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arXiv:hep-th/0405162

Boundary massive sine-Gordon model at the free Fermi limit and RG flow of Casimir energy

Chaiho P. Rim

Published May 19, 2004• 4 citations
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Abstract

RG flow of central charge $c_{\rm eff}$ is investigated for the two boundary sine-Gordon model at the free Fermi limit. Thermodynamic Bethe ansatz approach is used to check the non-monotonic decreasing properties of $c_{\rm eff}$, its resonance, and the modification of $c_{\rm eff}$ due to the mismatch of the periodicity of a Lagrangian parameter and that of the boundary scattering parameter. The detailed analysis uses the singularity structure of the system on the complex rapidity plane.

DOI
10.48550/arxiv.hep-th/0405162

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•Jan 1, 2018•0 citations
RG flow of central charge ceffc_{\rm eff}ceff​ is investigated for the two boundary sine-Gordon model at the free Fermi limit. Thermodynamic Bethe ansatz approach is used to check the non-monotonic decreasing properties of ceffc_{\rm eff}ceff​, its resonance, and the modification of ceffc_{\rm eff}ceff​ due to the mismatch of the periodicity of a Lagrangian parameter and that of the boundary scattering parameter. The detailed analysis uses the singularity structure of the system on the complex rapidity plane.
Abstract We investigate the free-Fermion point of a boundary sine-Gordon model with nondiagonal boundary interactions for the ground state using auxiliary functions obtained from T − Q equations of a corresponding inhomogeneous open spin- 1 2 XXZ chain with nondiagonal boundary terms. In particular, we obtain the Casimir energy. Our result for the Casimir energy is shown to agree with the result from the TBA approach. The analytical result for the effective central charge in the ultraviolet (UV) limit is also verified from the plots of effective central charge for intermediate values of volume.
We present exact results for the thermodynamic properties of the interacting resonant level model in equilibrium. Detailed simulations using both the Numerical Renormalization Group and Density Matrix Renormalization Group were performed in order to compare with closed analytical expressions. By first bosonizing the model and then utilizing the integrability of the resulting boundary sine-Gordon model, one finds an analytic expression for the relevant energy scale TKT_KTK​ with excellent agreement to the numerical results. On the other hand, direct application of the Bethe ansatz of the interacting resonant level model does not correctly reproduce TKT_KTK​ - however if the bare parameters in the model are renormalised, then quantities obtained via the direct Bethe ansatz such as the occupation of the resonant level as a function of the local chemical potential do match the numerical results. The case of one lead is studied in the most detail, with many results also extending to multiple leads, although there still remain open questions in this case.