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

Fermionic linearization approach to interacting electron systems

Arianna Montorsi

Published Jan 1, 1991• 2 citations
OpenAlex

Abstract

We review here the fermi-linarization approach to interacting electron systems. We focus our attention on its application to a particular version of the K.S.S.H. model, which has recently been solved exacty, and was found to exhibit a Mott-transition. Indeed, also our mean-field approach seems to describe, at half filling and for sufficiently low temperature, two different phases, depending on the Coulomb repulsion strenght.

Related papers

BETHE APPROXIMATION SCHEME FOR ITINERANT ELECTRON SYSTEMS

MARIA BECHI, Roberto Livi, Arianna Montorsi

After reviewing the fermi-linearization approach to interacting electron systems, we propose here a refinement of the method based on the extension to itinerant ferminon systems of the philosophy of the Bethe-Peierls treatment of classical systems. We focus our attention on a Hubbard-like model, deriving a general self-consistent scheme which we solve explicitly in the simplest case. We obtain a rich phase-space, exhibiting in particular two phase transitions depending on the band filling. Among the results, we discuss in detail the local magnetic moment, by comparing the outcome of our scheme to some known numerical results in one and two dimensions respectively.

International Journal of Modern Physics B•Nov 10, 1991•0 citations

Enhanced Strange Metallicity due to Hubbard- U Coulomb Repulsion

Andrew Hardy, Olivier Parcollet, Antoine Georges +1 more

We solve a model of electrons with Hubbard-U Coulomb repulsion and a random Yukawa coupling to a two-dimensional bosonic bath, using an extended dynamical mean field theory scheme. Our model exhibits a quantum critical point, at which the repulsive component of the electron interactions strongly enhances the effects of the quantum critical bosonic fluctuations on the electrons, leading to a breakdown of Fermi liquid physics and the formation of a strange metal with "Planckian" [O(k_{B}T/ℏ)] quasiparticle decay rates at low temperatures T→0. Furthermore, the eventual Mott transition that occurs as the repulsion is increased seemingly bounds the maximum decay rate in the strange metal. Our results provide insight into low-temperature strange metallicity observed in proximity to a Mott transition, as is observed, for instance, in recent experiments on certain moiré materials.

arXiv:2407.21102•Physical Review Letters•Jan 23, 2025•10 citations

SUPERFLUID, STAGGERED STATE, AND MOTT INSULATOR OF REPULSIVELY INTERACTING THREE-COMPONENT FERMIONIC ATOMS IN OPTICAL LATTICES

KENSUKE INABA, SEI-ICHIRO SUGA

We review our theoretical analysis of repulsively interacting three-component fermionic atoms in optical lattices. We discuss quantum phase transitions at around half filling with a balanced population by focusing on Mott transitions, staggered ordering, and superfluidity. At half filling (with 3/2 atoms per site), characteristic Mott transitions are induced by the anisotropic interactions, where two-particle repulsions between any two of the three colors have different strengths. At half filling, two types of staggered ordered states appear at low temperatures depending on the anisotropy of the interactions. As the temperature increases, phase transitions occur from the staggered ordered states to the unordered Mott states. Deviating from half filling, an exotic superfluid state appears close to a regime in which the Mott transition occurs. We explain the origin of these phase transitions and present the finite-temperature phase diagrams.

arXiv:1305.1972•Modern Physics Letters B•Apr 11, 2013•14 citations

Bosonization of Fermi gases

Phan Thành Nam

We review the bosonization method for Fermi gases, initiated by Sawada, Bohm–Pines, and Gell-Mann–Brueckner in the 1950s, and present recent rigorous results that justify this approach in the mean-field regime with regular and Coulomb interactions, as well as in the low-density regime leading to the Huang–Yang formula. We also discuss some open questions on related topics.

Journal of Mathematical Physics•Mar 1, 2026•0 citations

Fermi linearization scheme for itinerant electrons with Clifford variables

Arianna Montorsi, Alessandro Pelizzola

The authors propose an alternative interpretation of the Fermi linearization approach to interacting electron systems, based on the requirement that the coefficients of the linearized operators are Clifford-like variables, whose anticommutator equals an unknown constant c. They apply the approximation to the Falicov-Kimball model (1969), explicitly solving the self-consistency equation for the unknown, which turns out to behave as an order parameter. They discuss its relation with a metal-insulator transition and some thermodynamical quantities. In particular they show that the approximation in the T=0 limit reproduces exactly the Gutzwiller results (1965) for the Hubbard model.

arXiv:cond-mat/9209018•Journal of Physics A Mathematical and General•Nov 21, 1992•6 citations

Orbital-selective crossover and Mott transitions in an asymmetric Hubbard model of cold atoms in optical lattices

