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

Modern Physics Letters B

THE DIMER-CLUSTER FERMI-LINEARIZED HUBBARD MODEL: GROUND STATE AND PHASE SPACE

Arianna Montorsi, Mario Rasetti

Published May 10, 1990• 5 citations
Publisher

Abstract

The zero temperature phase space for the Hubbard model is constructed — in the frame of fermionic linearization with a two-site (dimer) cluster — resorting to its ground state, realized in the form of supercoherent state for the model dynamical superalgebra. Such phase space is characterized by the existence of regions in which the pairing order parameter is different from zero.

DOI
10.1142/s0217984990000763

Related papers

THERMODYNAMICS OF THE FERMI-LINEARIZED EXTENDED HUBBARD MODEL

Andrea Danani, Arianna Montorsi, Mario Rasetti

The fermi linearization scheme for a two-site cluster (dimer) is applied to the extended Hubbard model, including Coulomb interaction between nearest neighbour sites. The partition function and the order parameter, as well as the average double-occupation and local magnetic moment are evaluated. The theory is checked by extended numerical analysis, performed here in the homogeneous case, when pairing is zero, and deriving the explicit temperature and filling dependence of the above quantities. An interesting feature that emerges from such calculations is that the mean-field parameter characteristic of fermi-linearization is capable of describing two different phases, one of which is not present in the conventional Hubbard model. The order parameters corresponding to the two phases are explicitly derived. The novel phase can be ascribed to the n.n. Coulomb interaction, the role of whose strength V is analysed.

International Journal of Modern Physics B•Nov 20, 1992•1 citation

The dimer Fermi-linearized Hubbard model: ground state and phase space

Arianna Montorsi, Mario Rasetti

•Jan 1, 1990•0 citations

Phase Diagrams and Charge-Spin Separation in Two and Four Site Hubbard Clusters

ARMEN N. KOCHARIAN, Gayanath Fernando, J. W. Davenport

The charge spin-separation, pseudogap formation and phase diagrams are studied in two and four site Hubbard clusters using analytical diagonalization and grand canonical ensemble method in a multidimensional parameter space of temperature, magnetic field, on-site Coulomb interaction ($U\ge 0$), and chemical potential. The numerically evaluated, exact expressions for charge and spin susceptibilities provide clear evidence for the existence of true gaps in the ground state and pseudogaps in a limited range of temperature. In particular, Mott-Hubbard type charge crossover, spin pseudogap and magnetic correlations with antiferromagnetic (spin) pseudogap structure for two and four site clusters closely resemble the pseudogap phenomena and the normal-state phase diagram in high T$_c$ superconductors. ~ ~

arXiv:cond-mat/0510609•Oct 23, 2005•1 citation

Myriad phases of the checkerboard Hubbard model

Hong Yao, Wei-Feng Tsai, Steven Allan Kivelson

The zero-temperature phase diagram of the checkerboard Hubbard model is obtained in the solvable limit in which it consists of weakly coupled square plaquettes. As a function of the on-site Coulomb repulsion $U$ and the density of holes per site, $x$, we demonstrate the existence of at least 16 distinct phases. For instance, at zero doping, the ground state is a novel $d$-wave Mott insulator ($d$-Mott), which is not adiabatically continuable to a band insulator; by doping the $d$-Mott state with holes, depending on the magnitude of $U$, it gives way to a $d$-wave superconducting state, a two-flavor spin-$1∕2$ Fermi liquid (FL), or a spin-$3∕2$ FL.

arXiv:0706.0761•Physical Review B•Oct 24, 2007•52 citations

Cluster perturbation theory in Hubbard model exactly taking into account the short-range magnetic order in 2 × 2 cluster

Sergey V. Nikolaev, Sergei G. Ovchinnikov

The cluster perturbation theory is presented in the 2D Hubbard model constructed using X operators in the Hubbard-I approximation. The short-range magnetic order is taken into account by dividing the entire lattice into individual 2 × 2 clusters and solving the eigenvalue problem in an individual cluster using exact diagonalization taking into account all excited levels. The case of half-filling taking into account jumps between nearest neighbors is considered. As a result of numerical solution, a shadow zone is discovered in the quasiparticle spectrum. It is also found that a gap in the density of states in the quasiparticle spectrum at zero temperature exists for indefinitely small values of Coulomb repulsion parameter U and increases with this parameter. It is found that the presence of this gap in the spectrum is due to the formation of a short-range antiferromagnetic order. An analysis of the temperature evolution of the density of states shows that the metal-insulator transition occurs continuously. The existence of two characteristic energy scales at finite temperatures is demonstrated, the larger scale is associated with the formation of a pseudogap in the vicinity of the Fermi level, and the smaller scale is associated with the metal-insulator transition temperature. A peak in the density of states at the Fermi level, which is predicted in the dynamic mean field theory in the vicinity of the metal-insulator transition, is not observed.

