exact diagonalization of small model systems gives the thermodynamics of spin chains or quantum cell models at high temperatures $T$. Density matrix renormalization group 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 $\ensuremath{\chi}(T)$ and specific heat $C(T)$ of spin-$1/2$ chains with isotropic exchange such as the linear Heisenberg antiferromagnet and the frustrated ${J}_{1}\ensuremath{-}{J}_{2}$ model with ferromagnetic ${J}_{1}l0$ and antiferromagnetic ${J}_{2}g0$. The hybrid approach is fully validated by comparison with Heisenberg antiferromagnet results. It extends ${J}_{1}\ensuremath{-}{J}_{2}$ thermodynamics down to $T\ensuremath{\sim}0.01|{J}_{1}|$ for ${J}_{2}/|{J}_{1}|\ensuremath{\ge}{\ensuremath{\alpha}}_{c}=1/4$ 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 $N$.