Using an imaginary-time path integral approach, we develop the perturbation theory suited to the boson Hubbard model and apply it to calculate the effects of a dilute gas of spin-polarized fermions weakly interacting with the bosons. The full theory captures both the static and the dynamic effects of the fermions on the generic superfluid-insulator phase diagram. We find that, in a homogenous system described by a single-band boson Hubbard Hamiltonian, the intrinsic perturbative effect of the fermions is to generically suppress the insulating lobes and to enhance the superfluid phase.Using an imaginary-time path integral approach, we develop the perturbation theory suited to the boson Hubbard model and apply it to calculate the effects of a dilute gas of spin-polarized fermions weakly interacting with the bosons. The full theory captures both the static and the dynamic effects of the fermions on the generic superfluid-insulator phase diagram. We find that, in a homogenous system described by a single-band boson Hubbard Hamiltonian, the intrinsic perturbative effect of the fermions is to generically suppress the insulating lobes and to enhance the superfluid phase.

arXiv:0806.2865Physical Review BDec 8, 200814 citations

Coupled Boson—Fermion Systems

C. B. Dover

Springer eBooksJan 1, 19690 citations

Efficient parametrization of the vertex function, Ω scheme, and the t,t′ Hubbard model at van Hove filling

Christoph Husemann, Manfred Salmhofer B

We propose a parametrization of the four-point vertex function in the one-loop one-particle irreducible renormalization group (RG) scheme for fermions. It is based on a decomposition of the effective two-fermion interaction into fermion bilinears that interact via exchange bosons. The numerical computation of the RG flow of the boson propagators reproduces the leading weak-coupling instabilities of the two-dimensional Hubbard model at van Hove filling as they were obtained in a temperature RG scheme [C. Honerkamp and M. Salmhofer, Phys. Rev. B 64, 184516 (2001)]. Instead of regularizing with temperature, we here use a soft frequency $\ensuremath{\Omega}$ regularization that likewise does not artificially suppress ferromagnetism. Besides being more efficient than previous $N$ -patch schemes, this parametrization also reduces the ambiguities in introducing boson fields.We propose a parametrization of the four-point vertex function in the one-loop one-particle irreducible renormalization group (RG) scheme for fermions. It is based on a decomposition of the effective two-fermion interaction into fermion bilinears that interact via exchange bosons. The numerical computation of the RG flow of the boson propagators reproduces the leading weak-coupling instabilities of the two-dimensional Hubbard model at van Hove filling as they were obtained in a temperature RG scheme [C. Honerkamp and M. Salmhofer, Phys. Rev. B 64, 184516 (2001)]. Instead of regularizing with temperature, we here use a soft frequency $\ensuremath{\Omega}$ regularization that likewise does not artificially suppress ferromagnetism. Besides being more efficient than previous $N$-patch schemes, this parametrization also reduces the ambiguities in introducing boson fields.

arXiv:0812.3824Physical Review BMay 26, 2009186 citations

Correlated Fermion Systems on a Lattice: Hubbard Model

WORLD SCIENTIFIC eBooksMar 5, 20170 citations

N

-patch schemes, this parametrization also reduces the ambiguities in introducing boson fields.