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

Physical review. B, Condensed matter

Metal-insulator transition in the Hubbard model with a magnetic field: Exact results

Yu. A. Dimashko

Published Nov 15, 1993• 1 citation
Publisher

Abstract

The Hubbard model with unit concentration of electrons per one site in the external magnetic field H is considered. In the H\ensuremath{\rightarrow}\ensuremath{\infty} limit the ground state is ferromagnetic and dielectric. A decrease of H results in the phase transition to a new ground state. The electric properties of this state depend on (1) the lattice dimensionality and (2) the U/t ratio (U,t are the standard parameters of the Hubbard model). The linear [one-dimensional (1D)], square (2D), and simple cubic (3D) lattices are considered. In the 1D and 2D cases the new ground state is always dielectric. In the 3D case this state is dielectric only at U/(12t)>${\mathit{W}}^{\mathrm{\ensuremath{-}}1}$, where W=1.516. . . is the Watson integral. At U/(12t)${\mathit{W}}^{\mathrm{\ensuremath{-}}1}$ it becomes a conducting one. The line of phase transition with respect to the field is constructed in the H-U coordinates. It is found that the transition to the dielectric state results in the transformation of the ferromagnetic order to the spin-flip phase. The transition to the conducting state results only in a decrease of the average local spin.

DOI
10.1103/physrevb.48.15434

Related papers

Classical Linear-Chain Hubbard Model: Metal-Insulator Transition

Robert A. Bari

The linear-chain Hubbard model with nearest-neighbor hopping parameter $t$ is reexpressed in terms of pseudospin operators according to the Jordan-Wigner transformation. The resulting spin model is then treated classically. It is found that for a half-filled band there is a phase transition in the ground state as a function of $t$. The electrical conductivity is calculated and shown to vanish discontinuously at the critical value of $4t = U$ (Coulomb repulsion). A Josephson-type relation is obtained between the difference in azimuthal angles of adjacent spins and the potential difference between sites. It is also shown that a local magnetic moment exists in the insulating state. For the non-half-filled band, it is shown that the ground state is ferromagnetic for $4t < U$.

Physical review. B, Solid state•May 15, 1973•12 citations

Phase transitions and exact ground-state properties of the one-dimensional Hubbard model in a magnetic field

Chia‐Wei Yang, ARMEN N. KOCHARIAN, Y. L. Chiang

The exact phase diagrams of the one-dimensional Hubbard model, both attractive and repulsive, in the presence of an arbitrary magnetic field h for various electron concentrations n and on-site interaction strengths U <0 or U >0 are calculated and investigated. The exact ground-state properties, namely, the ground-state energy, the average spin (magnetization), the concentration of the doubly occupied sites, the kinetic energy, the chemical potential, the spin (magnetic) susceptibility and the charge compressibility, are calculated and examined over a wide range of interaction strengths U for various h and n . It is found that the spin susceptibility at half-filling is non-analytic and changes discontinuously as U →0. The exact theory shows the absence of a charge energy gap in the U ⩽0 region for all n and provides, for the chemical potential, the rigorous upper and lower bounds for half-filled and empty bands respectively. The analytical results derived for the weak-coupling limit and asymptotic expansions for strong coupling are in full agreement with the numerical calculations.

Journal of Physics Condensed Matter•Aug 2, 2000•24 citations

Magnetic crossover in the one-dimensional Hubbard model in the presence of a magnetic field

ARMEN N. KOCHARIAN, Nicholas Kioussis, S H Park

The ground-state (GS) properties of the one-dimensional (1D) Hubbard model at half-filling are examined in the presence of a magnetic field using the generalized mean-field (GMF) approach, which includes the spin-density and the electron-hole correlations on an equal footing. The GMF formalism provides insight into both the metal-insulator transition and the transition from itinerant to localized magnetism with applied field. The GMF theory can differentiate the energy gap from the antiferromagnetic order parameter in the presence of a magnetic field. The numerical results for the GS energy, the magnetization, the spin susceptibility, and the number of doubly occupied sites are in good agreement with the exact results over a wide range of U / t and h / t . The calculated h - U phase diagram exhibits a magnetic crossover from itinerant electron-hole pairs to a Bose-Einstein condensate state of local pairs. The overall picture of the magnetic crossover in 1D is found to be similar for the simple case of constant density of states, putting the GMF approach on a firmer basis in two and three dimensions.

