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arXiv:cond-mat/0005395 · Physical review. B, Condensed matter

Effects of boson dispersion in fermion-boson coupled systems

Yukitoshi Motome, Gabriel Kotliar

Published Nov 15, 2000• 20 citations
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Abstract

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.

DOI
10.1103/physrevb.62.12800

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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.
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 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
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.
Using the bosonization approach, we study fermionic systems with a nonlinear dispersion relation in dimension d> 2.d>~2.d> 2. We explicitly show how the band curvature gives rise to interaction terms in the bosonic version of the model. Although these terms are perturbatively irrelevant in relation to the Landau Fermi-liquid fixed point, they become relevant perturbations when instabilities take place. Using a coherent-state path-integral technique, we built up the effective action that governs the dynamics of the Fermi-surface fluctuations. We consider the combined effect of fermionic interactions and band curvature on possible anisotropic phases triggered by negative Landau parameters (Pomeranchuck instabilities). In particular, we study in some detail the phase diagram for the isotropic/nematic/hexatic quantum phase transition.
We develop an effective field theory to describe the superfluid pairing in strongly interacting fermions with arbitrary short-range attractions by extending Kaplan's idea of coupling fermions to a fictitious boson state [presented in Nucl. Phys. B 494, 471 (1997)]. This boson field is assigned with an unconventional kinetic term to recover the exact scattering phase shift obtained either from scattering data or model calculations. The theory works even if the explicit form of the interaction potential has not been constructed from scattering data. The contact boson-fermion coupling allows us to go beyond mean-field to include Gaussian pair fluctuations, yielding reliable predictions on equations of state. As an application, we use our theory to address the nonuniversal ground-state energy of strongly paired fermions due to the nontrivial momentum dependence of the phase shift characterized, for example, by effective range. We find a good agreement between our predictions and recent quantum Monte Carlo simulations on the effective-range dependence in both three and two spatial dimensions. We propose that in cold-atom experiments, the nonuniversal dependence in thermodynamics can be probed using dark-state optical control of Feshbach resonances.
The interaction effects in ultracold Fermi gases with SU(N) symmetry are studied nonperturbatively in half filled one-dimensional lattices by employing quantum Monte Carlo simulations. We find that, as N increases, weak and strong interacting systems are driven to a crossover region, but from opposite directions as a convergence of itinerancy and Mottness. In the weak interaction region, particles are nearly itinerant, and interparticle collisions are enhanced by N, resulting in the amplification of interaction effects. In contrast, in the strong coupling region, increasing N softens the Mott-insulating background through the enhanced virtual hopping processes. The crossover region exhibits nearly N-independent physical quantities, including the relative bandwidth, Fermi distribution, and the spin structure factor. The difference between even-N and odd-N systems is most prominent at small N's with strong interactions, since the odd case allows local real hopping with an energy scale much larger than the virtual one. The above effects can be experimentally tested in ultracold atom experiments with alkaline-earth(-like) fermions such as ^{87}Sr (^{173}Yb).