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Physical review. B, Condensed matter

Harper’s equation for two-dimensional systems of antiferromagnetically correlated electrons

Seung-Pyo Hong, Sung‐Ho Suck Salk

Published Oct 1, 1999• 4 citations
Publisher

Abstract

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., $p/q.$

DOI
10.1103/physrevb.60.9550

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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.
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.
By deriving a generalized Harper's equation, we investigate the effects of temperature TTT and hole doping $\d$ on antiferromagnetically correlated electrons under the influence of an applied magnetic field. We obtain a phase diagram in a TTT-$\d$ 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.
We study the properties of a two-dimensional interacting electronic system in the presence of a staggered magnetic field. We find that metal-insulator transitions can be achieved at both zero and non-zero temperatures. A d-wave-like pseudogap is opened on the two-dimensional square Fermi surface. The staggered magnetic flux is found to suppress the antiferromagnetic order. When random fluctuations of the perfect staggered field are turned on and increased, a finite region of Fermi surface around (±π/2,±π/2) will be gradually formed as the bandwidth decreases. We also find that the assumed disturbed staggered field in our model can actually simulate the spin fluctuations occurring in the interacting system.
We present the first exact results for the T=0 dynamical structure factor of finite-sized two-dimensional square-lattice spin-(1/2 antiferromagnetic Heisenberg systems with up to 16 spins. Our results are compared to a recently proposed Schwinger boson mean-field theory. We find that the mean-field theory represents an excellent approximation to the exact spin excitation spectra at all allowed wave vectors and for all system sizes studied. We also determine the mean-field value for the T=0 staggered magnetization, mMF=0.306{m}^{\mathrm{MF}=0.306}mMF=0.306, to be in excellent agreement with published Monte Carlo results.
In the presence of a staggered magnetic field, the plaquette expansion of the Lanczos matrix elements are obtained for the antiferromagnetic 2D Heisenberg model up to order 1/Np (Np is the number of plaquettes on the lattice). The resulting approximate tri-diagonal form of the Hamiltonian is diagonalised for various values of the field strength in the -> 00 limit for the ground state energy density. From the behaviour of the ground-state energy density at weak fields, the staggered magnetisation at this order in the plaquette expansion is found to be 0·71 (in units where the Neel state staggered magnetisation is 1· 0).