The open XXZ-chain: Bosonisation, Bethe ansatz and logarithmic corrections

Abstract

We calculate the bulk and boundary parts of the free energy for an open spin-1/2 XXZ-chain in the critical regime by bosonisation. We identify the cutoff independent contributions and determine their amplitudes by comparing with Bethe ansatz calculations at zero temperature T. For the bulk part of the free energy we find agreement with Lukyanov's result [Nucl.Phys.B 522, 533 (1998)]. In the boundary part we obtain a cutoff independent term which is linear in T and determines the temperature dependence of the boundary susceptibility in the attractive regime for $T\ll 1$. We further show that at particular anisotropies where contributions from irrelevant operators with different scaling dimensions cross, logarithmic corrections appear. We give explicit formulas for these terms at those anisotropies where they are most important. We verify our results by comparing with extensive numerical calculations based on a numerical solution of the T=0 Bethe ansatz equations, the finite temperature Bethe ansatz equations in the quantum-transfer matrix formalism, and the density-matrix renormalisation group applied to transfer matrices.

35 pages, 8 figures

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• Quantum Impurity Entanglement
• Boundary susceptibility in the spin-1/2 chain: Curie like behavior without magnetic impurities
• Boundary contributions to specific heat and susceptibility in the spin-1/2 XXZ chain
• Local Magnetic Susceptibility of the Positive Muon in the Quasi 1D S=1/2 Antiferromagnet dichlorobis (pyridine) copper (II)
• Surface free energy for systems with integrable boundary conditions
• Boundary susceptibility in the open XXZ-chain

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