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FLEX Study on Two-Dimensional t-t -Hubbard Model: Enhanced Charge Susceptibility near Antiferromagnetic Mott Transition

K Morita

Published Mar 25, 2003• 0 citations
OpenAlex

Abstract

Since the two-dimensional (2D) Hubbard model is one of the simplest model having features of layered cuprates which is widely known as high-Tc superconductor, many researchers pay their attention to this model. One of the purposes of this thesis is to discuss, on the basis of the fluctuation exchange (FLEX) approximation which satisfies the conservation law and takes account of the spin fluctuations, how the shape of the Fermi surface (FS) is modified and how the charge susceptibility behaves in the 2D t−t′−U Hubbard model near half filling as strength of the onsite Coulomb interaction U is increased. The antiferromagnetic (AF) correlation length is shown to be enhanced as the Coulomb interaction get closer to the critical value Uc for the critical point to onset AF order. At the same time, the shape of the renormalized FS is deformed showing the tendency of nesting and the charge susceptibility shows a pronounced enhancement near Uc. This result is consistent with experimental observations in under-doped cuprates LSCO. The enhancement of the charge susceptibility is so large that it cannot be explained by the van Hove singularity of the density of states (DOS) due to the nesting of FS. Indeed, the van Hove singularity of DOS is easily cancelled by the RPA type contribution. Another purpose of this thesis is to investigate an origin of the divergent charge susceptibility. It is expected that the effect of the AF spin fluctuations is the main origin for this divergence of the charge susceptibility from the fact that the anomaly is observed near the antiferromagnetic insulating (AFI) phase. In order to verify this physical picture, we calculate the Aslamasov-Larkin (AL) type contribution to the charge susceptibility, and compare its value with that calculated by the FLEX approximation. The result is that the AL-type contribution nearly exhaust the value of the enhanced charge susceptibility where the charge susceptibility is enhanced enough as

