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AIP conference proceedings

Fluctuation effects by boson dispersion in fermion-boson coupled systems

Yukitoshi Motome

Published Jan 1, 2001• 0 citations
Publisher

Abstract

Nonlinear feedback effects due to dispersive bosons are studied in fermion-boson coupled systems by using an extension of dynamical mean-field theory. In the nonperturbative regime, strong coupling and nonadiabaticity reduce effective interaction between fermions as the width of boson dispersion increases. The boson field is completely softened at the crossover to this regime. The softening is significantly enhanced by the boson dispersion. We elucidate the controlling parameters of this nonperturbative regime where fluctuations of the dispersive bosons accelerate the delocalization of fermions.

DOI
10.1063/1.1363065

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Nonlinear feedback effects due to dispersive bosons are studied in fermion-boson coupled systems by using an extension of dynamical mean-field theory. In the nonperturbative regime, strong coupling and nonadiabaticity reduce effective interaction between fermions as the width of boson dispersion increases. The boson field is completely softened at the crossover to this regime. The softening is significantly enhanced by the boson dispersion. We elucidate the controlling parameters of this nonperturbative regime where fluctuations of the dispersive bosons accelerate the delocalization of fermions.
We study the nonlinear feedback in a fermion-boson system using an extension of dynamical mean-field theory and the quantum Monte Carlo method. In the perturbative regimes (weak-coupling and atomic limits) the effective interaction among fermions increases as the width of the boson dispersion increases. In the strong-coupling regime away from the antiadiabatic limit, the effective interaction decreases as we increase the width of the boson dispersion. This behavior is closely related to complete softening of the boson field. We elucidate the parameters that control this nonperturbative region where fluctuations of the dispersive bosons enhance the delocalization of fermions.
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.
We study the mean-field dynamic of a interacting boson-fermion mixture in an harmonic trap, by means of a Gaussian variational ansatz. We find concentric stationary solutions in the repulsive regime and in the regime of weak boson-fermion attraction. Above a threshold value of the repulsion parameter, a stable symmetry-broken stationary solution bifurcates, characterized by the displacement of the center of mass of the bosonic and fermionic clouds in opposite directions away from the trap center. We observe linear and nonlinear oscillations of the width and center of mass of the boson and fermion distributions whenever we let the system evolve starting from a non stationary initial condition. Advisor: Dr. Nicola Manini Co-Advisor: Dr. Luca Salasnich
The boson-fermion model, describing a mixture of itinerant electrons hybridizing with tightly bound electron pairs represented as hardcore bosons, is here generalized with the inclusion of a term describing on-site Coulomb repulsion between fermions with opposite spins. Within the general framework of the dynamical mean-field theory, it is shown that around the symmetric limit of the model this interaction strongly competes with the local boson-fermion exchange mechanism, smoothly driving the system from a pseudogap phase with poor conducting properties to a metallic regime characterized by a substantial reduction of the fermionic density. On the other hand, if one starts from correlated fermions described in terms of the one-band Hubbard model, the introduction in the half-filled insulating phase of a coupling with hardcore bosons leads to the disappearance of the correlation gap, with a consequent smooth crossover to a metallic state.
The boson-fermion model, describing a mixture of tightly bound electron pairs and quasifree electrons hybridized with each other via a charge exchange term, is studied in the limit of infinite dimensions using the noncrossing approximation within the dynamical mean field theory. It is shown that a metal-insulator crossover, driven by strong pair fluctuations, takes place as the temperature is lowered. It manifests itself in the opening of a pseudogap in the electron density of states, accompanied by a corresponding effect in the optical and the dc conductivity.
Entanglement fluctuations associated with the Schrödinger evolution of wave functions offer a unique perspective on various fundamental issues ranging from quantum thermalization to state preparation in quantum devices. Very recently, a subset of the present authors showed that, in a class of free-fermion lattice models and interacting spin chains, entanglement dynamics enters into a new regime at long time, with entanglement probes displaying persistent temporal fluctuations, whose statistics falls into the seemingly disparate paradigm of mesoscopic fluctuations in condensed-matter physics. This motivates us to revisit here entanglement dynamics of a canonical bosonic model in many-body physics, i.e., a coupled harmonic oscillator chain. We find that when the system is driven out of equilibrium, the long-time entanglement dynamics exhibits strictly the same statistical behaviors as those of free-fermion models. Specifically, irrespective of entanglement probes and microscopic parameters, the statistical distribution of entanglement fluctuations is flanked by asymmetric tails: sub-Gaussian for upward fluctuations and sub-Gamma for downward; moreover, the variance exhibits a crossover from the scaling ∼ 1 / L to ∼ L A 3 / L 2 as the subsystem size L A increases ( L the total system size). This insensitivity to the particle statistics, dubbed boson-fermion universality, is contrary to the common wisdom that statistical phenomena of a many-body nature depend strongly on particle statistics. Together with our previous work, the present study indicates rich fluctuation phenomena in long-time entanglement dynamics that await in-depth exploration.