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arXiv:cond-mat/9609225

Antiferromagnetic Correlation under the External Magnetic Field in the Hubbard Model

Sungkun Hong, Hyeonjin Doh, S. H. Suck Salk

Published Sep 24, 1996• 0 citations
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Abstract

By deriving a generalized Harper's equation, we investigate the effects of temperature $T$ and hole doping $\d$ on antiferromagnetically correlated electrons under the influence of an applied magnetic field. We obtain a phase diagram in a $T$-$\d$ plane for staggered magnetization under the external field. We find that away from half filling the maximum values of staggered magnetization occur with rapid convergence to a finite temperature constant near half filling. We discover the reentrant behavior of the staggered magnetization in the presence of the magnetic field.

DOI
10.48550/arxiv.cond-mat/9609225

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By deriving a generalized Harper's equation, we investigate the effects of temperature TTT and hole doping \d\d\d on antiferromagnetically correlated electrons under the influence of an applied magnetic field. We obtain a phase diagram in a TTT-\d\d\d plane for staggered magnetization under the external field. We find that away from half filling the maximum values of staggered magnetization occur with rapid convergence to a finite temperature constant near half filling. We discover the reentrant behavior of the staggered magnetization in the presence of the magnetic field.
Considering interacting (antiferromagnetically correlated) electrons, we derive a generalized Harper's equation for the square lattice of infinite size. We obtain an analytic expression for the density of states from the newly derived Harper's equation. We present a predicted phase diagram of staggered magnetization in the plane of temperature vs doping rate and discover a possibility of reentrant behavior of the staggered magnetization even in the presence of applied magnetic field. It is shown that below a critical electron correlation strength (Coulomb repulsion) the staggered magnetization in the presence of magnetic field vanishes at an even denominator qqq value but not at odd qqq of a given magnetic flux quantum per plaquette, p/qp/qp/q.
Considering interacting (antiferromagnetically correlated) electrons, we derive a generalized Harper's equation in a mean-field approximation for a square lattice of infinite size. In the present study with the aid of a gap equation we explain the cause of the oscillatory behavior in staggered magnetization with the variation of an applied magnetic field for two-dimensional systems of antiferromagnetically correlated electrons. Exact diagonalization calculations on small clusters show additional evidence for the oscillatory behavior of staggered magnetization. We find that for systems of weakly correlated electrons both mean-field and exact diagonalization calculations yield an identical behavior in the propensity of diminishing staggered magnetization for even-denominator (but not for odd-denominator) values of q in the magnetic flux quanta per plaquette, i.e., p/q.p/q.p/q.
We study the infinite-dimensional Hubbard model within the self-consistent second-order U-perturbation treatment (SOPT), which is a conserving approximation and the simplest systematic improvement of the Hartree approximation (HA). For half filling we find antiferromagnetic solutions, but even for small Coulomb repulsion U the critical temperature is substantially reduced compared to that obtained in the HA. We construct the phase diagram as a function of doping and find regions of re-entrant behaviour in the temperature dependence of the staggered magnetization away from half filling. The stability of the ordered solutions is investigated by calculation of the grand canonical potential and the filling fraction dependence of the chemical potential; for small values of U the antiferromagnetic phase transition is continuous (as usual), but for larger U the SOPT yields a first-order phase transition. For low temperatures and away from half filling there may be a region of phase coexistence between the antiferromagnetic and homogeneous phases.
The influence of the staggered magnetic field h on properties of the one-dimensional t-J and Hubbard models with nearly half-filled bands are studied. Using the exact diagonalization method for small systems as well as analytical approaches possible in the anisotropic model and for h\ensuremath{\gg}t, we determine the phase diagram of the t-J-h model at low doping, which displays three different regimes: the phase with repelling holes for JJc{\mathit{J}}_{\mathit{c}}Jc​, the phase with paired holes for Jc{\mathit{J}}_{\mathit{c}}Jc​JJs{\mathit{J}}_{\mathit{s}}Js​, and the phase separation for J>Js{\mathit{J}}_{\mathit{s}}Js​. Employing for h\ensuremath{\ne}0 the analogy with the universal behavior of one-dimensional interacting fermions within the Luther-Emery regime, we calculate the charge exponent ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$, which can be ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$>1 in the pairing regime, indicating dominant superconducting fluctuations. An analogous analysis, in particular the perturbation expansion in t/h, performed for the Hubbard t-U-h model shows a phase of stable hole pairs for UUc{\mathit{U}}_{\mathit{c}}Uc​. Again ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$ seems to approach a nonuniversal value at half-filling.
We have studied the single-band Hubbard model on a two-dimensional square lattice slightly below half filling. Using the canonical transformation and a form of variational wave function that allows an expansion in terms of hole concentration $\ensuremath{\delta}$ with respect to half filling, we find that a nonzero $\ensuremath{\delta}$ results in a frustration of the antiferromagnetic (AF) order favored by the superexchange interaction. Use of a variational Monte Carlo calculation enables us to construct a phase diagram in the $\frac{t}{U\ensuremath{-}\ensuremath{\delta}}$ plane in which the AF order disappears at $\ensuremath{\delta}\ensuremath{\approx}0.06$ for a typical value of tU=14\frac{t}{U}=\frac{1}{4}Ut​=41​.