Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2005-11-11
J.Stat.Mech.0601:P01007,2006
Physics
Condensed Matter
Strongly Correlated Electrons
35 pages, 8 figures
Scientific paper
10.1088/1742-5468/2006/01/P01007
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.
Bortz Michael
Sirker Jesko
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