Extended two-level quantum dissipative system from bosonization of the elliptic spin-1/2 Kondo model

TL;DR

This paper maps the elliptic spin-1/2 Kondo model to a bosonic system, revealing a two-level quantum dissipative system with unique bath-mediated transitions, potentially advancing understanding of quantum random walks.

Contribution

It introduces a novel bosonic representation of the elliptic spin-1/2 Kondo model, highlighting new bath-mediated transitions and their implications for quantum dynamics.

Findings

Bosonic system describes a two-level quantum dissipative system.

Identification of bath-mediated transitions affecting degeneracy.

Potential for exactly solvable quantum random walk models.

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.