Emilio A. Winograd, R. Chitra, Marcelo J. Rozenberg

We study the asymmetric Hubbard model at half filling as a generic model to describe the physics of two species of repulsively interacting fermionic cold atoms in optical lattices. We use dynamical mean-field theory to obtain the paramagnetic phase diagram of the model as a function of temperature, interaction strength, and hopping asymmetry. A Mott transition with a region of two coexistent solutions is found for all nonzero values of the hopping asymmetry. At low temperatures the metallic phase is a heavy Fermi liquid, qualitatively analogous to the Fermi-liquid state of the symmetric Hubbard model. Above a coherence temperature, an orbital-selective crossover takes place, wherein one fermionic species effectively localizes, and the resulting bad metallic state resembles the non-Fermi-liquid state of the Falicov-Kimball model. We compute observables relevant to cold atom systems such as the double occupation, the specific heat, and entropy, and characterize their behavior in the different phases.

arXiv:1201.2068•Physical Review B•Dec 8, 2011•14 citations
We review here the fermi-linarization approach to interacting electron systems. We focus our attention on its application to a particular version of the K.S.S.H. model, which has recently been solved exacty, and was found to exhibit a Mott-transition. Indeed, also our mean-field approach seems to describe, at half filling and for sufficiently low temperature, two different phases, depending on the Coulomb repulsion strenght.
After reviewing the fermi-linearization approach to interacting electron systems, we propose here a refinement of the method based on the extension to itinerant ferminon systems of the philosophy of the Bethe-Peierls treatment of classical systems. We focus our attention on a Hubbard-like model, deriving a general self-consistent scheme which we solve explicitly in the simplest case. We obtain a rich phase-space, exhibiting in particular two phase transitions depending on the band filling. Among the results, we discuss in detail the local magnetic moment, by comparing the outcome of our scheme to some known numerical results in one and two dimensions respectively.
We solve a model of electrons with Hubbard-U Coulomb repulsion and a random Yukawa coupling to a two-dimensional bosonic bath, using an extended dynamical mean field theory scheme. Our model exhibits a quantum critical point, at which the repulsive component of the electron interactions strongly enhances the effects of the quantum critical bosonic fluctuations on the electrons, leading to a breakdown of Fermi liquid physics and the formation of a strange metal with "Planckian" [O(k_{B}T/ℏ)] quasiparticle decay rates at low temperatures T→0. Furthermore, the eventual Mott transition that occurs as the repulsion is increased seemingly bounds the maximum decay rate in the strange metal. Our results provide insight into low-temperature strange metallicity observed in proximity to a Mott transition, as is observed, for instance, in recent experiments on certain moiré materials.
We review our theoretical analysis of repulsively interacting three-component fermionic atoms in optical lattices. We discuss quantum phase transitions at around half filling with a balanced population by focusing on Mott transitions, staggered ordering, and superfluidity. At half filling (with 3/2 atoms per site), characteristic Mott transitions are induced by the anisotropic interactions, where two-particle repulsions between any two of the three colors have different strengths. At half filling, two types of staggered ordered states appear at low temperatures depending on the anisotropy of the interactions. As the temperature increases, phase transitions occur from the staggered ordered states to the unordered Mott states. Deviating from half filling, an exotic superfluid state appears close to a regime in which the Mott transition occurs. We explain the origin of these phase transitions and present the finite-temperature phase diagrams.
The authors propose an alternative interpretation of the Fermi linearization approach to interacting electron systems, based on the requirement that the coefficients of the linearized operators are Clifford-like variables, whose anticommutator equals an unknown constant c. They apply the approximation to the Falicov-Kimball model (1969), explicitly solving the self-consistency equation for the unknown, which turns out to behave as an order parameter. They discuss its relation with a metal-insulator transition and some thermodynamical quantities. In particular they show that the approximation in the T=0 limit reproduces exactly the Gutzwiller results (1965) for the Hubbard model.
We study the asymmetric Hubbard model at half filling as a generic model to describe the physics of two species of repulsively interacting fermionic cold atoms in optical lattices. We use dynamical mean-field theory to obtain the paramagnetic phase diagram of the model as a function of temperature, interaction strength, and hopping asymmetry. A Mott transition with a region of two coexistent solutions is found for all nonzero values of the hopping asymmetry. At low temperatures the metallic phase is a heavy Fermi liquid, qualitatively analogous to the Fermi-liquid state of the symmetric Hubbard model. Above a coherence temperature, an orbital-selective crossover takes place, wherein one fermionic species effectively localizes, and the resulting bad metallic state resembles the non-Fermi-liquid state of the Falicov-Kimball model. We compute observables relevant to cold atom systems such as the double occupation, the specific heat, and entropy, and characterize their behavior in the different phases.