Entanglement dynamics in itinerant fermionic and bosonic systems

Allana Doughty, Anastasia A. Baboolal

O. S. Zozulya, Masudul Haque, Kareljan Schoutens

For itinerant fermionic and bosonic systems, we study ``particle entanglement,'' defined as the entanglement between two subsets of particles making up the system. We formulate the general structure of particle entanglement in many-fermion ground states, analogous to the ``area law'' for the more usually studied entanglement between spatial regions. Basic properties of particle entanglement are uncovered by considering relatively simple itinerant models.

Luís Miguel Martelo, Natan Andrei

The progress in ultra-cold atoms experiments allowing to tune fermionic systems through a Feshbach resonance where itinerant fermionic atoms may form tightly bound pairs ("bosonic" molecules) [1,2] has led to a renewed theoretical interest in boson-fermion models. We study a 1D boson fermion resonance model describing itinerant spin-1/2 fermions and itinerant scalar bosons coupled through a local interaction of strength g, which describes the binding of a pair of opposite spin fermions to form a scalar boson and the reverse process. The model also includes a detuning term characterized by a detuning parameter ν. It is found that the model has an exact solution by Bethe Ansatz.

Bei Zeng

T. Domański, J. Ranninger

We address ourselves to a class of systems composed of two coupled subsystems without any intrasubsystem interaction: itinerant fermions and localized bosons on a lattice. Switching on an interaction between the two subsystems leads to feedback effects which result in a rich dynamical structure in both of them. Such feedback features are studied on the basis of the flow equation technique---an infinite series of infinitesimal unitary transformations---which leads to a gradual elimination of the intersubsystem interaction. As a result the two subsystems get decoupled but their renormalized kinetic energies become mutually dependent on each other. Choosing for the intersubsystem interaction a charge exchange term,---the boson-fermion model---the initially localized bosons acquire itinerancy through their dependence on the renormalized fermion dispersion. This latter evolves from a free particle dispersion into one showing a pseudogap structure near the chemical potential. Upon lowering the temperature both subsystems simultaneously enter a macroscopic coherent quantum state. The bosons become superfluid, exhibiting a soundwavelike dispersion while the fermions develop a true gap in their dispersion. The essential physical features described by this technique are already contained in the renormalization of the kinetic terms in the respective Hamiltonians of the two subsystems. The extra interaction terms resulting in the process of iteration only strengthen this physics. We compare the results with previous calculations based on self-consistent perturbative approaches.

Hernán Santos, J. E. Alvarellos, Javier Rodríguez-Laguna