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Physical Review Letters

Mott transition near the ferromagnetic state

P. G. J. van Dongen, V. Janiš

Published May 16, 1994• 21 citations
Publisher

Abstract

We consider the Hubbard model, either in a magnetic field (model I) or with a general nearest-neighbor interaction (model II). For these models we determine criteria for the instability of the fully polarized ferromagnet. We show that the ground state below the instability contains an exactly soluble Mott transition. The transition occurs at a critical interaction ${\mathit{U}}_{\mathit{c}}$, at which perturbation theory breaks down. Extended metallic states are found for U${\mathit{U}}_{\mathit{c}}$, insulating bound states for U>${\mathit{U}}_{\mathit{c}}$. Details of the transition strongly depend on dimension.

DOI
10.1103/physrevlett.72.3258

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We consider the Hubbard model, either in a magnetic field (model I) or with a general nearest-neighbor interaction (model II). For these models we determine criteria for the instability of the fully polarized ferromagnet. We show that the ground state below the instability contains an exactly soluble Mott transition. The transition occurs at a critical interaction Uc{\mathit{U}}_{\mathit{c}}Uc​, at which perturbation theory breaks down. Extended metallic states are found for UUc{\mathit{U}}_{\mathit{c}}Uc​, insulating bound states for U>Uc{\mathit{U}}_{\mathit{c}}Uc​. Details of the transition strongly depend on dimension.
Metal–insulator transition in the ground state of the Hubbard chain with the next-nearest-neighbor hopping is studied by exact diagonalization method. This model shows the partially ferromagnetic metal near the Mott insulator for large Coulomb repulsion while the model reveals the non-magnetic metal for small but finite Coulomb repulsion. We find the transition between the partially ferromagnetic metal and the Mott insulator without phase separation. A new critical exponent of the diverging charge compressibility with respect to the hole density is observed when the system approaches the metal–Mott-insulator transition point from the side of the partially ferromagnetic metal. We also find the occurrence of the phase separation between partially ferromagnetic metal and the Mott insulator for even larger Coulomb repulsion. The model proposed here is interesting in view of the magnetism as well as the metal–insulator transition.
The Hubbard model was originally introduced as the simplest system which may exhibit an insulating (Mott) state. This state is the result of strong electron–electron interactions. In this chapter we consider the Hubbard model at half-filling. The main goal here is the study of the magnetic properties of its ground state. Apart from an exact solution in one dimension, no exact results are available for this problem. This leads to the use of several approximations. The most popular one, and the oldest, is the mean-field theory (MFT). In the MFT one has the bias that the ground state does have some sort of magnetic order (i.e. ferromagnetic, Néel antiferromagnetic, etc.). The problem is then usually solved by means of a variational ansatz. However, one is usually interested in more than just the ground-state energy, which, after all, is not directly measurable and depends very sensitively on the properties at short distances. Most often we wish to evaluate the long-distance, low-frequency, properties of the correlation and response functions of this theory. Moreover, in some cases, such as in one dimension, the fluctuations overwhelm the MFT predictions. In this chapter we will consider the standard MFT (i.e. Hartree–Fock), which is expected to become accurate at weak coupling. We will consider both ferromagnetic and antiferromagnetic states. We will also rederive these results using path integrals. As a byproduct, we will also have a theory of the fluctuations: the non-linear sigma model.
We study the low energy behavior of the one dimensional Hubbard model across the Mott metal-insulator phase transition in an external magnetic field. In particular we calculate elements of the dressed charge matrix at the critical point of the Mott transition for arbitrary Hubbard repulsion and magnetization numerically and, in certain limiting cases, analytically. These results are combined with a non-perturbative effective field theory approach to reveal how the breaking of time reversal symmetry influences the Mott transition.
We study the properties of a quarter-filled system of electrons on a square lattice interacting through a local repulsion U and a nearest-neighbor repulsion V in the limit V=+\ensuremath{\infty}. We identify the ground state for U large enough and show that domain walls appear below a critical value Uc{\mathit{U}}_{\mathit{c}}Uc​=4t/\ensuremath{\pi}. We argue that this corresponds to a metal-insulator transition due to Mott localization.
We study the low energy behavior of the one dimensional Hubbard model across the Mott metal–insulator phase transition in an external magnetic field. In particular we calculate elements of the dressed charge matrix at the critical point of the Mott transition for arbitrary Hubbard repulsion and magnetization numerically and, in certain limiting cases, analytically. These results are combined with a non-perturbative effective field theory approach to reveal how the breaking of time reversal symmetry influences the Mott transition.
Abstract We study the density of states (DOS) as a function of the interaction U in the half‐filled simplified Hubbard model in a magnetic field. This model is considered on the Bethe lattice in the limit of high dimensions. We show that the DOS can be calculated exactly, and that many of its properties have an astonishingly simple form. In particular, the DOS can be investigated explicitly in the limits of weak and strong coupling and near the metal‐insulator transition. E.g., we find an explicit result for the critical value Uc, at which the metal‐insulator transition occurs, as a function of the magnetization. The relation between the magnetization and the magnetic field is calculated numerically. An important result is that the metal‐insulator transition, occurring in the model with B = 0, is continuously connected to the metal‐insulator transition in the subspace of single spin flips.