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Journal of the Physical Society of Japan

Boundary Critical Phenomena in the Heisenberg Spin-1/2 Chain with Open Ends

Satoshi Fujimoto, Sebastian Eggert

Published Jan 1, 2005• 3 citations
Publisher

Abstract

We present a brief review on the recent theoretical developement about boundary effects in one-dimensional quantum spin systems focusing on the application of boundary conformal field theory. We discuss about low-temperature behaviors of the boundary contributions of the spin susceptibility and the specific heat coefficient. The anomalous behaviors at boundaries are deeply related with finite-temperature corrections of the boundary entropy or the ground state degeneracy, which yields a highly sensitive response of spin excitations in the vicinity of open boundaries.

DOI
10.1143/jpsjs.74s.36

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Exact low-temperature asymptotic behavior of boundary contribution to specific heat and susceptibility in the one-dimensional spin-12\frac{1}{2}21​ XXZ\mathrm{XXZ}XXZ model with exchange anisotropy $1/2<\ensuremath{\Delta}<~1$ is analytically obtained using the Abelian bosonization method. The boundary spin susceptibility is divergent in the low-temperature limit. This singular behavior is caused by the first-order contribution of a bulk leading irrelevant operator to boundary free energy. The result is confirmed by numerical simulations of finite-size systems. The anomalous boundary contributions in the spin isotropic case are universal.
Abstract We discuss the Renyi entanglement entropies of descendant states in critical one-dimensional systems with boundaries, that map to boundary conformal field theories in the scaling limit. We unify the previous conformal-field-theory approaches to describe primary and descendant states in systems with both open and closed boundaries. We provide universal expressions for the first two descendants in the identity family. We apply our technique to critical systems belonging to different universality classes with non-trivial boundary conditions that preserve conformal invariance, and find excellent agreement with numerical results obtained for finite spin chains. We also demonstrate that entanglement entropies are a powerful tool to resolve degeneracy of higher excited states in critical lattice models.
We discuss the R´enyi entanglement entropies of descendant states in critical one- dimensional systems with boundaries, that map to boundary conformal field theories in the scaling limit. We unify the previous conformal-field-theory approaches to describe primary and descendant states in systems with both open and closed boundaries. We provide universal expressions for the first two descendants in the identity family. We apply our technique to critical systems belonging to different universality classes with non-trivial boundary conditions that preserve conformal invariance, and find excellent agreement with numerical results obtained for finite spin chains. We also demonstrate that entanglement entropies are a powerful tool to resolve degeneracy of higher excited states in critical lattice models.
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We report on exact results for the low-temperature thermodynamics of a spin- 12\frac{1}{2}21​ magnetic impurity coupled to a one-dimensional interacting electron system. By using boundary conformal field theory, we show that there are only two types of critical behaviors consistent with the symmetries of the problem: either a local Fermi liquid or a theory with an anomalous response identical to that recently proposed by Furusaki and Nagaosa. Suppression of backscattering off the impurity leads to the same critical properties as for the two-channel Kondo effect.