Extended two-level quantum dissipative system from bosonization of the elliptic spin-\frac{1}{2} Kondo model

DOI10.1088/1751-8113/44/11/115003zbMATH Open1213.82102arXiv1102.4404OpenAlexW2059155210MaRDI QIDQ3085231

Publication date: 31 March 2011

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Abstract: We study the elliptic spin-1/2 Kondo model (spin-1/2 fermions in one dimension with fully anisotropic contact interactions with a magnetic impurity) in the light of mappings to bosonic systems using the fermion-boson correspondence and associated unitary transformations. We show that for fixed fermion number, the bosonic system describes a two-level quantum dissipative system with two noninteracting copies of infinitely-degenerate upper and lower levels. In addition to the standard tunnelling transitions, and the transitions driven by the dissipative coupling, there are also bath-mediated transitions between the upper and lower states which simultaneously effect shifts in the horizontal degeneracy label. We speculate that these systems could provide new examples of continuous time quantum random walks, which are exactly solvable.

Full work available at URL: https://arxiv.org/abs/1102.4404

zbMATH Keywords

Kondo model bosonization quantum random walks fermion-boson correspondence

Mathematics Subject Classification ID

Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Statistical mechanics of magnetic materials (82D40)