Monte Carlo Simulation of the Quantum Sine-Gordon Chain

Abstract

One-dimensional (ID) lattice-dynamical models exhibiting soliton-like features have been studied by a variety of methods. In particular the sine-Gordon (sG) and φ⁴ models have been the subject of much theoretical research [1–15]. The former is also relevant-to experiments on magnetic chain materials [16–24]. Most theoretical studies have been carried out within the framework of classical statistical mechanics. As these ID models contain up to nearest-neighbor interactions only, the transfer matrix method has been employed to compute numerically exact results [2]. Partially motivated by significant discrepancies between experiment and classical theory [25], the question to what extent quantum effects are important has been addressed. The Bethe-Ansatz solution of the continuum sG chain, [4, 10] semi-classical approximation schemes [5,7,14] as well as variational path-integral [9,13] calculations all indicate that there remains a quantitative disagreement between theory and experiment which may be due to the fact that the sG model neglects the out-of-plane motion of the spins. Recent Quantum Monte Carlo simulations and transfer-matrix calculations suggest that the S=l/2 model, assumed to be applicable to CHAB [(C₆H₁lNH₃)CuBr₃], cannot adequately reproduce experimental facts [26].