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IMPERIAL COLLEGE PRESS eBooks

Finite Size Effects in Correlated Electron Models - Exact Results

Andrei A. Zvyagin

Published Jan 1, 2005• 21 citations
Publisher

Abstract

Quantum Spin- Chain with the Nearest-Neighbour Couplings Co-Ordinate Bethe Ansatz for a Heisenberg-Ising Ring Correlated Electron Chains: Co-Ordinate Bethe Ansatz Algebraic Bethe Ansatz Correlated Quantum Chains with Open Boundary Conditions Correlated Quantum Chains with Isolated Impurities Correlated Quantum Chains with a Finite Concentration of Impurities Finite Size Corrections in Quantum Correlated Chains Beyond the Integrability: Approximate Methods.

DOI
10.1142/9781860946868

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Chinese Physics B•Apr 12, 2020•0 citations
Quantum Spin- Chain with the Nearest-Neighbour Couplings Co-Ordinate Bethe Ansatz for a Heisenberg-Ising Ring Correlated Electron Chains: Co-Ordinate Bethe Ansatz Algebraic Bethe Ansatz Correlated Quantum Chains with Open Boundary Conditions Correlated Quantum Chains with Isolated Impurities Correlated Quantum Chains with a Finite Concentration of Impurities Finite Size Corrections in Quantum Correlated Chains Beyond the Integrability: Approximate Methods.
We propose an integrable model of the spin-1/2 Heisenberg chain coupled to two impurity moments. With the open boundary conditions at the impurity sites, the model can be exactly solved for arbitrary impurity spin and arbitrary exchange constants between the bulk and the impurities. The absence of redundant terms in the Hamiltonian makes the model very reasonable. The Hamiltonian is diagonalized via algebraic Bethe ansatz. It is found that the impurity spins can only be screened (partially for S>1/2S>1/2S>1/2) for antiferromagnetic coupling between the impurity and the bulk. Otherwise the impurity spins cannot be screened. The residual entropy of the ground state and the Kondo temperature are also derived explicitly based on the Bethe ansatz and the local Fermi-liquid theory.
The spin-1/2 Heisenberg chain coupled to a spin-S impurity moment with anti-periodic boundary condition is studied via the off-diagonal Bethe ansatz method. The twisted boundary breaks the U(1) symmetry of the system, which leads to that the spin ring with impurity can not be solved by the conventional Bethe ansatz methods. By combining the properties of the R-matrix, the transfer matrix, and the quantum determinant, we derive the T–Q relation and the corresponding Bethe ansatz equations. The residual magnetizations of the ground states and the impurity specific heat are investigated. It is found that the residual magnetizations in this model strongly depend on the constraint of the topological boundary condition, the inhomogeneity of the impurity comparing with the hosts could depress the impurity specific heat in the thermodynamic limit. This method can be expand to other integrable impurity models without U(1) symmetry.