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Since the two-dimensional (2D) Hubbard model is one of the simplest model having features of layered cuprates which is widely known as high-Tc superconductor, many researchers pay their attention to this model. One of the purposes of this thesis is to discuss, on the basis of the fluctuation exchange (FLEX) approximation which satisfies the conservation law and takes account of the spin fluctuations, how the shape of the Fermi surface (FS) is modified and how the charge susceptibility behaves in the 2D t−t′−U Hubbard model near half filling as strength of the onsite Coulomb interaction U is increased. The antiferromagnetic (AF) correlation length is shown to be enhanced as the Coulomb interaction get closer to the critical value Uc for the critical point to onset AF order. At the same time, the shape of the renormalized FS is deformed showing the tendency of nesting and the charge susceptibility shows a pronounced enhancement near Uc. This result is consistent with experimental observations in under-doped cuprates LSCO. The enhancement of the charge susceptibility is so large that it cannot be explained by the van Hove singularity of the density of states (DOS) due to the nesting of FS. Indeed, the van Hove singularity of DOS is easily cancelled by the RPA type contribution. Another purpose of this thesis is to investigate an origin of the divergent charge susceptibility. It is expected that the effect of the AF spin fluctuations is the main origin for this divergence of the charge susceptibility from the fact that the anomaly is observed near the antiferromagnetic insulating (AFI) phase. In order to verify this physical picture, we calculate the Aslamasov-Larkin (AL) type contribution to the charge susceptibility, and compare its value with that calculated by the FLEX approximation. The result is that the AL-type contribution nearly exhaust the value of the enhanced charge susceptibility where the charge susceptibility is enhanced enough as
It is discussed on the fluctuation-exchange (FLEX) approximation that the charge susceptibility χ c increases divergently in the 2D t – t ' Hubbard model near the half-filling as the strength of the onsite Coulomb interaction U is approached to the critical value U cr for the critical point to onset of the antiferromagnetic (AF) order. It turns out that the main origin of the divergence of χ c is the Aslamazov–Larkin (AL) type contribution which can be taken into account by the FLEX approximation and is enhanced by the strong AF correlations because two AF-fluctuation modes and the vertex corretions work cooperatively to enhance χ c . Indeed, AL-type contribution almost exhausts the enhanced part of χ c in the region U ≃ U cr . This result is consistent with experimental observations in under-doped cuprates LSCO and quantum Monte Carlo simulations by Furukawa and Imada [J. Phys. Soc. Jpn. 62 (1993) 2557].
The Hubbard model on a square lattice in the ground state is investigated. Various aspects of Mott transition at half-filling are clarified from the quantum Monte Carlo study. Critical exponents of the transition for charge and spin correlations are estimated. For the doping concentration δ, the charge susceptibility is proportional to δ -1 indicating the divergence of charge mass for δ→0, while the spin susceptibility is always finite and not singular near δ=0. Several theoretical consequences of the above results are discussed. Incommensurate peak amplitude of spin correlation scales as (δ-δ c ) -1 with δ c <0.01 in disagreement with RPA results ln (δ-δ c ). The antiferromagnetic order at the half-filling also shows strong correlation character and is not sensitive to the shape of the fermi surface, while the incommensurate peak observed away from the half-filling is sensitively suppressed by the loss of partial nesting consistently with the weak coupling picture. Comparisons with experimental indications of high- T c oxides are made.
We investigate the spin and charge susceptibilities of the two-dimensional Hubbard model based upon the perturbative calculation in the strength of correlation U. For U comparable to a bare bandwidth, the charge susceptibility decreases near half filling as hole doping approaches zero. This behavior suggesting the precursor of the Mott-Hubbard gap formation cannot be obtained without the vertex corrections beyond the random-phase approximation. In the low-temperature region, the spin susceptibility deviates from the Curie-Weiss-like law and finally turns to decrease with the decrease of temperature. This spin-gap-like behavior originates from the van Hove singularity in the density of states. \textcopyright{} 1996 The American Physical Society.
To understand nontrivial edge electronic states in strongly-correlated metals such as cuprate superconductors, we study the two-dimensional Hubbard models with open edge boundary. The position-dependences of the spin susceptibility and the self-energy are carefully analyzed self-consistently, by using the fluctuation-exchange (FLEX) approximation. It is found that spin susceptibilities are strongly enlarged near the (1,1) open edge when the system is near the half-filling. The enhancement is large even if the negative feedback from the self-energy is considered in the FLEX approximation. The present study predicts the emergence of nontrivial spin-fluctuation-driven phenomena near the edge, like the quantum criticality, edge superconductivity, and the bond-density-wave order.
We study the magnetic and charge dynamical response of a Hubbard model in a two-leg ladder geometry using the density matrix renormalization group (DMRG) method and the random phase approximation within the fluctuation-exchange approximation (FLEX). Our calculations reveal that FLEX can capture the main features of the magnetic response from weak up to intermediate Hubbard repulsion for doped ladders, when compared with the numerically exact DMRG results. However, while at weak Hubbard repulsion both the spin and charge spectra can be understood in terms of weakly interacting electron-hole excitations across the Fermi surface, at intermediate coupling DMRG shows gapped spin excitations at large momentum transfer that remain gapless within the FLEX approximation. For the charge response, FLEX can only reproduce the main features of the DMRG spectra at weak coupling and high doping levels, while it shows an incoherent character away from this limit. Overall, our analysis shows that FLEX works surprisingly well for spin excitations at weak and intermediate Hubbard UUU values even in the difficult low-dimensional geometry such as a two-leg ladder. Finally, we discuss the implications of our results for neutron scattering and resonant inelastic x-ray scattering experiments on two-leg ladder cuprate compounds.
To clarify the origin of the pseudogap and strange metal states as well as their mutual relationship in cuprate superconductors, a comprehensive study on the spectral function, Fermi surface, resistivity and dynamical spin susceptivity of the Hubbard model on the square lattice has been conducted by means of the ladder dual-fermion approximation with an electron self-energy correction. It is found that the appearance of these two states requires that the characteristic hole concentration below which the Mott-Heisenberg and Slater mechanisms of electron localization occurs pMSp_{\rm MS}pMS​ nearly coincides with the hole concentration where the Van Hove singularity (VHS) point is placed at the vicinity of the Fermi level. When this condition is met the VHS point is pinned at which the nesting condition of the antiferromagnetic (AFM) fluctuation is fulfilled almost everywhere on the Fermi surface in wide range of the hole concentration in a metallic state, i.e., the strange metal state. The spin fluctuation of the strange metal state is nearly quantum critical and the dynamical spin susceptivity is well described by overdamped spin wave having the ω/Tω/Tω/T scaling with the relaxation rate at the Planckian limit. Because of these distinctive features of the strange metal state, the kkk dependence of scattering rate of electrons is small and electrons behave as the marginal Fermi liquid, resulting in TTT-linear resistivity. In contrast, the pseudogap state is magnetically in the renormalized classical regime and the pseudogap is formed near the X point where the nesting condition of the short-range AFM order is fulfilled.