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:1003.1946 · Journal of Physical Studies

Magnetic properties of a strongly correlated system on the Bethe lattice

Francesco Paolo Mancini

Published Jan 1, 2009• 3 citations
arXivHTMLPDF

Abstract

We study the influence of an external magnetic field h on the phase diagram of a system of Fermi particles living on the sites of a Bethe lattice with coordination number z and interacting through on-site U and nearest-neighbor V interactions. This is a physical realization of the extended Hubbard model in the narrow-band limit. Our results establish that the magnetic field may dramatically affect the critical temperature below which a long-range charge ordered phase is observed, as well as the behavior of physical quantities, inducing, for instance, magnetization plateaus in the magnetization curves. Relevant thermodynamic quantities - such as the specific heat and the susceptibility - are also investigated at finite temperature by varying the on-site potential, the particle density and the magnetic field.

DOI
10.30970/jps.13.4702

Related papers

Exact solution of the extended Hubbard model in the atomic limit on the Bethe Lattice

Ferdinando Mancini, Francesco Paolo Mancini, Adele Naddeo

We study the phase diagram at finite temperature of a system of Fermi particles on the sites of the Bethe lattice with coordination number z and interacting through onsite U and nearest-neighbor V interactions. This is a physical realization of the extended Hubbard model in the atomic limit. By using the equations of motion method, we exactly solve the model. For an attractive intersite potential, we find, at half filling, a phase transition towards a broken particle-hole symmetry state. The critical temperature, as a function of the relevant parameters, has a re-entrant behavior as already observed in the equivalent spin-1 Ising model on the Bethe lattice.

arXiv:0711.0318•Journal of Optoelectronics and Advanced Materials•Nov 2, 2007•3 citations

Inhomogeneous charge ordering of a spinless fermionic system on the Bethe lattice

Ferdinando Mancini, Francesco Paolo Mancini, Adele Naddeo

We show that a system of spinless Fermi particles, localized on the sites of the Bethe lattice with coordination number z and interacting through a repulsive nearest-neighbor interaction, exhibits a phase transition to a charge-ordered state. The phase diagram in the n-T plane is derived. Relevant thermodynamic quantities, such as the free energy, the specific heat, the entropy and the compressibility are analyzed in detail.

arXiv:0710.5824•Journal of Optoelectronics and Advanced Materials•Oct 31, 2007•0 citations

Exploring the magnetic phases in the one-band Hubbard model: Impact of long-range hopping

Sudip Mandal, Sandip Halder, Kalpataru Pradhan

Correlated electron systems with competing interactions provide a valuable platform for examining exotic magnetic phases. Theoretical models often focus on nearest-neighbor interactions, although long-range interactions can have a considerable impact on the behavior of the system, creating distinct and complicated magnetic phases. We investigate the consequences of competing interactions in a half-filled one-band Hubbard model on a simple cubic lattice, incorporating hopping processes up to third-nearest-neighbors, to explore the underlying magnetotransport properties. Our magnetic phase diagrams at low temperatures, obtained using semiclassical Monte Carlo analysis, reveal that the long-range interactions can disrupt one form of magnetic phase while creating a new type of magnetic order. For the nonperturbative regime (on-site Hubbard repulsive strength $U\ensuremath{\sim}$ bandwidth), the C-type antiferromagnetic ground state is preferred over the G-type antiferromagnetic phase when the interaction between second-nearest-neighbor sites becomes significant relative to the nearest-neighbor interactions. However, interactions beyond the second-nearest-neighbors are required to stabilize the A-type antiferromagnetic ground state. Remarkably, at low temperatures, a highly correlated paramagnetic insulating phase develops at the intersection between the antiferromagnetic phases, which might promote a three-dimensional spin-liquid state.

Physical review. B./Physical review. B•Aug 14, 2025•2 citations

Extended Hubbard model in the presence of a magnetic field

Francesco Paolo Mancini, Francesco Paolo Mancini

Abstract. Within the Green’s function and equations of motion formalism it is possible to exactly solve a large class of models useful for the study of strongly correlated systems. Here, we present the exact solution of the one-dimensional extended Hubbard model with on-site U and first nearest neighbor repulsive V interactions in the presence of an external magnetic field h, in the narrow band limit. At zero temperature

•Nov 20, 2012•8 citations

Exact mean-field theory of the extended simplified Hubbard model

P. G. J. van Dongen

The recently introduced concept of exact mean-field theories is applied to the extended simplified Hubbard model, which is a one-band extended Hubbard model (including nearest-neighbor interaction) where only the \ensuremath{\downarrow} electrons can hop. An exact mean-field Hamiltonian is derived for the model on a Bethe lattice in the limit of a large coordination number (Z\ensuremath{\rightarrow}\ensuremath{\infty}). The mean-field Hamiltonian is used to calculate the Green functions and the free energy at half-filling. This exact solution is analyzed analytically at small and large values of the on-site (U) and nearest-neighbor (V) interaction strengths. One finds that a phase transition occurs at sufficiently low temperatures for all U,V>0. The low-temperature phase is a charge-density wave for V>1/2U and a spin-density wave for V1/2U. Special attention is paid to (i) the critical temperature as a function of U and V, (ii) the order parameter as a function of temperature, and (iii) the density of states. The density of states shows that the low-temperature phase is an insulator for all U,V provided that V/U\ensuremath{\ne}1/2, while the high-temperature phase is a paramagnetic metal for all V if U2, and a paramagnetic insulator if U>2. Many detailed results are given.