Journal of Physics Condensed Matter•Jul 20, 2001•3 citations

Phase diagram of the simplified Hubbard model with a generalized type of hopping in an external magnetic field

Pavol Farkašovský

The extrapolation of small-cluster exact-diagonalization calculations is used to examine the zero-temperature phase diagram of the simplified Hubbard model in an external magnetic field. Using a general expression for hopping matrix elements ${(t}_{\mathrm{ij}}\ensuremath{\sim}{q}^{|i\ensuremath{-}j|})$ the influence of the long-range hopping (the asymmetry of the density of states) on ground-state properties, and particularly on ferromagnetism is studied. It is found that the long-range hopping (the asymmetric density of states) stabilizes the ferromagnetic state for a wide range of electron interactions $U$ and electron concentrations $n$. The critical value of magnetic field $h$ below which the ferromagnetic state becomes unstable is calculated numerically. It is shown that below this critical value the ferromagnetic state breaks down into a metallic state for weak coupling and an insulating state for strong coupling. The phase diagram of the model in the $h\ensuremath{-}U$ plane is presented for physically the most interesting cases.

Physical review. B, Condensed matter•Jun 15, 1998•6 citations

Bond-charge–site-charge interaction and metal-insulator transitions

Kristel F. L. Michielsen

Exact-diagonalization and quantum Monte Carlo methods are used to study the occurrence of a metal-insulator transition and the distribution of charges and magnetic moments in the ground state of a one- and two-dimensional half-filled system of correlated electrons, described by a one-band simplified Hubbard model extended with bond-charge--site-charge interactions. Numerical results for the electrical conductivity, the density of states, and the spin- and charge-density correlation functions strongly suggest that the bond-charge--site-charge interaction plays a fundamental role in the occurrence of a metal-insulator transition and of ferromagnetic order.

Physical review. B, Condensed matter•Aug 15, 1994•18 citations

Metal-insulator transition in an one-dimensional two-band Hubbard-like model

P. Schlottmann

We consider a one-dimensional two-band model of electrons on a lattice with equal nearest-neighbour hopping, an interband splitting Delta and a Hubbard-like repulsion U. The model is defined via the SU(4) generalization of Lieb and Wu's Bethe ansatz solution of the one-dimensional Hubbard model. At T=0 the model has a Mott metal-insulator transition at a critical value U c ( Delta ) for a band filling of exactly one electron per site. U c decreases with Delta , being zero if the excited-electron band is empty, and U c =2.981 when the bands are degenerate. We discuss the ground-state properties, the spectrum of elemental excitations, the specific heat and the magnetic susceptibility, in both the metallic and insulating phases, as a function of the crystal-field splitting for exactly one electron per site. There are four branches of elemental excitations: (i) charge excitations, (ii) crystalline-field excitations and (iii) two branches of spin waves. The Fermi velocity is finite in the metallic phase, diverges as the metal-insulator transition is approached from the metallic side and vanishes for the insulator. Each band contributes to the susceptibility with a term that is inversely proportional to the spin-wave velocity for that band. The low-temperature specific heat is proportional to T and to the sum of the inverses of the velocities of the four branches.

