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Journal of the Physical Society of Japan

Effect of Gauge Fields in a Uniform RVB State

Kazuhiro Kuboki

Published Feb 15, 1993• 6 citations
Publisher

Abstract

The effect of gauge fields representing the fluctuations of the local constraint and those of the phases of the bond order parameters is examined for the uniform RVB state, which is a mean-field (MF) solution of the t-J model within the slave-boson formalism. It is found that the crossover temperature for the Bose condensation of holons, T BE , below which the system may be essentially considered to be a Fermi liquid, is considerably reduced as compared with that in the MF approximation. The temperature dependences of the transport relaxation rate and the electrical resistivity are also examined

DOI
10.1143/jpsj.62.420

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The effect of gauge fields representing the fluctuations of the local constraint and those of the phases of the bond order parameters is examined for the uniform RVB state, which is a mean-field (MF) solution of the t-J model within the slave-boson formalism. It is found that the crossover temperature for the Bose condensation of holons, T BE , below which the system may be essentially considered to be a Fermi liquid, is considerably reduced as compared with that in the MF approximation. The temperature dependences of the transport relaxation rate and the electrical resistivity are also examined
We study a version of the uniform resonating-valence-band state in which fermions and spinless bosons are coupled by a gauge field. We show that above the Bose-Einstein temperature, the boson inverse lifetime due to scattering by the gauge field is of order kT, which suppresses the condensation temperature and leads to a linear T resistivity. The Hall number is proportional to the hole density and temperature dependent. The single-particle spectral weight exhibits a continuum plus a broadened peak. The ``Fermi surface'' area satisfies Luttinger's theorem. Comparison with the anomalous normal-state properties of oxide superconductors is made.
The t ′ - J model ( t ′ : transfer integral between next nearest neighbor sites) on a square lattice is studied within the slave-fermion formalism. In a mean-field approximation the antiferromagnetic long-range order (AFLRO), which is represented by the Bose condensation of the spinon at T =0, persists even for large doping rate. It is shown that the gauge field representing the fluctuations around the mean-field solution works in reducing the AFLRO, making the phase diagram of the ground state closer to that observed experimentally.
The competition and possible coexistence of the flux phase and pairing states are considered within the slave-boson approach. In addition to the gauge field, coupling holons, and spinons, a statistical gauge field is introduced to account for the hard-core nature of holons. Using the equivalence of \ensuremath{\pi}-uniform and -staggered fluxes, we show the possibility of reducing the staggered flux and guaranteeing the commensurability condition of the uniform flux for holons at the same time. For certain dopings the frustration of the spinon gauge field to holon motion can be compensated by the holon's own statistical gauge field. Contrary to earlier conclusions of other authors, we find that the flux phase can coexist with the resonating-valence-bond (RVB) states below a critical doping concentration ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$, beyond which the d-wave RVB state takes over.
We study the effect of a strongly fluctuating gauge field on a degenerate Bose liquid, relevant to the charge degrees of freedom in doped Mott insulators. We find that the superfluidity is destroyed. The resulting metallic phase is studied using quantum Monte Carlo methods. Gauge fluctuations cause the boson world lines to retrace themselves. We examine how this world-line geometry affects the physical properties of the system. In particular, we find a transport relaxation rate of the order of 2kBT{2k}_{B}T2kB​T, consistent with the normal state of the cuprate superconductors. We also find that the density excitations of this model resemble those of the full ttt- JJJ model.
This Thesis analyzes the role of a mean-field theory and of the fluctuations in two different fermionic systems: the BCS-BEC crossover and high-Tc superconducting cuprates. In the first part of the Thesis we introduce the mean-field theory and the Gaussian-level fluctuations for the BCS-BEC crossover, i.e. the continuous evolution observed in ultracold neutral fermionic systems, from a weakly-coupled regime where fermions form Cooper pairs, to a strongly-coupled regime where the fermions at first form bosonic molecular dimers, subsequently undergoing Bose-Einstein condensation for low enough temperatures. We then analyze some problems related to the crossover: the condensate fraction for a spin-unbalanced Fermi gas, the Beliaev decay for collective excitations and the case of a two-dimensional Fermi gas, for which we calculate the first sound velocity and the Berezinskii-Kosterlitz-Thouless critical temperature, in very good agreement with recent experimental data. Finally we analyze a regularization procedure for the equation of state in the deep-BEC limit, allowing one to analytically derive the correct ratio between the fermionic and bosonic scattering lengths. In the second part of the Thesis we introduce a gauge approach to superconductivity in cuprates in which the hole is decomposed as the product of a spinful neutral particle, the spinon, and a spinless charged particle, the holon. The statistics of each particle is modified by binding it to a gauge field providing a statistical flux, this approach being analogous to Chern-Simons bosonization. We thus obtain a model characterized by three characteristic temperatures corresponding, respectively, to the appearance of a finite density of incoherent holon pairs, of a finite density of incoherent spinon pairs and, finally, to the phase coherence leading to superconductivity. Specifically in the present Thesis within this model we study the superfluid density, demonstrating that the spinon and holon contributions sum according to a Ioffe-Larking-like rule, analogous to that they found for resistivity, showing excellent agreement with experimental data in the moderate underdoping up to optimal doping region. We also demonstrated that the formalism reproduces the quasi-universality observed in experimental data at different dopings and allows for an analytical derivation of a relation that approximates the Uemura relation for moderate dopings.
A two-dimensional square-lattice Hubbard model is investigated. A slave-fermion formulation, in which the electron operator is expressed by a combination of bose operators for the spin freedom, and fermi operators for the charge freedom, is used. The phase diagram for the resonating valence bond (RVB) state is obtained. The RVB state shows long-range antiferromagnetic order at T =0, the period of which deviates from that of the commensurate Néel order as the system deviates from the half-filled case.