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Nuclear Physics B

The thermodynamic limit and the finite-size behaviour of the fundamental Sp(2N) spin chain

Marcio Jose Martins

Published Aug 1, 2002• 9 citations
Publisher
DOI
10.1016/s0550-3213(02)00339-5

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The spectral shape of one-dimensional systems (describing for instance the behaviour of Frenkel excitons) is approached through the exactly solvable model of the XXO Heisenberg quantum spin chain in a transverse magnetic field. Some results for finite size chains concerning 2N-point correlators are presented in detail. In particular, the finite lattice, finite temperature 2-point correlators are explicitly worked out. Moreover, results in closed form are given for 2N-point correlators in the most general situation (finite lattice and thermodynamic limit, finite temperature, finite space and/or time separations). Their relations with frequency moments of the spectral shape are pointed out and the connection with moment expansion through continued fraction representation is given.
We explore how the spiral spin (SP) state, a spin singlet known to accompany fully polarized ferromagnetic (F) states in the Hubbard model, is related with the F state in the thermodynamic limit using the density-matrix renormalization group and exact diagonalization. We first obtain an indication that when the F state is the ground state the SP state is also eligible as the ground state in that limit. We then follow the general argument by Koma and Tasaki [J. Stat. Phys. 76, 745 (1994)] to find that (i) the SP state possesses a kind of order parameter, and (ii) although the SP state does not break the SU(2) symmetry in finite systems, it does so in the thermodynamic limit by making a linear combination with other states that are degenerate in that limit. We also calculate the one-particle spectral function and dynamical spin and charge susceptibilities for various one-dimensional finite-size lattices. We find that the excitation spectra of the SP state and the F state are almost identical. The present results suggest that the SP and the F states are equivalent in the thermodynamic limit. These properties may be exploited to determine the magnetic phase diagram from finite-size studies.