Quantum spin chains with nonlocally-correlated random exchange coupling and random-mass Dirac fermions

Abstract

S = 1 2 quantum spin chains and ladders with random exchange coupling are studied by using an effective low-energy field theory and transfer matrix methods. Effects of the nonlocal correlations of exchange couplings are investigated numerically. In particular we calculate localization length of magnons, density of states, correlation functions and multifractal exponents as a function of the correlation length of the exchange couplings. As the correlation length increases, there occurs a "phase transition" and the above quantities exhibit different behaviors in two phases. This suggests that the strong-randomness fixed point of the random spin chains and random-singlet state get unstable by the long-range correlations of the random exchange couplings.In this paper we consider the random exchange couplings J n which have a uniform constant part J and a random fluctuating part δJ n = (−) n m(n), where m(n) is a "smooth function" of site index n;J n = J + δJ n = J + (−) n m(n).