Physical review. B, Condensed matter•Feb 1, 1992•84 citations

Properties of the one-dimensional half-filled-band extended Hubbard model

Fernando O. Freire, Cláudio Andrade Macedo

With the aim of contributing to a better understanding of the finite-temperature properties of low-dimensional strongly correlated systems we study a one-dimensional half-filled-band extended Hubbard model with a term of exchange interaction between neighboring sites. We analyze the temperature dependence of the specific heat, internal energy, entropy, number of doubly occupied sites, magnetic susceptibility, spin-spin correlation functions, and also investigate a detailed diagram of magnetic correlations. We use the method of small-cluster exact diagonalization calculations with the application of the grand canonical ensemble and of extrapolation techniques to the infinite chain. Our results show that the examined model exhibits a rich structure of magnetic properties due to the competition between the onsite Coulombian repulsion and the exchange interaction.

Journal of Physics Conference Series•Jan 1, 2010•0 citations
We study the influence of an external magnetic field h on the phase diagram of a system of Fermi particles living on the sites of a Bethe lattice with coordination number z and interacting through on-site U and nearest-neighbor V interactions. This is a physical realization of the extended Hubbard model in the narrow-band limit. Our results establish that the magnetic field may dramatically affect the critical temperature below which a long-range charge ordered phase is observed, as well as the behavior of physical quantities, inducing, for instance, magnetization plateaus in the magnetization curves. Relevant thermodynamic quantities - such as the specific heat and the susceptibility - are also investigated at finite temperature by varying the on-site potential, the particle density and the magnetic field.
We study the phase diagram at finite temperature of a system of Fermi particles on the sites of the Bethe lattice with coordination number z and interacting through onsite U and nearest-neighbor V interactions. This is a physical realization of the extended Hubbard model in the atomic limit. By using the equations of motion method, we exactly solve the model. For an attractive intersite potential, we find, at half filling, a phase transition towards a broken particle-hole symmetry state. The critical temperature, as a function of the relevant parameters, has a re-entrant behavior as already observed in the equivalent spin-1 Ising model on the Bethe lattice.
Correlated electron systems with competing interactions provide a valuable platform for examining exotic magnetic phases. Theoretical models often focus on nearest-neighbor interactions, although long-range interactions can have a considerable impact on the behavior of the system, creating distinct and complicated magnetic phases. We investigate the consequences of competing interactions in a half-filled one-band Hubbard model on a simple cubic lattice, incorporating hopping processes up to third-nearest-neighbors, to explore the underlying magnetotransport properties. Our magnetic phase diagrams at low temperatures, obtained using semiclassical Monte Carlo analysis, reveal that the long-range interactions can disrupt one form of magnetic phase while creating a new type of magnetic order. For the nonperturbative regime (on-site Hubbard repulsive strength $U\ensuremath{\sim}$ bandwidth), the C-type antiferromagnetic ground state is preferred over the G-type antiferromagnetic phase when the interaction between second-nearest-neighbor sites becomes significant relative to the nearest-neighbor interactions. However, interactions beyond the second-nearest-neighbors are required to stabilize the A-type antiferromagnetic ground state. Remarkably, at low temperatures, a highly correlated paramagnetic insulating phase develops at the intersection between the antiferromagnetic phases, which might promote a three-dimensional spin-liquid state.
The recently introduced concept of exact mean-field theories is applied to the extended simplified Hubbard model, which is a one-band extended Hubbard model (including nearest-neighbor interaction) where only the \ensuremath{\downarrow} electrons can hop. An exact mean-field Hamiltonian is derived for the model on a Bethe lattice in the limit of a large coordination number (Z\ensuremath{\rightarrow}\ensuremath{\infty}). The mean-field Hamiltonian is used to calculate the Green functions and the free energy at half-filling. This exact solution is analyzed analytically at small and large values of the on-site (U) and nearest-neighbor (V) interaction strengths. One finds that a phase transition occurs at sufficiently low temperatures for all U,V>0. The low-temperature phase is a charge-density wave for V>1/2U and a spin-density wave for V1/2U. Special attention is paid to (i) the critical temperature as a function of U and V, (ii) the order parameter as a function of temperature, and (iii) the density of states. The density of states shows that the low-temperature phase is an insulator for all U,V provided that V/U\ensuremath{\ne}1/2, while the high-temperature phase is a paramagnetic metal for all V if U2, and a paramagnetic insulator if U>2. Many detailed results are given.
With the aim of contributing to a better understanding of the finite-temperature properties of low-dimensional strongly correlated systems we study a one-dimensional half-filled-band extended Hubbard model with a term of exchange interaction between neighboring sites. We analyze the temperature dependence of the specific heat, internal energy, entropy, number of doubly occupied sites, magnetic susceptibility, spin-spin correlation functions, and also investigate a detailed diagram of magnetic correlations. We use the method of small-cluster exact diagonalization calculations with the application of the grand canonical ensemble and of extrapolation techniques to the infinite chain. Our results show that the examined model exhibits a rich structure of magnetic properties due to the competition between the onsite Coulombian repulsion and the exchange interaction.