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Quantum Coherence in an Exactly Solvable One-dimensional Model with Defects

Peter Schmitteckert, P. Schwab, U. Eckern

Published Jan 1, 1995• 14 citations
OpenAlex

Abstract

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:

Related papers

Quantum Coherence in an Exactly Solvable One-Dimensional Model with Defects

Peter Schmitteckert, P. Schwab, Ulrich Eckern

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.

Europhysics Letters (EPL)•Jun 20, 1995•54 citations

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.

Europhysics Letters (EPL)•Jul 10, 1996•0 citations

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

Andrei A. Zvyagin, Henrik Johannesson

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.

Europhysics Letters (EPL)•Jul 10, 1996•7 citations

Hubbard model with next-nearest-neighbour interaction terms in higher dimensions: New, exactly solvable cases

Péter Gurin, Zsolt Gulácsi

The exact ground-state wavefunction and energy of an extended Hubbard model are presented containing also next-nearest-neighbour hopping, bond-charge and density interaction terms besides the nearest-neighbour and on-site contributions. Our results are valid at half-filling for a wide range of parameters, on simple hypercubic lattices in arbitrary D > I dimensions.

Philosophical Magazine B•Nov 1, 1997•2 citations

Phase coherence in a random one-dimensional system of interacting fermions: A density-matrix renormalization-group study

Peter Schmitteckert, Ulrich Eckern

Using the density-matrix renormalization-group algorithm, we study the model of spinless fermions with nearest-neighbor interaction on a ring in the presence of disorder. We determine the spatial decay of the density induced by a defect (Friedel oscillations), and the phase sensitivity of the ground-state energy \ensuremath{\Delta}E=(-${)}^{\mathit{N}}$[E(\ensuremath{\varphi}=0)-E(\ensuremath{\varphi}=\ensuremath{\pi})], where \ensuremath{\varphi}=2\ensuremath{\pi}\ensuremath{\Phi}/${\mathrm{\ensuremath{\Phi}}}_{0}$ (N is the number of fermions, \ensuremath{\Phi} the magnetic flux, and ${\mathrm{\ensuremath{\Phi}}}_{0}$=h/e the flux quantum), for a disordered system versus the system size M. The quantity ln(M\ensuremath{\Delta}E) is found to have a normal distribution to a good approximation. The ``localization length'' decreases (increases) for a repulsive (attractive) interaction. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9604005•Physical review. B, Condensed matter•Jun 15, 1996•41 citations

Generalized dimer states

M W Long, C A Hayward

We present a new class of variational wavefunctions that can be used to investigate quantum antiferromagnetic systems. The states are a natural generalization of the nearest-neighbour dimer phases which have been thoroughly studied in the literature. We describe a one-dimensional class of total-spin-singlet wavefunctions, which include as special cases the two nearest-neighbour dimer phases and the exact solution to the total-spin-two projector Hamiltonian. These different solutions are 'smoothly' interpolated by a range of singlets with short-range correlations. Although the states have only short-range order, we can obtain over 98% of the ground-state energy of the nearest-neighbour Heisenberg model. We apply our basis to the J 1 -J 2 Heisenberg model and the single hole in the t 1 -t 2 infinite-U Hubbard model, successfully predicting the behaviour observed in finite-size scaling calculations.

Journal of Physics Condensed Matter•Apr 4, 1994•2 citations
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.
Using the density-matrix renormalization-group algorithm, we study the model of spinless fermions with nearest-neighbor interaction on a ring in the presence of disorder. We determine the spatial decay of the density induced by a defect (Friedel oscillations), and the phase sensitivity of the ground-state energy \ensuremath{\Delta}E=(-)N{)}^{\mathit{N}})N[E(\ensuremath{\varphi}=0)-E(\ensuremath{\varphi}=\ensuremath{\pi})], where \ensuremath{\varphi}=2\ensuremath{\pi}\ensuremath{\Phi}/${\mathrm{\ensuremath{\Phi}}}_{0}$ (N is the number of fermions, \ensuremath{\Phi} the magnetic flux, and ${\mathrm{\ensuremath{\Phi}}}_{0}$=h/e the flux quantum), for a disordered system versus the system size M. The quantity ln(M\ensuremath{\Delta}E) is found to have a normal distribution to a good approximation. The ``localization length'' decreases (increases) for a repulsive (attractive) interaction. \textcopyright{} 1996 The American Physical Society.
We present a new class of variational wavefunctions that can be used to investigate quantum antiferromagnetic systems. The states are a natural generalization of the nearest-neighbour dimer phases which have been thoroughly studied in the literature. We describe a one-dimensional class of total-spin-singlet wavefunctions, which include as special cases the two nearest-neighbour dimer phases and the exact solution to the total-spin-two projector Hamiltonian. These different solutions are 'smoothly' interpolated by a range of singlets with short-range correlations. Although the states have only short-range order, we can obtain over 98% of the ground-state energy of the nearest-neighbour Heisenberg model. We apply our basis to the J 1 -J 2 Heisenberg model and the single hole in the t 1 -t 2 infinite-U Hubbard model, successfully predicting the behaviour observed in finite-size scaling calculations.