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Progress of Theoretical Physics

Adiabatic Change from Mott Insulator to Nagaoka Ferromagnetic State

Seiji Miyashita

Published Oct 1, 2008• 14 citations
Publisher

Abstract

We study a quantum mechanical transition from the nonmagnetic Mott insulator state in the half-filled Hubbard model to a state of the Nagaoka ferromagnetism when we remove an electron from the system. To study this transition, we introduce a quantum mechanical procedure to remove an electron from the system. We demonstrate the removal of the particle from the system by making use of an additional lattice point on which we can control the density of the particle by the chemical potential. We realize an adiabatic transition between the two states under a local magnetic field, which destroys the conservation of the total spin. We study the changes in several quantities during the transition.

DOI
10.1143/ptp.120.785

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We study a quantum mechanical transition from the nonmagnetic Mott insulator state in the half-filled Hubbard model to a state of the Nagaoka ferromagnetism when we remove an electron from the system. To study this transition, we introduce a quantum mechanical procedure to remove an electron from the system. We demonstrate the removal of the particle from the system by making use of an additional lattice point on which we can control the density of the particle by the chemical potential. We realize an adiabatic transition between the two states under a local magnetic field, which destroys the conservation of the total spin. We study the changes in several quantities during the transition.
Inspired by the Nagaoka ferromagnetism, we propose an itinerant model to study the transition between the Mott singlet state and a ferromagnetic state by emulating a doping process in finite lattices. In the Nagaoka ferromagnetism, the total spin of the system takes the maximum value when an electron is removed from the half-filled system. To incorporate a procedure of the electron removal, our model contains extra sites as a reservoir of electrons, and the chemical potential of the reservoir controls the distribution of electrons. As a function of the chemical potential, the system exhibits ground-state phase transitions among various values of the total spin, including a saturated ferromagnetic state due to the Nagaoka mechanism at finite hole density. We discuss the nature of the ferromagnetism by measuring various physical quantities, such as the distribution of electrons, the spin correlation functions, the magnetization process in the magnetic field, and also the entanglement entropy.
We study finite-temperature properties of a Hubbard model including sites of a particle bath, which was proposed as a microscopic model to show itinerant ferromagnetism at finite electron density. We use direct numerical methods, such as exact diagonalization and random vector methods. The temperature dependence of quantities is surveyed in the full range of the temperature. We find that the specific heat has several peaks, which correspond to ordering processes in different energy scales. In particular, magnetic correlations develop at very low temperature. The system exhibits an itinerant ferromagnetic state or an antiferromagnetic state of the Mott insulator depending on the chemical potential of the particle bath and the Coulomb interaction. From a microscopic viewpoint, the competition between these two types of magnetic states causes a peculiar ordering process of local spin correlations. Some local ferromagnetic correlations are found to be robust, which indicates that the ferromagnetic correlation originates from the motion of itinerant electrons in a short-range cluster.
We study the metal-insulator transition and magnetic ordering in the Hubbard model using the particle-hole mapping. This representation facilitates the exact solution of the half-filled band in the limit of high spin. We find that the two-dimensional Hubbard model has a charge-excitation gap at half filling for any finite U in the high-spin region on both the bipartite square lattice and the nonbipartite triangular lattice. We show, using the Kohn insulator criteria, that this bound-state phase is indeed insulating. Using the information from the single-pair solution, we construct a generalized BCS type of many-body wave function and derive the gap equation for lower-spin states. We find that in some cases, the system goes through a phase transition to become a metal as the total spin Sz{\mathit{S}}_{\mathit{z}}Sz​ is lowered.
We study the metal-insulator transition and magnetic ordering in the Hubbard model using the particle-hole mapping. The analysis simplifies near the ferromagnetic limit. We find that the two-dimensional Hubbard model has a charge excitation gap at half filling for any finite U in this region on both the bipartite square lattice and the nonbipartite triangular lattice. In some cases, the system goes through a first-order phase transition to become a paramagnetic metal as Sz{\mathit{S}}_{\mathit{z}}Sz​ is lowered. We also discuss the extension to the doped case. We find that in the large U limit, a single doped hole has a bandwidth of order of J rather than t at Sz{\mathit{S}}_{\mathit{z}}Sz​=0.
Abstract We investigate a metal–insulator Mott transition in the half‐filled Hubbard model on the triangular lattice. In this study, we make use of the path‐integral renormalization group method with an iteration and truncation scheme proposed recently, which allows us to access the competing ground states around the transition point. We find for a cluster with 36 sites that as the Hubbard interaction U increases, the paramagnetic metallic (PM) state undergoes a metal–insulator phase transition to a nonmagnetic insulating (NMI) state at Uc∼7.4tU_{\rm c} \sim 7.4tUc​∼7.4t , where t is the transfer integral. A detailed analysis around the transition point shows that the Mott transition is of first order.
Starting from the standard Hubbard model, this paper obtained an asymmetric Hamiltonian for the half-filled strongly correlated system by ignoring the jumping of electrons with spin-σ between lattice sites when the motion of electrons with spin σ is considered. The mean field approximation is applied to get the quasi-particle spectrum of the Hamiltonian. The results at zero-temperature and finite temperature are analyzed,the possibility and critical temperature of Mott metal-insulator transition is also investigated.