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The exact solution and the finite size behaviour of the Osp(1|2) invariant spin chain

Martins, M J

Published Feb 22, 1995• 30 citations
OpenAlex

Abstract

We have solved exactly the Osp(1|2) spin chain by the Bethe ansatz approach. The completeness of the Bethe ansatz equations is discussed for a system with four sites and is noted the appearance of special string structures. The Bethe ansatz presents an important phase-factor which distinguishes the even and odd sectors of the theory. The finite size properties are governed by a conformal field theory with central charge c=1.

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We have solved exactly the Osp(1|2) spin chain by the Bethe ansatz approach. The completeness of the Bethe ansatz equations is discussed for a system with four sites and is noted the appearance of special string structures. The Bethe ansatz presents an important phase-factor which distinguishes the even and odd sectors of the theory. The finite size properties are governed by a conformal field theory with central charge c=1.
This note is a supplement to our previous papers: Mod. Phys. Lett. A14 (1999) 2427 (math-ph/9911010); Int. J. Mod. Phys. A15 (2000) 2329 (math-ph/9912014). The thermodynamic Bethe ansatz (TBA) equation for an integrable spin chain related to the Lie superalgebra osp(1|2) is analyzed. The central charge determined by low temperature asymptotics of the specific heat can be expressed by the Rogers dilogarithmic function, and identified to be 1. Solving the TBA equation numerically, we evaluate the several thermodynamic quantities. The excited state TBA equation is also discussed.
Bethe ansatz equations (BAE) are investigated for the isotropic spin- 1 / 2 Heisenberg chain as well as the XXZ chain with real solutions characterized by identical integers in the logarithmic form of the BAE. Such states do not belong to the usual classification scheme (string hypothesis). They always exist in critical sectors with respect to the total spin of the chain and the anisotropy. The conception of holes has to be changed in this case, because there occur more holes than expected. The finite-size corrections for the XXX model are calculated including complex roots and the new type of real solutions with repeating integers. The 'tower structure' predicted by the hypothesis of conformal invariance is shown to remain unchanged.
We present the exact solution of the Osp(1∣2)\mathrm{Osp}(1|2)Osp(1∣2) invariant magnet by the Bethe ansatz approach. The associated Bethe ansatz equation exhibits a new feature by presenting an explicit and distinct phase behavior in even and odd sectors of the theory. The ground state, the low-lying excitations, and the critical properties are discussed by exploiting the Bethe ansatz solution.
We studied a quantum spin chain invariant by the superalgebra osp(1|2). We derived non-linear integral equations for the row-to-row transfer matrix eigenvalue in order to analyze its finite size scaling behavior and we determined its central charge. We also studied the thermodynamical properties of the spin chain via non-linear integral equations for the quantum transfer matrix eigenvalue. We numerically solved these NLIE and evaluated the specific heat and magnetic susceptibility. The analytical low temperature analysis was performed providing the effective central charge. The computed values are in agreement with the numerical predictions in the literature.
The Bethe-ansatz equations for the integrable spin-s isotropic Heisenberg antiferromagnet are solved numerically at a finite number of sites N. The vacuum and the lowest singlet and triplet solutions are presented for s=1/2, . . ., 2 up to sN=240. Through extrapolation of the finite-size data, the central charge and anomalous dimensions of the scaling operators for the underlying conformal field theory are calculated and found to agree with the expected theoretical values. The status of the Bethe string hypothesis about the structure of the solutions is discussed based on the obtained computer data up to s=9/2.
The authors are concerned with the critical properties of the anisotropic Heisenberg chain, or XXZ model, with arbitrary integer or half-integer spin. The eigenspectra of these Hamiltonians, with periodic boundaries, are calculated for finite chains by solving numerically their associated Bethe ansatz equations. The resulting spectra are found to be in accord with the predictions of conformal invariance and the operator content is identified, for lattices with an even and odd number of sites. The results for spin 1 and spin 3/2 indicate that the conformal anomaly c for these models, in the gapless regime, has the value c=3S/(1+S), independent of the anisotropy, and the exponents vary continuously with the anisotropy as in the eight-vertex model. The operator content of these models indicate that the underlying field theory governing these critical spin-S models is described by composite fields formed by the product of Gaussian and Z(N) fields, with N=2S. Finally some of the irrelevant operators which produce the leading finite-size corrections of the eigenenergies are identified.