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Physics of the Solid State

The ground state of a strongly correlated fermion system in a magnetic field

Yu. B. Kudasov

Published Aug 1, 2001• 0 citations
Publisher

Abstract

A new variational method is used to investigate the ground state of the Hubbard model with a half-filled band for a one-dimensional chain, a planar square lattice, and a simple cubic lattice. A metamagnetic transition is found to occur in a one-dimensional chain and a simple square lattice. A simple cubic lattice does not undergo the metamagnetic transition.

DOI
10.1134/1.1395101

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A new variational method is used to investigate the ground state of the Hubbard model with a half-filled band for a one-dimensional chain, a planar square lattice, and a simple cubic lattice. A metamagnetic transition is found to occur in a one-dimensional chain and a simple square lattice. A simple cubic lattice does not undergo the metamagnetic transition.
A new variational method is developed to calculate the ground state energy of Fermi systems with strong short-range correlations. A trial wave function of Gutzwiller's type contains additional variational parameters corresponding to configurations of pairs of nearest-neighbor sites. To evaluate the ground state energy, generalized Kikuchi's pseudo-ensemble method is used. The Hubbard model at half band-filling is investigated. The ground state energy of the paramagnetic phase is calculated for a chain, square and simple cubic lattices. It is shown that the short-range order lowers drastically the ground state energy of the Hubbard model at intermediate interaction strength. The paramagnetic phase of the Kondo-Hubbard model (S=1/2S=1/2S=1/2 and S=5/2S=5/2S=5/2) at half band-filling is investigated. The ground state energy, correlation functions and effective mass are calculated for chain, square and simple cubic lattices. A quantum phase transition was found for simple cubic lattice.
The ground state of the two-dimensional Hubbard model on a square lattice is studied in the large-U limit in a half-filled band with a dynamical hole. For a 4\ifmmode\times\else\texttimes\fi{}4 lattice with hopping t=1 and coupling JJc{J}_{c}Jc​\ensuremath{\approxeq}0.075, the ground state has zero momentum (k) and spin 15/2 (ferromagnetic background). For J\ensuremath{\ge}Jc{J}_{c}Jc​ the ground state is degenerate with nonzero k and spin 1/2, in agreement with recent variational calculations. The nonzero k of the ground state comes from a nontrivial phase in the overlap of the spin states before and after a hole move. For small lattices we show that the effective Hamiltonian of the hole is that of a particle moving in a magnetic field. We also find that many of the features of the weak-coupling region carry over continuously to the strong-coupling region.
We investigate the ground state (T = 0 K) of the one-dimensional symmetrical (n = 1) Hubbard model formalized in terms of the system of integral equations, which we previously obtained using the method of the generating functional of Green’s functions with the subsequent Legendre transformation. In a wide range of variations in the parameter of Coulomb interaction U, the following characteristics of the system have been calculated: the electron density of states, the electron band spectrum, the number of doubly occupied lattice sites, the localized magnetic moment, the correlator of the square of the longitudinal component of spin at a site,<S Z 2>, and the internal energy of the system. It has been shown that, for all U > 0, the model yields two solutions, i.e., an antiferromagnetic insulator and a paramagnetic insulator, in which there are no single-electron quasi-particles at the Fermi level. The energy of the paramagnetic solution in the region of U < 1.1 is considerably less than that of the antiferromagnetic solution for the case of U > 1.1, we have the opposite situation.
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.
The Hubbard model has been widely used to describe magnetism due to itinerant electrons. However, except for the one-dimensional case, no exact solution of the model exists. We have studied the two-dimensional Hubbard model on a square lattice using a Monte Carlo simulation technique. Simulations were performed on lattices of up to 8×8 in spatial size. We will discuss results for thermodynamic properties and correlation functions as a function of temperature and interaction strength. For the half-filled band case, our results indicate that the system exhibits long-range antiferromagnetic order in the ground state for any nonzero interaction, although substantially reduced from the classical Néel state due to both charge and spin fluctuations. For the non-half-filled band case, our results suggest that no long-range magnetic order exists. We also don’t find any indication of short-ranged ferromagnetic correlations in the parameter range studied. We have also studied the predictions of various approximate treatments for this model, particularly the static approximation and the coherent potential approximation (CPA). By comparison with the Monte Carlo results, we discuss the validity of these schemes. Finally, we discuss the effect of changing the band structure on the magnetic properties of the system.