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Spin and charge response to magnetic frustration in the Hubbard model

Yang Liu

Published May 29, 2019• 0 citations
Publisher

Abstract

Unusual normal-state properties of strongly correlated electron materials have been discovered in recent years. They can not be explained by traditional theories. Much work has been devoted to exploring the physical insight into these properties. In the dissertation, the study of spin and charge response to magnetic frustration in the Hubbard Model is presented. Using exact diagonalization techniques, the eigenvalues and eigenvectors of a two-dimensional Hubbard model applied to a cluster with periodic boundary conditions have been obtained. Static and dynamic spin and charge correlation functions as well as one-particle excitation spectra have been calculated. The effects of magnetic frustration due to geometrical competition of different electron hopping terms are studied for various doping and short-range Coulomb interaction parameters. The calculated results are discussed in the framework of many-body physics.

DOI
10.25669/9zea-x9xq

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Unusual normal-state properties of strongly correlated electron materials have been discovered in recent years. They can not be explained by traditional theories. Much work has been devoted to exploring the physical insight into these properties. In the dissertation, the study of spin and charge response to magnetic frustration in the Hubbard Model is presented. Using exact diagonalization techniques, the eigenvalues and eigenvectors of a two-dimensional Hubbard model applied to a cluster with periodic boundary conditions have been obtained. Static and dynamic spin and charge correlation functions as well as one-particle excitation spectra have been calculated. The effects of magnetic frustration due to geometrical competition of different electron hopping terms are studied for various doping and short-range Coulomb interaction parameters. The calculated results are discussed in the framework of many-body physics.
We investigate the effects of magnetic frustration on spin and charge dynamics in strongly correlated itinerant electron systems by using the exact diagonalization technique. A Hubbard model with adjustable degree of magnetic frustration is constructed. Static and dynamic spin and charge correlation functions show different dependence on the degree of magnetic frustration in the system. With increasing magnetic frustration, the spin and charge correlation function spectra become more sparse, indicating a decreased level of mixing of the spin and charge degrees of freedom or a partial spin-charge separation.
A review of the physical properties of small systems described by various model Hamiltonians is given. Their physical properties are found either exactly or by using Monte-Carlo methods, and are compared with properties of bulk systems. It is shown that (i) clusters differ in an essential way from the bulk, having electronic states strongly dependent on the geometry and cluster size, but, at the same time, (ii) important insights into the nature of electron correlation and low-energy excitations in solids may be gained by cluster studies. In particular, the cluster calculations allow one to identify the tendencies to various kinds of symmetry-broken states in the (extended) Hubbard model and give a simple qualitative understanding of the low temperature properties of the Kondo and the heavy-fermion systems. Furthermore, cluster calculations allow one to study such problems as the development of magnetic moment at chemisorbed atoms for strong correlations and the suppression of frustration by quantum fluctuations. Recently, cluster calculations gave important information about the possible role of charge transfer processes and magnetic interactions in the microscopic mechanism of pairing in high temperature superconducting oxides.
We examine the optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ and the chemical potential $\ensuremath{\mu}$, together with the spin correlation, in the strong-coupling limit of a hole-doped two-dimensional triangular Hubbard model near half filling by using an exact diagonalization technique. In contrast to the case of a square lattice without frustration, the doping dependences of $\ensuremath{\mu}$ and the Drude weight indicate that the charge degree of freedom is weakly coupled to the spin degree of freedom. However, we find that $\ensuremath{\sigma}(\ensuremath{\omega})$ shows strong incoherent excitations extended to a higher energy region. This implies that geometrical frustration in strongly correlated electron systems influences incoherent charge dynamics.
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.
This work deals with the calculation of magnetic properties for strongly correlated electron systems. One of most important model in this field of physics is the Hubbard model. It describes the situation of, for example, transition metal oxides. This particular class of materials is known for magnetic order at low temperatures. The reason for this and at the same time the difficulty for theoretically describing them are strong electron-electron-interactions. For calculating the magnetic properties I used the dynamical mean field theory (DMFT), which relates the lattice model to an impurity model. Even this simplified model is highly non trivial. For solving it I used two different renormalization group approaches. I used the numerical renormalization group (NRG) and the density matrix renormalization group (DMRG) and also compared both methods with each other. These modern non-perturbative techniques are able to solve the impurity model, which then can be used for calculating the magnetic phases of the lattice models. In this work I mainly focused on the frustrated one-orbital Hubbard model and the two-orbital Hubbard model. Frustration represents a situation where the aimed magnetic solution cannot be stabilized for the used lattice. Frustration can, for example, be generated by long range hopping of the electrons. This can lead to a situation where new magnetic phases are stable. For systematically analyzing the effects of frustration, I performed calculations for a Bethe lattice with nearest and next nearest neighbor hopping, for which I varied the strength of the interaction and the next nearest neighbor hopping. Another very important aspect for describing transition metal oxides are orbital degrees of freedom. For analyzing the influence of these degrees of freedom I used the two-orbital Hubbard model, which shows new effects.
We calculate spin and charge excitation spectra of the one-dimensional (1D) quarter-filled Hubbard model with nearest-neighbor ttt and next-nearest-neighbor ${t}^{\ensuremath{'}}$ hopping integrals using the dynamical density-matrix renormalization group technique. We consider a case where ttt (>0)(>0)(>0) is much smaller than ${t}^{\ensuremath{'}}$ (>0)(>0)(>0). First, we examine the accuracy of our method based on comparison between our result and exact noninteracting spectrum. Next, we investigate the spectra with the on-site Coulomb interaction. We find that the spin and charge excitation spectra are essentially the same as those of the 1D quarter-filled Hubbard (and $t\text{\ensuremath{-}}J$) model for the two 1D chains along the hopping integral ${t}^{\ensuremath{'}}$. However, the hopping integral ttt $(<{t}^{\ensuremath{'}})$ plays a crucial role in the short-range correlations and low-energy excitaions; ferromagnetic correlation between electrons on neighboring sites is enhanced and pairing correlation between the electrons is induced. Consequently, a spin-triplet superconducting state may be derived.