Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0701626 · Nuclear Physics B

Slave bosons in radial gauge: A bridge between path integral and Hamiltonian language

Raymond Frésard, Henni Ouerdane, Thilo Kopp

Published Jun 8, 2007• 28 citations
arXivHTMLPDF
DOI
10.1016/j.nuclphysb.2007.05.025

Related papers

Slave bosons in radial gauge: the correct functional integral representation and inclusion of non-local interactions

Raymond Frésard, Thilo Kopp

arXiv:cond-mat/0011296•Nuclear Physics B•Feb 1, 2001•25 citations

Slave fermions, slave bosons, and semions from bosonization of the two-dimensionalt-Jmodel

Jürg Martin Fröhlich, P. A. Marchetti

We extend Abelian and non-Abelian bosonization formulas found in a previous paper, in combination with coherent-state methods, to present a systematic derivation of the slave-fermion, slave-boson, and semion representations of the two-dimensional t-J model in path-integral form. The slave-fermion and slave-boson representations are shown to arise from two different gauge fixing constraints introduced in the path-integral representation of the bosonized t-J model. For each representation we discuss the approximations leading to a mean-field theory. In the mean-field theory based on the semion representation, the holons are shown to be ``Dirac semions.''

Physical review. B, Condensed matter•Sep 1, 1992•45 citations

Combining Complex and Radial Slave Boson Fields within the Kotliar–Ruckenstein Representation of Correlated Impurities

Vu Hung Dao, Raymond Frésard

Abstract The gauge symmetry group of any slave boson representation allows to gauge away the phase of bosonic fields. One benefit of this radial field formulation is the elimination of spurious Bose condensations when saddle‐point approximation is performed. Within the Kotliar–Ruckenstein representation, three of the four bosonic fields can be radial while the last one has to remain complex. In this work, the procedure to carry out the functional integration involving constrained fermionic fields, complex bosonic fields, and radial bosonic fields is presented. The correctness of the representation is verified by exactly evaluating the partition function and the Green's function of the Hubbard model in the atomic limit.

arXiv:1910.11787•Annalen der Physik•Dec 4, 2019•8 citations

Path Integral Treatment of Interacting Bosons or Fermions

J. T. Devreese, L. F. Lemmens, F. Brosens

•Jun 14, 2017•0 citations

Path Integrals for Bosons

Abdulla Rakhimov, Sh. Mardonov

Lecture notes in physics•Jan 1, 2026•0 citations

Exact results with the Kotliar‐Ruckenstein slave‐boson representation

Raymond Frésard, Thilo Kopp

Abstract Radial slave boson representations have the particular advantage that the expectation values of their respective fields are finite even without the formal introduction of spurious Bose condensates for each of the bosonic fields. The expectation values of the radial (real) fields are in fact to be interpreted as the density of empty or singly occupied sites. Whereas the radial representation of the Barnes slave bosons has been investigated before, a setup for the functional integral of radial bosonic fields in the more physical Kotliar‐Ruckenstein representation has not been accomplished to date. We implement a path integral procedure with suitable renormalization factors for a strongly correlated two‐site model which allows to control the formal steps in the intricate evaluation, as the results for the partition function and the expectation values are known from exact diagonalization for such a minimal single impurity Anderson model. The partition function is shown to be a trace over a product of matrices local in time and therefore can be calculated analytically. Eventually, we establish the scheme for the evaluation of correlation functions and thermodynamic properties.

arXiv:1205.0421•Annalen der Physik•Jan 26, 2012•15 citations
We extend Abelian and non-Abelian bosonization formulas found in a previous paper, in combination with coherent-state methods, to present a systematic derivation of the slave-fermion, slave-boson, and semion representations of the two-dimensional t-J model in path-integral form. The slave-fermion and slave-boson representations are shown to arise from two different gauge fixing constraints introduced in the path-integral representation of the bosonized t-J model. For each representation we discuss the approximations leading to a mean-field theory. In the mean-field theory based on the semion representation, the holons are shown to be ``Dirac semions.''
Abstract The gauge symmetry group of any slave boson representation allows to gauge away the phase of bosonic fields. One benefit of this radial field formulation is the elimination of spurious Bose condensations when saddle‐point approximation is performed. Within the Kotliar–Ruckenstein representation, three of the four bosonic fields can be radial while the last one has to remain complex. In this work, the procedure to carry out the functional integration involving constrained fermionic fields, complex bosonic fields, and radial bosonic fields is presented. The correctness of the representation is verified by exactly evaluating the partition function and the Green's function of the Hubbard model in the atomic limit.
Abstract Radial slave boson representations have the particular advantage that the expectation values of their respective fields are finite even without the formal introduction of spurious Bose condensates for each of the bosonic fields. The expectation values of the radial (real) fields are in fact to be interpreted as the density of empty or singly occupied sites. Whereas the radial representation of the Barnes slave bosons has been investigated before, a setup for the functional integral of radial bosonic fields in the more physical Kotliar‐Ruckenstein representation has not been accomplished to date. We implement a path integral procedure with suitable renormalization factors for a strongly correlated two‐site model which allows to control the formal steps in the intricate evaluation, as the results for the partition function and the expectation values are known from exact diagonalization for such a minimal single impurity Anderson model. The partition function is shown to be a trace over a product of matrices local in time and therefore can be calculated analytically. Eventually, we establish the scheme for the evaluation of correlation functions and thermodynamic properties.