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Europhysics Letters (EPL)

Comment on “Quantum coherence in an exactly solvable one-dimensional model with defects”

Andrei A. Zvyagin, Henrik Johannesson

Published Jul 10, 1996• 7 citations
Publisher

Abstract

In a recent paper by Schmitteckert et al. , an exactly solvable XXZ chain with defects was studied. We here point out that, for this type of model, the critical exponents for the asymptotic correlation functions are insensitive to the presence of defects. Also, the defects do not enhance the persistent current of the equivalent fermionic model, contrary to a claim by Schmitteckert et al.

DOI
10.1209/epl/i1996-00534-y

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Reply to the comment by A.A. Zvyagin and H. Johannesson on our paper “Quantum coherence in an exactly solvable one-dimensional model with defects”

Peter Schmitteckert, P. Schwab, Ulrich Eckern

The comment [CITE] by Zvyagin and Johannesson (ZJ) discusses some of the issues raised in our recent letter [CITE] in which we construct an exactly solvable one-dimensional quantum model, which corresponds to a Heisenberg- XXZ model or spinless fermions on a ring, with defects. In particular, we presented results for the finite-size corrections to the ground-state energy as well as for its flux sensitivity, as a function of a parameter ν which characterizes the strength of the defects.

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Quantum coherence in an exactly solvable one-dimensional model with defects

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Universality relations in non-solvable quantum spin chains

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•Jan 1, 2009•10 citations
In a recent paper by Schmitteckert et al. , an exactly solvable XXZ chain with defects was studied. We here point out that, for this type of model, the critical exponents for the asymptotic correlation functions are insensitive to the presence of defects. Also, the defects do not enhance the persistent current of the equivalent fermionic model, contrary to a claim by Schmitteckert et al.
Abstract. – Using the Quantum Inverse Scattering Method we construct an integrable Heisenberg-XXZ-model, or equivalently a model for spinless fermions with nearest-neighbour interaction, with defects. Each defect involves three sites with a fine tuning between nearest-neighbour and nextnearest-neighbour terms. We investigate the finite size corrections to the ground state energy and its dependence on an external flux as a function of a parameter ν, characterizing the strength of the defects. For intermediate values of ν, both quantities become very small, although the ground state wavefunction remains extended. ( ∗) Electronic mail:
Using the Quantum Inverse Scattering Method we construct an integrable Heisenberg-XXZ model, or equivalently a model for spinless fermions with nearest-neighbour interaction, with defects. Each defect involves three sites with a fine tuning between nearest-neighbour and next-nearest-neighbour terms. We investigate the finite-size corrections to the ground-state energy and its dependence on an external flux as a function of a parameter ν, characterizing the strength of the defects. For intermediate values of ν, both quantities become very small, although the ground-state wave function remains extended.
A new family of exactly solvable models is introduced. These models are generalizations of the XXZ chain where the distance among spins up (σzσ^zσz-basis) cannot be smaller or equal to t (t=0,1,2,...). The case t=0 recovers the standard XXZ chain. The coordinate Bethe ansatz is applied and the phase diagram is calculated. Exploring the finite-size consequences of conformal invariance the critical exponents are evaluated exactly at the critical regions of the phase diagram
We prove the exact relations between the critical exponents and the susceptibility, implied by the Haldane Luttinger liquid conjecture, for a generic lattice fermionic model or a quantum spin chain with short range weak interaction. The validity of such relations was only checked in some special solvable models, but there was up to now no proof of their validity in non-solvable models. 1 Introduction and Main results One dimensional (1D) electron systems can be experimentally realized [1, 2] and their properties can be measured with increasing precision. Realistic models are very difficult to study and most of the theoretical predictions for such systems (for some recent experiments see [3]) are based on a number of