Slave Bosons in Radial Gauge: the Correct Functional Integral Representation and Inclusion of Non-Local Interactions

Abstract

We introduce a new path integral representation for slave bosons in the radial gauge which is valid beyond the conventional fluctuation corrections to a mean-field solution. For electronic lattice models, defined on the constrained Fock space with no double occupancy, all phase fluctuations of the slave particles can be gauged away if the Lagrange multipliers which enforce the constraint on each lattice site are promoted to time-dependent fields. Consequently, only the amplitude (radial part) of the slave boson fields survives. It has the special property that it is equal to its square in the physical subspace. This renders the functional integral for the radial field Gaussian, even when non-local Coulomb-type interactions are included. We propose i) a continuum integral representation for the set-up of further approximation schemes, and ii) a discrete representation with an Ising-like radial variable, valid for long-ranged interactions as well. The latter scheme can be taken as a starting point for numerical evaluations.

16 pages, 2 figures, minor modifications

References in corpus (1)

• Compressibility of the Two-Dimensional infinite-U Hubbard Model

Cited by in corpus (20)

• Slave-boson approach to the metallic stripe phases with large unit cells
• Rotationally-invariant slave-bosons for Strongly Correlated Superconductors
• Slave bosons in radial gauge: a bridge between path integral and hamiltonian language
• Collective modes in the paramagnetic phase of the Hubbard model
• Capacitance and compressibility of heterostructures with strong electronic correlations
• Fermi-liquid Landau parameters for a nondegenerate band: Spin and charge instabilities in the extended Hubbard model
• Exact results with the Kotliar-Ruckenstein slave-boson representation
• Spin and charge modulations of a half-filled extended Hubbard model
• The Functional Integral formulation of the Schrieffer-Wolff transformation
• Barnes slave boson approach to the two-site single impurity Anderson model with non-local interaction
• Combining complex and radial slave boson fields within the Kotliar-Ruckenstein representation of correlated impurities
• Exact results in a slave boson saddle point approach for a strongly correlated electron model
• Charge instabilities of the extended attractive Hubbard Model on the cubic lattice
• Charge instabilities of the two-dimensional Hubbard model with attractive nearest neighbour interaction
• Particle-hole symmetry of charge excitation spectra in the paramagnetic phase of the Hubbard model
• Exact functional integration of radial and complex slave-boson fields: thermodynamics and dynamics of the two-site extended Hubbard model
• Charge Collective Modes in Correlated Electron Systems: Plasmons Beyond the Random Phase Approximation
• Effect of the next-nearest-neighbor hopping on the charge collective modes in the paramagnetic phase of the Hubbard model
• Bad metal and negative compressibility transitions in a two-band Hubbard model
• Phase coexistence in a half-filled extended Hubbard model