Finite-size effects in the integrable XXZ Heisenberg model with arbitrary spin

The finite-size effects in the spectrum of the integrable XXZ Heisenberg chain with arbitrary spin-S are studied analytically on the basis of the string hypothesis for bound states and numerically by solving the associated Bethe ansatz equations. The finite-size corrections to the spectrum and to the low-temperature behaviour of the free energy are found to be similar to the universal predictions for conformally invariant theories, although the model is, in general, not Lorentz invariant, since it can have an arbitrary number of branches for low-energy excitations with different Fermi velocities depending on the value of S and the anisotropy parameter gamma .

[1]  F. Woynarovich.  Finite-size effects in a non-half-filled Hubbard chain , 1989 .

[2]  F. Woynarovich,et al.  Non-analytic finite-size corrections in the one-dimensional Bose gas and Heisenberg chain , 1989 .

[3]  B. Dorfel.  Finite-size corrections for spin-S Heisenberg chains and conformal properties , 1989 .

[4]  L. Avdeev.  Bethe-ansatz solutions of a non-string type: numerical results , 1989 .

[5]  N. Reshetikhin,et al.  Conformal dimensions in Bethe ansatz solvable models , 1989 .

[6]  F. C. Alcaraz,et al.  Conformal invariance and the operator content of the XXZ model with arbitrary spin , 1989 .

[7]  Nienhuis,et al.  Bethe-Ansatz results for a solvable O(n) model on the square lattice. , 1989, Physical review letters.

[8]  H. Blöte,et al.  Conformal invariance and critical behavior of the O(n) model on the honeycomb lattice. , 1989, Physical review. B, Condensed matter.

[9]  J. Suzuki.  Simple excitations in the nested Bethe-ansatz model , 1988 .

[10]  H. Johannesson.  Universality classes of critical antiferromagnets , 1988 .

[11]  H. Vega.  Integrable vertex models and extended conformal invariance , 1988 .

[12]  M. N. Barber,et al.  Conformal invariance, the XXZ chain and the operator content of two-dimensional critical systems , 1988 .

[13]  N. Reshetikhin,et al.  Properties of kernels of integral equations in XXZ models of arbitrary spin , 1988 .

[14]  N. Reshetikhin,et al.  Finite-size effects and infrared asymptotics of the correlation functions in two dimensions , 1987 .

[15]  N. Reshetikhin,et al.  Exact solution of the integrable XXZ Heisenberg model with arbitrary spin. II. Thermodynamics of the system , 1987 .

[16]  N. Reshetikhin,et al.  Exact solution of the integrable XXZ Heisenberg model with arbitrary spin. I. The ground state and the excitation spectrum , 1987 .

[17]  Barber,et al.  Conformal invariance and the spectrum of the XXZ chain. , 1987, Physical review letters.

[18]  F. Woynarovich,et al.  Finite-size corrections and numerical calculations for long spin 1/2 Heisenberg chains in the critical region , 1987 .

[19]  Zongan Qiu,et al.  Modular invariant partition functions for parafermionic field theories , 1987 .

[20]  V. Korepin,et al.  Critical exponents for integrable models , 1986 .

[21]  C. Hamer.  Finite-size corrections for ground states of the XXZ Heisenberg chain , 1986 .

[22]  I. Affleck.  Universal Term in the Free Energy at a Critical Point and the Conformal Anomaly , 1986 .

[23]  J. Cardy,et al.  Conformal invariance, the central charge, and universal finite-size amplitudes at criticality. , 1986, Physical review letters.

[24]  H. Ruegg,et al.  Conformal invariance and finite one-dimensional quantum chains , 1986 .

[25]  J. Cardy.  Operator Content of Two-Dimensional Conformally Invariant Theories , 1986 .

[26]  L. Avdeev,et al.  Solutions of the Bethe ansatz equations for XXX antiferromagnet of arbitrary spin in the case of a finite number of sites , 1987 .

[27]  H. Vega,et al.  Method for calculating finite size corrections in Bethe ansatz systems: Heisenberg chain and six-vertex model , 1985 .

[28]  K. Sogo.  Ground state and low-lying excitations in the Heisenberg XXZ chain of arbitrary spin S , 1984 .

[29]  D. Huse.  Exact exponents for infinitely many new multicritical points , 1984 .

[30]  C. Hamer,et al.  Finite-lattice extrapolations for Z3 and Zs models , 1981 .

[31]  V. Korepin.  Direct calculation of the S matrix in the massive thirring model , 1979 .

[32]  Alan C. Brown,et al.  Correlation functions on the critical lines of the Baxter and Ashkin-Teller models☆ , 1979 .

[33]  M. Suzuki,et al.  One-Dimensional Anisotropic Heisenberg Model at Finite Temperatures , 1972 .

[34]  C. Yang,et al.  Thermodynamics of a One‐Dimensional System of Bosons with Repulsive Delta‐Function Interaction , 1969 .