A general approach to bosonization

David Sénéchal

En-Jui Kuo, Yijia Xu, Dominik Hangleiter +2 more

We introduce the notion of ``generalized bosons'' whose exchange statistics resemble those of bosons, but the local bosonic commutator $[a,{a}^{\ifmmode\dagger\else\textdagger\fi{}}]=1$ is replaced by an arbitrary single-mode operator that is diagonal in the generalized Fock basis. Examples of generalized bosons include boson pairs and spins. We consider the analog of the boson sampling task for these particles and observe that its output probabilities are still given by permanents, so that the results regarding hardness of sampling directly carry over. Finally, we propose implementations of generalized boson sampling in circuit-QED and ion-trap platforms.

Alexei M. Tsvelik

Fan Hong-Yi

The formalism of the generalized fermionic Bogolyubov transformation, previously by Fan and VanderLinde (1990), is extended to the bosonic case. The corresponding bosonic quasi-particle and quasi-vacuum state are derived; the bosonic generalized Bogolyubov operator is decomposed as a normal product form by the technique of integration within an ordered product (IWOP).

P. Hasenfratz, Michele Maggiore

Davide Lonigro

Generalized spin-boson (GSB) models describe the interaction between a quantum mechanical system and a structured boson environment, mediated by a family of coupling functions known as form factors. We propose an extension of the class of GSB models, which can accommodate non-normalizable form factors provided that they satisfy a weaker growth constraint, thus accounting for a rigorous description of a wider range of physical scenarios; we also show that such “singular” GSB models can be rigorously approximated by GSB models with normalizable form factors. Furthermore, we discuss in greater detail the structure of the spin-boson model with a rotating wave approximation: for this model, the result is improved via a nonperturbative approach that enables us to further extend the class of admissible form factors as well as to compute its resolvent and characterize its self-adjointness domain.