Interaction of classical fermions with bosons

Morikazu TODA

Harriet Apel, Burak Şahinoğlu

Simulating interactions between fermions and bosons is central to understanding correlated phenomena, yet these systems are inherently difficult to treat classically. Previous quantum algorithms for fermion-boson models exhibit computation costs that scale polynomially with the bosonic truncation parameter, $Λ$. In this work we identify the efficient unitary transformation enabling fast-forwarded evolution of the fermion-boson interaction term, yielding an interaction-picture based simulation algorithm with complexity polylogarithmic in $Λ$. We apply this transformation to explicitly construct an efficient quantum algorithm for the Hubbard-Holstein model and discuss its generalisation to other fermion-boson interacting models. This approach yields an important asymptotic improvement in the dependence on the bosonic cutoff and establishes that, for certain models, fermion-boson interactions can be simulated with resources comparable to those required for purely fermionic systems.

Jing Sun, Sudip Sasmal, Oriol Vendrell

We consider the application of the original Meyer-Miller (MM) Hamiltonian to mapping fermionic quantum dynamics to classical equations of motion. Non-interacting fermionic and bosonic systems share the same one-body density dynamics when evolving from the same initial many-body state. The MM classical mapping is exact for non-interacting bosons, and therefore, it yields the exact time-dependent one-body density for non-interacting fermions as well. Starting from this observation, the MM mapping is compared to different mappings specific for fermionic systems, namely, the spin mapping with and without including a Jordan-Wigner transformation and the Li-Miller mapping (LMM). For non-interacting systems, the inclusion of fermionic anti-symmetry through the Jordan-Wigner transform does not lead to any improvement in the performance of the mappings, and instead, it worsens the classical description. For an interacting impurity model and for models of excitonic energy transfer, the MM and LMM mappings perform similarly, and in some cases, the former outperforms the latter when compared to a full quantum description. The classical mappings are able to capture interference effects, both constructive and destructive, that originate from equivalent energy transfer pathways in the models.

Morikazu Toda

Thierry Giamarchi, Pierre Le Doussal, E. Orignac

We study the competition between a random potential and a commensurate potential on interacting fermionic and bosonic systems using a variety of methods. We focus on one-dimensional interacting fermionic systems, but higher-dimensional bosonic and fermionic extensions, as well as classical equivalents, are also discussed. Our methods, which include the bosonization method, the replica variational method, the functional renormalization group method, and perturbation around the atomic limit, go beyond conventional perturbative expansions around the Luttinger liquid in one dimension. All these methods agree on the prediction in these systems of a phase, the Mott glass, intermediate between the Anderson (compressible, with a pseudogap in the optical conductivity) and the Mott (incompressible with a gap in the optical conductivity) insulator. The Mott glass, which was unexpected from a perturbative renormalization-group point of view has a pseudogap in the conductivity while remaining incompressible. Having derived the existence of a Mott glass phase in one dimension, we show qualitatively that its existence can also be expected in higher dimensions. We discuss the relevance of this phase to experimental systems such as disordered classical elastic systems and dirty bosons.

V. A. Yatsun