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Journal of the Physical Society of Japan

FLEX Study on Enhanced Charge Susceptibility near Antiferromagnetic Mott Transition in Two-Dimensionalt–t' Hubbard Model

K Morita, Hideaki Maebashi, Kazumasa Miyake

Published Dec 15, 2003• 9 citations
Publisher

Abstract

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].

DOI
10.1143/jpsj.72.3164

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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].
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
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.
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.
(1) The wave number dependence of the static spin susceptibility χ( q ) and (2) the effective interaction between quasiparticles mediated by spin fluctuations in the dilute two dimensional Hubbard model are investigated. The quantum Monte Carlo method (QMC) and the fluctuation exchange approximation (FLEX) are applied to this model. It is found that a maximum at wave number q =0 emerges and develops in χ( q ) as the interaction U gets strong. It is also found that the most attractive component of the effective interaction mediated by spin fluctuations is the p -wave component in the strong coupling region where a maximum at q =0 devolops in χ( q ).
(1) The wave number dependence of the static spin susceptibility χ( q ) and (2) the effective interaction between quasiparticles mediated by spin fluctuations in the dilute two dimensional Hubbard model are investigated. The quantum Monte Carlo method (QMC) and the fluctuation exchange approximation (FLEX) are applied to this model. It is found that a maximum at wave number q =0 emerges and develops in χ( q ) as the interaction U gets strong. It is also found that the most attractive component of the effective interaction mediated by spin fluctuations is the p -wave component in the strong coupling region where a maximum at q =0 devolops in χ( q ).
We study the low-temperature critical behavior of the one-dimensional Hubbard model near half filling caused by enhanced antiferromagnetic fluctuations. We use a mean-field-type approximation with a two-particle self-consistency renormalizing the bare interaction. It allows us to control a transition from high to low temperatures as well as from weak to strong-coupling. We show that there is a crossover temperature T0 = t exp{−1/Uρ(0)} for arbitrary interaction U > 0 and the bare density of states at the Fermi energy ρ(0) > 0. The solution at lower temperatures goes over to strong coupling and approaches a quantum critical point with the diverging staggered susceptibility and a gap in the excitation spectrum at zero temperature.