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Equivalences between spin models induced by defects

Zoltán Bajnok

Published Jan 16, 2006• 32 citations
OpenAlex

Abstract

By introducing defects in two boundary spin chains we show the spectral equivalence of different boundary conditions. In particular we relate certain nondiagonal boundary conditions to diagonal ones.

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Equivalences between spin models induced by defects

Z Bajnok

The spectra of integrable spin chains are shown to be independent of the ordering of their spins. As an application we introduce defects (local spin inhomogeneities in homogenous chains) in two-boundary spin systems and, by changing their locations, we show the spectral equivalence of different boundary conditions. In particular we relate certain nondiagonal boundary conditions to diagonal ones.

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A bstract Topological/perfectly-transmissive defects play a fundamental role in the analysis of the symmetries of two dimensional conformal field theories (CFTs). In the present work, spin chain regularizations for these defects are proposed and analyzed in the case of the three-state Potts CFT. In particular, lattice versions for all the primitive defects are presented, with the remaining defects obtained from the fusion of the primitive ones. The defects are obtained by introducing modified interactions around two given sites of an otherwise homogeneous spin chain with periodic boundary condition. The various primitive defects are topological on the lattice except for one, which is topological only in the scaling limit. The lattice models are analyzed using a combination of exact diagonalization and density matrix renormalization group techniques. Low-lying energy spectra for different defect Hamiltonians as well as entanglement entropy of blocks located symmetrically around the defects are computed. The latter provides a convenient way to compute the g -function which characterizes various defects. Finally, the eigenvalues of the line operators in the “crossed channel” and fusion of different defect lines are also analyzed. The results are all in agreement with expectations from conformal field theory.

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Energy of bond defects in quantum spin chains obtained from local approximations and from exact diagonalization

Valter L. Líbero, Klaus Capelle, Fabiana Souza +1 more

arXiv:0708.4004•Journal of Magnetism and Magnetic Materials•Mar 21, 2008•5 citations
We consider the SU q ( N ) invariant spin chain with diagonal and non-diagonal integrable boundary terms. The algebraic study of spin chains with different kinds of boundary terms is used to motivate a set of spectral equivalences between integrable chains with purely diagonal boundary terms and ones with an arbitrary non-diagonal term at one end. For each choice of diagonal boundary terms there is an iso-spectral one-boundary problem and vice versa. The cases N = 2, 3, 4 are used as examples throughout to illustrate the general structure. The quantum group SU q ( N ) symmetry is broken by the presence of a non-diagonal boundary term; however, one can use the spectral equivalence with the diagonal chain to easily understand the residual symmetries of the system. This is described in detail for the case of SU (3).
A bstract Topological/perfectly-transmissive defects play a fundamental role in the analysis of the symmetries of two dimensional conformal field theories (CFTs). In the present work, spin chain regularizations for these defects are proposed and analyzed in the case of the three-state Potts CFT. In particular, lattice versions for all the primitive defects are presented, with the remaining defects obtained from the fusion of the primitive ones. The defects are obtained by introducing modified interactions around two given sites of an otherwise homogeneous spin chain with periodic boundary condition. The various primitive defects are topological on the lattice except for one, which is topological only in the scaling limit. The lattice models are analyzed using a combination of exact diagonalization and density matrix renormalization group techniques. Low-lying energy spectra for different defect Hamiltonians as well as entanglement entropy of blocks located symmetrically around the defects are computed. The latter provides a convenient way to compute the g -function which characterizes various defects. Finally, the eigenvalues of the line operators in the “crossed channel” and fusion of different defect lines are also analyzed. The results are all in agreement with expectations from conformal field theory.