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Hubbard model: Field theory and critical phenomena

M. L. Lyra, Mauricio D. Coutinho-Filho, A. M. Nemirovsky

In this work we use field-theoretic and renormalization-group methods to study the finite-temperature ferromagnetic phase transition in the three-dimensional Hubbard model. We show that the nature of the ferromagnetic transition may strongly depend on the constraint imposed on the system. For example, if the system is allowed to exchange particles with a reservoir, the stability criterion for the occurrence of a continuous phase transition can be calculated using the mean-field approximation. On the other hand, if the total charge is conserved and charge- and spin-density fluctuations are considered in the theory, a different criterion, quite distinct from the mean-field one, is found, resulting in a fluctuation-induced renormalized Heisenberg tricritical point. The tricritical behavior is studied by calculating the one-loop renormalized free energy and using scaling analysis to determine the tricritical exponents. Finally, the exact solution of the model in the spherical limit and near the ferromagnetic transition is presented, in which case no fluctuation-induced tricritical point is found.In this work we use field-theoretic and renormalization-group methods to study the finite-temperature ferromagnetic phase transition in the three-dimensional Hubbard model. We show that the nature of the ferromagnetic transition may strongly depend on the constraint imposed on the system. For example, if the system is allowed to exchange particles with a reservoir, the stability criterion for the occurrence of a continuous phase transition can be calculated using the mean-field approximation. On the other hand, if the total charge is conserved and charge- and spin-density fluctuations are considered in the theory, a different criterion, quite distinct from the mean-field one, is found, resulting in a fluctuation-induced renormalized Heisenberg tricritical point. The tricritical behavior is studied by calculating the one-loop renormalized free energy and using scaling analysis to determine the tricritical exponents. Finally, the exact solution of the model in the spherical limit and near the ferromagnetic transition is presented, in which case no fluctuation-induced tricritical point is found.

Physical review. B, Condensed matterAug 1, 199315 citations

Can the hubbard model be a ferromagnet in the strong correlation limit?

Katsunori Kubo, Masahito Tada

Journal of Magnetism and Magnetic MaterialsFeb 1, 19830 citations

Band-structure effects in the Hubbard chain

Haranath Ghosh, Raimundo R. dos Santos

We present results of quantum Monte Carlo simulations for the one-dimensional Hubbard model with next-nearest-neighbour hopping (t2). The appearance of double peaks in the spin and charge structure factors is identified with the doubling of ground states, each with its corresponding excitation modes. A quantitative phase diagram in the t2- (density) plane for fixed on-site coupling is obtained, and compared with weak-coupling renormalization group predictions. Four regions in this phase diagram are clearly identified: (i) singly peaked charge and spin structure factors; (ii) singly peaked ferromagnetic and charge fluctuations; (iii) singly peaked charge fluctuations and doubly peaked spin fluctuations; and (iv) doubly peaked spin and charge fluctuations.We present results of quantum Monte Carlo simulations for the one-dimensional Hubbard model with next-nearest-neighbour hopping (t2). The appearance of double peaks in the spin and charge structure factors is identified with the doubling of ground states, each with its corresponding excitation modes. A quantitative phase diagram in the t2- (density) plane for fixed on-site coupling is obtained, and compared with weak-coupling renormalization group predictions. Four regions in this phase diagram are clearly identified: (i) singly peaked charge and spin structure factors; (ii) singly peaked ferromagnetic and charge fluctuations; (iii) singly peaked charge fluctuations and doubly peaked spin fluctuations; and (iv) doubly peaked spin and charge fluctuations.

Journal of Physics Condensed MatterJan 1, 19991 citation

An exact result on ferromagnetism in the Hubbard model with an infinite-range hopping

P. Pieri

arXiv:cond-mat/9605156Physics Letters AOct 1, 19970 citations

Ferromagnetic-paramagnetic state transition in the ground state of the Hubbard model

E. G. Goryachev, Evgeniy V. Kuz’min

Physics Letters ASep 1, 19887 citations

Ferromagnetism of the Low-Density Hubbard Model in the Hartree-Fock Approximation

Volker Bach, Élliott H. Lieb, Marcos V. Travaglia

We prove rigorously that the Hartree-Fock approximation to the ground state of the d-dimensional Hubbard model leads to saturated ferromagnetism when the particle density (more precisely, the chemical potential µ) is small and the coupling constant U is large, but finite. As in the usual Hartree-Fock theory we restrict attention to Slater determinants that are eigenvectors of the z-component of the total spin, Sz = ∑ x nx, ↑ − nx,↓, and we find that the choice 2Sz = N = particle number gives the lowest energy at fixed 0 < µ < 4d. 1 BLT, Version of 27-Jun-2005 2 1We prove rigorously that the Hartree-Fock approximation to the ground state of the d-dimensional Hubbard model leads to saturated ferromagnetism when the particle density (more precisely, the chemical potential µ) is small and the coupling constant U is large, but finite. As in the usual Hartree-Fock theory we restrict attention to Slater determinants that are eigenvectors of the z-component of the total spin, Sz = ∑ x nx, ↑ − nx,↓, and we find that the choice 2Sz = N = particle number gives the lowest energy at fixed 0 < µ < 4d. 1 BLT, Version of 27-Jun-2005 2 1

Jun 27, 20051 citation

FERROMAGNETIC PHASE TRANSITIONS IN THE HUBBARD MODEL

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FERROMAGNETIC PHASE TRANSITIONS IN THE HUBBARD MODEL

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