Exactly solvable three-level quantum dissipative systems via bosonisation of fermion gas-impurity models

Abstract

We study the relationship between one-dimensional fermion gas-impurity models and quantum dissipative systems, via the method of constructive bosonisation and unitary transformation. Starting from an anisotropic Coqblin-Schrieffer model, a new, exactly solvable, three-level quantum dissipative system is derived as a generalisation of the standard spin-half spin-boson model. The new system has two environmental oscillator baths with ohmic coupling, and admits arbitrary detuning between the three levels. All tunnelling matrix elements are equal, up to one complex phase which is itself a function of the longitudinal and transverse couplings in the integrable limit. Our work underlines the importance of re-examining the detailed structure of fermion-gas impurity models and spin chains, in the light of connections to models for quantum dissipative systems.