Journal of Experimental and Theoretical Physics•Oct 1, 2010•15 citations

Variational ground states of the two-dimensional Hubbard model

D. Baeriswyl, David Eichenberger, M. Z. Menteshashvili

Recent refinements of analytical and numerical methods have improved our understanding of the ground-state phase diagram of the two-dimensional (2D) Hubbard model. Here, we focus on variational approaches, but comparisons with both quantum cluster and Gaussian Monte Carlo methods are also made. Our own ansatz leads to an antiferromagnetic ground state at half filling with a slightly reduced staggered order parameter (as compared to simple mean-field theory). Away from half filling, we find d-wave superconductivity, but confined to densities where the Fermi surface passes through the antiferromagnetic zone boundary (if hopping between both nearest-neighbour and next-nearest-neighbour sites is considered). Our results agree surprisingly well with recent numerical studies using the quantum cluster method. An interesting trend is found by comparing gap parameters Δ (antiferromagnetic or superconducting) obtained with different variational wave functions. Δ varies by an order of magnitude and thus cannot be taken as a characteristic energy scale. In contrast, the order parameter is much less sensitive to the degree of sophistication of the variational schemes, at least at and near half filling.

arXiv:0907.1593•New Journal of Physics•Jul 23, 2009•45 citations
The zero temperature phase space for the Hubbard model is constructed — in the frame of fermionic linearization with a two-site (dimer) cluster — resorting to its ground state, realized in the form of supercoherent state for the model dynamical superalgebra. Such phase space is characterized by the existence of regions in which the pairing order parameter is different from zero.
The fermi linearization scheme for a two-site cluster (dimer) is applied to the extended Hubbard model, including Coulomb interaction between nearest neighbour sites. The partition function and the order parameter, as well as the average double-occupation and local magnetic moment are evaluated. The theory is checked by extended numerical analysis, performed here in the homogeneous case, when pairing is zero, and deriving the explicit temperature and filling dependence of the above quantities. An interesting feature that emerges from such calculations is that the mean-field parameter characteristic of fermi-linearization is capable of describing two different phases, one of which is not present in the conventional Hubbard model. The order parameters corresponding to the two phases are explicitly derived. The novel phase can be ascribed to the n.n. Coulomb interaction, the role of whose strength V is analysed.
The charge spin-separation, pseudogap formation and phase diagrams are studied in two and four site Hubbard clusters using analytical diagonalization and grand canonical ensemble method in a multidimensional parameter space of temperature, magnetic field, on-site Coulomb interaction (U≥0U\ge 0U≥0), and chemical potential. The numerically evaluated, exact expressions for charge and spin susceptibilities provide clear evidence for the existence of true gaps in the ground state and pseudogaps in a limited range of temperature. In particular, Mott-Hubbard type charge crossover, spin pseudogap and magnetic correlations with antiferromagnetic (spin) pseudogap structure for two and four site clusters closely resemble the pseudogap phenomena and the normal-state phase diagram in high Tc_cc​ superconductors. ~ ~
The zero-temperature phase diagram of the checkerboard Hubbard model is obtained in the solvable limit in which it consists of weakly coupled square plaquettes. As a function of the on-site Coulomb repulsion UUU and the density of holes per site, xxx, we demonstrate the existence of at least 16 distinct phases. For instance, at zero doping, the ground state is a novel ddd-wave Mott insulator (ddd-Mott), which is not adiabatically continuable to a band insulator; by doping the ddd-Mott state with holes, depending on the magnitude of UUU, it gives way to a ddd-wave superconducting state, a two-flavor spin-1∕21∕21∕2 Fermi liquid (FL), or a spin-3∕23∕23∕2 FL.
The cluster perturbation theory is presented in the 2D Hubbard model constructed using X operators in the Hubbard-I approximation. The short-range magnetic order is taken into account by dividing the entire lattice into individual 2 × 2 clusters and solving the eigenvalue problem in an individual cluster using exact diagonalization taking into account all excited levels. The case of half-filling taking into account jumps between nearest neighbors is considered. As a result of numerical solution, a shadow zone is discovered in the quasiparticle spectrum. It is also found that a gap in the density of states in the quasiparticle spectrum at zero temperature exists for indefinitely small values of Coulomb repulsion parameter U and increases with this parameter. It is found that the presence of this gap in the spectrum is due to the formation of a short-range antiferromagnetic order. An analysis of the temperature evolution of the density of states shows that the metal-insulator transition occurs continuously. The existence of two characteristic energy scales at finite temperatures is demonstrated, the larger scale is associated with the formation of a pseudogap in the vicinity of the Fermi level, and the smaller scale is associated with the metal-insulator transition temperature. A peak in the density of states at the Fermi level, which is predicted in the dynamic mean field theory in the vicinity of the metal-insulator transition, is not observed.
Recent refinements of analytical and numerical methods have improved our understanding of the ground-state phase diagram of the two-dimensional (2D) Hubbard model. Here, we focus on variational approaches, but comparisons with both quantum cluster and Gaussian Monte Carlo methods are also made. Our own ansatz leads to an antiferromagnetic ground state at half filling with a slightly reduced staggered order parameter (as compared to simple mean-field theory). Away from half filling, we find d-wave superconductivity, but confined to densities where the Fermi surface passes through the antiferromagnetic zone boundary (if hopping between both nearest-neighbour and next-nearest-neighbour sites is considered). Our results agree surprisingly well with recent numerical studies using the quantum cluster method. An interesting trend is found by comparing gap parameters Δ (antiferromagnetic or superconducting) obtained with different variational wave functions. Δ varies by an order of magnitude and thus cannot be taken as a characteristic energy scale. In contrast, the order parameter is much less sensitive to the degree of sophistication of the variational schemes, at least at and near half filling.