Jordan-Wigner approach to dynamic correlations in spin ladders

We present a method for studying the excitations of low-dimensional quantum spin systems based on the Jordan-Wigner transformation. Using an extended random-phase approximation (RPA) scheme we calculate the correlation function of neighboring spin flips for the one-dimensional spin-½ chain which well approximates the optical conductivity of Sr 2 CuO 3 . We analyze several possible generalizations of the Jordan-Wigner approach to the two-leg spin-½ ladder. On the mean-field level the most accurate results are obtained when the spin operators are numbered in a meanderlike sequence. Calculation of the optical conductivity based on an extended RPA scheme for the meander-path approach yields very good agreement with a previous density matrix renormalization group evaluation. For polarization along the legs higher-order correlations are important to explain the weight of high-energy continuum excitations and we estimate the contribution of 4- and 6-fermion processes.

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