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Journal of Physics A Mathematical and General

Non-analytic finite-size corrections for the Heisenberg chain in a magnetic field with free and twisted boundary conditions

Hans-Peter Eckle, Chris J. Hamer

Published Jan 7, 1991• 41 citations
Publisher

Abstract

The finite-size energy spectrum of the anisotropic Heisenberg chain in an external magnetic field is calculated for free and twisted boundary conditions. As with periodic boundary conditions, it is found that the spectra exhibit non-analytical terms which do not fit into the form predicted on the basis of conformal invariance unless extra commensurability conditions between the size of the system and the external field are introduced. Taking these conditions into account some scaling dimensions for associated models are derived.

DOI
10.1088/0305-4470/24/1/027

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Abstract. The Ising quantum chain with a peculiar twisted boundary condition is considered. This boundary condition, first introduced in the framework of the spin-1/2 XXZ Heisenberg quantum chain, is related to the duality transformation, which becomes a symmetry of the model at the critical point. Thus, at the critical point, the Ising quantum chain with the duality-twisted boundary is translationally invariant, similar as in the case of the usual periodic or antiperiodic boundary conditions. The complete energy spectrum of the Ising quantum chain is calculated analytically for finite systems, and the conformal properties of the scaling limit are investigated. This provides an explicit example of a conformal twisted boundary condition and a corresponding generalised twisted partition function. PACS numbers: 05.50.+q, 75.10.Jm, 71.10.Fd, 11.25.Hf Recently, there has been a lot of interest in generalised twisted partition functions of conformal field theory [1, 2, 3, 4] and the corresponding conformal twisted boundary conditions in solvable lattice models of statistical mechanics [5]. Examples of such boundary conditions leading to the appearance of “exotic ” spinor operators in the