The Interacting Spin Models and the Equivalent Boson Systems

Abstract We establish an approximate equivalence between a generalised quantum Rabi model and its nth order counterparts, where spin-boson interactions are nonlinear as they comprise a simultaneous exchange of n bosonic excitations. Although there exists no unitary transformation between these models, we demonstrate their equivalence to a good approximation in a wide range of parameters. This shows that nonlinear spin-boson couplings, i.e., nth order quantum Rabi models, are accessible to quantum systems with only linear coupling between boson and spin modes by simply adding spin rotations and after an appropriate transformation. Furthermore, our result prompts novel approximate analytical solutions to the dynamics of the quantum Rabi model in the ultrastrong coupling regime improving previous approaches.Abstract We establish an approximate equivalence between a generalised quantum Rabi model and its nth order counterparts, where spin-boson interactions are nonlinear as they comprise a simultaneous exchange of n bosonic excitations. Although there exists no unitary transformation between these models, we demonstrate their equivalence to a good approximation in a wide range of parameters. This shows that nonlinear spin-boson couplings, i.e., nth order quantum Rabi models, are accessible to quantum systems with only linear coupling between boson and spin modes by simply adding spin rotations and after an appropriate transformation. Furthermore, our result prompts novel approximate analytical solutions to the dynamics of the quantum Rabi model in the ultrastrong coupling regime improving previous approaches.

arXiv:1709.02714npj Quantum InformationSep 24, 201850 citations

Ground States in the Spin Boson Model

David Hasler, Ira Herbst

arXiv:1003.5923Annales Henri PoincaréMar 9, 201146 citations

Connecting nth order generalised quantum Rabi models: emergence of nonlinear spin-boson coupling via spin rotations

Jorge Casanova, Ricardo Puebla, H. M. Moya-Cessa +1 more

We establish an approximate equivalence between a generalised quantum Rabi model and its nth order counterparts, where spinboson interactions are nonlinear as they comprise a simultaneous exchange of n bosonic excitations. Although there exists no unitary transformation between these models, we demonstrate their equivalence to a good approximation in a wide range of parameters. This shows that nonlinear spin-boson couplings, i.e., nth order quantum Rabi models, are accessible to quantum systems with only linear coupling between boson and spin modes by simply adding spin rotations and after an appropriate transformation. Furthermore, our result prompts novel approximate analytical solutions to the dynamics of the quantum Rabi model in the ultrastrong coupling regime improving previous approaches.We establish an approximate equivalence between a generalised quantum Rabi model and its nth order counterparts, where spinboson interactions are nonlinear as they comprise a simultaneous exchange of n bosonic excitations. Although there exists no unitary transformation between these models, we demonstrate their equivalence to a good approximation in a wide range of parameters. This shows that nonlinear spin-boson couplings, i.e., nth order quantum Rabi models, are accessible to quantum systems with only linear coupling between boson and spin modes by simply adding spin rotations and after an appropriate transformation. Furthermore, our result prompts novel approximate analytical solutions to the dynamics of the quantum Rabi model in the ultrastrong coupling regime improving previous approaches.

Sep 28, 201821 citations

Test of the low-energy model for one-dimensional interacting Fermi systems

Andrey V. Chubukov, Dmitrii L. Maslov, Fabian H. L. Eßler

Bosonization predicts that the specific heat $C(T)$ of a one-dimensional interacting Fermi system is a sum of the specific heats of free collective charge and spin excitations, plus the term with the running backscattering amplitude which flows to zero logarithmically with decreasing $T$ . We verify whether this result is reproduced in the $g$ -ology model. Of specific interest are the anomalous terms in $C(T)$ that depend on the bare backscattering amplitude. We show that these terms can be incorporated into a renormalized spin velocity. We do this by proving the equivalence of the results for $C(T)$ obtained within the $g$ -ology model and by bosonization with velocities obtained by the numerical solution of the Bethe-ansatz equations for the Hubbard model.Bosonization predicts that the specific heat $C(T)$ of a one-dimensional interacting Fermi system is a sum of the specific heats of free collective charge and spin excitations, plus the term with the running backscattering amplitude which flows to zero logarithmically with decreasing $T$. We verify whether this result is reproduced in the $g$-ology model. Of specific interest are the anomalous terms in $C(T)$ that depend on the bare backscattering amplitude. We show that these terms can be incorporated into a renormalized spin velocity. We do this by proving the equivalence of the results for $C(T)$ obtained within the $g$-ology model and by bosonization with velocities obtained by the numerical solution of the Bethe-ansatz equations for the Hubbard model.

arXiv:0801.1837Physical Review BApr 14, 20084 citations

Some results on the spin-boson model

Juan José García‐Ripoll

Aug 20, 20140 citations

Bosonization predicts that the specific heat

C(T)

of a one-dimensional interacting Fermi system is a sum of the specific heats of free collective charge and spin excitations, plus the term with the running backscattering amplitude which flows to zero logarithmically with decreasing

T

. We verify whether this result is reproduced in the

g

-ology model. Of specific interest are the anomalous terms in

C(T)

that depend on the bare backscattering amplitude. We show that these terms can be incorporated into a renormalized spin velocity. We do this by proving the equivalence of the results for

C(T)

obtained within the

g

-ology model and by bosonization with velocities obtained by the numerical solution of the Bethe-ansatz equations for the Hubbard model.