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Journal of Physics A Mathematical and General

Conformal structure in the spectrum of an altered quantum Ising chain

Malte Henkel, A. Patkós

Published Jun 1, 1987• 41 citations
Publisher

Abstract

The Ising model with an infinite line of defects is mapped onto a strip with two defect lines. The Hamiltonian spectrum is studied at the bulk critical point. Its exact diagonal form is found for an infinite number of sites. The spectrum of physical excitations contains an infinite number of primary fields, while the leading ground-state energy correction is independent of the defect strength. A novel algebraic structure interpolating between those belonging to periodic and free boundary conditions is signalled.

DOI
10.1088/0305-4470/20/8/032

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The Ising model with an infinite line of defects is mapped onto a strip with two defect lines. The Hamiltonian spectrum is studied at the bulk critical point. Its exact diagonal form is found for an infinite number of sites. The spectrum of physical excitations contains an infinite number of primary fields, while the leading ground-state energy correction is independent of the defect strength. A novel algebraic structure interpolating between those belonging to periodic and free boundary conditions is signalled.
The spectrum of the quantum Ising chain is studied in the finite-size scaling limit for periodic and antiperiodic boundary conditions. The finite-size corrections are computed for all energy gaps. The results of the model are used to test the Privman-Fisher universality hypothesis and conformal theory. At the critical point, it is shown how to build the spectrum from the irreducible representations of the Virasoro algebra. In addition, the author finds evidence for an unsuspected symmetry for systems both non-critical and of finite size.
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The critical Ising model in two dimensions with a specific defect line is analyzed to deliver the first exact solution with twisted boundary conditions. We derive exact expressions for the eigenvalues of the transfer matrix and obtain analytically the partition function and the asymptotic expansions of the free energy and inverse correlation lengths for an infinitely long cylinder of circumference L x . We find that finite-size corrections to scaling are of the form a k / L x 2 k − 1 for the free energy f and b k ( p ) / L x 2 k − 1 and c k ( p ) / L x 2 k − 1 for inverse correlation lengths ξ p − 1 and ξ L − p − 1 , respectively, with integer values of k . By exact evaluation we find that the amplitude ratios b k ( p ) / a k and c k ( p ) / a k are universal and verify this universal behavior using a perturbative conformal approach.