Random Exchange Quantum Heisenberg Chains

TL;DR

This paper investigates the thermodynamic properties of one-dimensional quantum Heisenberg chains with random bonds, revealing unusual low-energy excitations and susceptibility behavior through series expansions and numerical methods.

Contribution

It provides new insights into the thermodynamics of disordered quantum spin chains using high-temperature series and transfer matrix techniques.

Findings

Susceptibility exhibits Curie-like behavior at all temperatures.

Specific heat indicates many low-lying excitations.

Exact diagonalization supports the presence of anomalous excitations.

Abstract

The one-dimensional quantum Heisenberg model with random $\pm J$ bonds is studied for $S=\frac{1}{2}$ and $S=1$. The specific heat and the zero-field susceptibility are calculated by using high-temperature series expansions and quantum transfer matrix method. The susceptibility shows a Curie-like temperature dependence at low temperatures as well as at high temperatures. The numerical results for the specific heat suggest that there are anomalously many low-lying excitations. The qualitative nature of these excitations is discussed based on the exact diagonalization of finite size systems.