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Lecture notes in computer science

Application of Numerical Quantum Transfer-Matrix Approach in the Randomly Diluted Quantum Spin Chains

R. Matysiak, P. Gegenwart, Akira Ochiai, F. Steglich

Published Jan 1, 2018• 1 citation
Publisher
DOI
10.1007/978-3-319-78054-2_34

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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. 1
We report a numerical study of the bond-diluted two-dimensional Potts model using transfer-matrix calculations. For different numbers of states per spin, we show that the critical exponents at the random fixed point are the same as in self-dual random-bond cases. In addition, we determine the multifractal spectrum associated with the scaling dimensions of the moments of the spin-spin correlation function in the cylinder geometry. We show that the behaviour is fully compatible with the one observed in the random-bond case, confirming the general picture according to which a unique fixed point describes the critical properties of different classes of disorder: dilution, self-dual binary random bond, self-dual continuous random bond.
New numerical results for the specific heat of a quantum spin-chain model believed to be appropriate for ferromagnetic (C6{\mathrm{C}}_{6}C6​H11{\mathrm{H}}_{11}H11​NH3{\mathrm{H}}_{3}H3​) CuBr3{\mathrm{Br}}_{3}Br3​ (CHAB) are obtained by a variant of the numerical exact transfer-matrix method. While agreement is found with some predictions of the classifical sine-Gordon approximation of this model, the results disagree with previous numerical results and are inconsistent with experimental data for CHAB.