Journal of Physics Condensed Matter•Jan 2, 1995•3 citations
The Hubbard model with unit concentration of electrons per one site in the external magnetic field H is considered. In the H\ensuremath{\rightarrow}\ensuremath{\infty} limit the ground state is ferromagnetic and dielectric. A decrease of H results in the phase transition to a new ground state. The electric properties of this state depend on (1) the lattice dimensionality and (2) the U/t ratio (U,t are the standard parameters of the Hubbard model). The linear [one-dimensional (1D)], square (2D), and simple cubic (3D) lattices are considered. In the 1D and 2D cases the new ground state is always dielectric. In the 3D case this state is dielectric only at U/(12t)>W\ensuremath−1{\mathit{W}}^{\mathrm{\ensuremath{-}}1}W\ensuremath−1, where W=1.516. . . is the Watson integral. At U/(12t)W\ensuremath−1{\mathit{W}}^{\mathrm{\ensuremath{-}}1}W\ensuremath−1 it becomes a conducting one. The line of phase transition with respect to the field is constructed in the H-U coordinates. It is found that the transition to the dielectric state results in the transformation of the ferromagnetic order to the spin-flip phase. The transition to the conducting state results only in a decrease of the average local spin.
The linear-chain Hubbard model with nearest-neighbor hopping parameter ttt is reexpressed in terms of pseudospin operators according to the Jordan-Wigner transformation. The resulting spin model is then treated classically. It is found that for a half-filled band there is a phase transition in the ground state as a function of ttt. The electrical conductivity is calculated and shown to vanish discontinuously at the critical value of 4t=U4t = U4t=U (Coulomb repulsion). A Josephson-type relation is obtained between the difference in azimuthal angles of adjacent spins and the potential difference between sites. It is also shown that a local magnetic moment exists in the insulating state. For the non-half-filled band, it is shown that the ground state is ferromagnetic for 4t<U4t < U4t<U.
The exact phase diagrams of the one-dimensional Hubbard model, both attractive and repulsive, in the presence of an arbitrary magnetic field h for various electron concentrations n and on-site interaction strengths U <0 or U >0 are calculated and investigated. The exact ground-state properties, namely, the ground-state energy, the average spin (magnetization), the concentration of the doubly occupied sites, the kinetic energy, the chemical potential, the spin (magnetic) susceptibility and the charge compressibility, are calculated and examined over a wide range of interaction strengths U for various h and n . It is found that the spin susceptibility at half-filling is non-analytic and changes discontinuously as U →0. The exact theory shows the absence of a charge energy gap in the U ⩽0 region for all n and provides, for the chemical potential, the rigorous upper and lower bounds for half-filled and empty bands respectively. The analytical results derived for the weak-coupling limit and asymptotic expansions for strong coupling are in full agreement with the numerical calculations.
The ground-state (GS) properties of the one-dimensional (1D) Hubbard model at half-filling are examined in the presence of a magnetic field using the generalized mean-field (GMF) approach, which includes the spin-density and the electron-hole correlations on an equal footing. The GMF formalism provides insight into both the metal-insulator transition and the transition from itinerant to localized magnetism with applied field. The GMF theory can differentiate the energy gap from the antiferromagnetic order parameter in the presence of a magnetic field. The numerical results for the GS energy, the magnetization, the spin susceptibility, and the number of doubly occupied sites are in good agreement with the exact results over a wide range of U / t and h / t . The calculated h - U phase diagram exhibits a magnetic crossover from itinerant electron-hole pairs to a Bose-Einstein condensate state of local pairs. The overall picture of the magnetic crossover in 1D is found to be similar for the simple case of constant density of states, putting the GMF approach on a firmer basis in two and three dimensions.
The extrapolation of small-cluster exact-diagonalization calculations is used to examine the zero-temperature phase diagram of the simplified Hubbard model in an external magnetic field. Using a general expression for hopping matrix elements ${(t}_{\mathrm{ij}}\ensuremath{\sim}{q}^{|i\ensuremath{-}j|})$ the influence of the long-range hopping (the asymmetry of the density of states) on ground-state properties, and particularly on ferromagnetism is studied. It is found that the long-range hopping (the asymmetric density of states) stabilizes the ferromagnetic state for a wide range of electron interactions UUU and electron concentrations nnn. The critical value of magnetic field hhh below which the ferromagnetic state becomes unstable is calculated numerically. It is shown that below this critical value the ferromagnetic state breaks down into a metallic state for weak coupling and an insulating state for strong coupling. The phase diagram of the model in the $h\ensuremath{-}U$ plane is presented for physically the most interesting cases.
Exact-diagonalization and quantum Monte Carlo methods are used to study the occurrence of a metal-insulator transition and the distribution of charges and magnetic moments in the ground state of a one- and two-dimensional half-filled system of correlated electrons, described by a one-band simplified Hubbard model extended with bond-charge--site-charge interactions. Numerical results for the electrical conductivity, the density of states, and the spin- and charge-density correlation functions strongly suggest that the bond-charge--site-charge interaction plays a fundamental role in the occurrence of a metal-insulator transition and of ferromagnetic order.
We consider a one-dimensional two-band model of electrons on a lattice with equal nearest-neighbour hopping, an interband splitting Delta and a Hubbard-like repulsion U. The model is defined via the SU(4) generalization of Lieb and Wu's Bethe ansatz solution of the one-dimensional Hubbard model. At T=0 the model has a Mott metal-insulator transition at a critical value U c ( Delta ) for a band filling of exactly one electron per site. U c decreases with Delta , being zero if the excited-electron band is empty, and U c =2.981 when the bands are degenerate. We discuss the ground-state properties, the spectrum of elemental excitations, the specific heat and the magnetic susceptibility, in both the metallic and insulating phases, as a function of the crystal-field splitting for exactly one electron per site. There are four branches of elemental excitations: (i) charge excitations, (ii) crystalline-field excitations and (iii) two branches of spin waves. The Fermi velocity is finite in the metallic phase, diverges as the metal-insulator transition is approached from the metallic side and vanishes for the insulator. Each band contributes to the susceptibility with a term that is inversely proportional to the spin-wave velocity for that band. The low-temperature specific heat is proportional to T and to the sum of the inverses of the velocities of the four branches.