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arXiv:cond-mat/9808328

Study of Harper's Equation for the 2-D Systems of Antiferromagnetically Correlated Electrons in an External Magnetic Field

Seung-Pyo Hong, Hyeonjin Doh, Sung‐Ho Suck Salk

Published Aug 29, 1998• 0 citations
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Abstract

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 $q$ value but not at odd $q$ of a given magnetic flux quantum per plaquette, $p/q$.

DOI
10.48550/arxiv.cond-mat/9808328

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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.
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.
The continuous imaginary-time quantum Monte Carlo method with the worm update algorithm is applied to explore the ground-state properties of the spin-1/2 Heisenberg model with antiferromagnetic (AF) coupling J>0 and ferromagnetic (F) coupling J^{'}<0 along zigzag and armchair directions, respectively, on honeycomb lattice. It is found that by enhancing the F coupling J^{'} between zigzag AF chains, the system is smoothly crossover from one-dimensional zigzag spin chains to a two-dimensional magnetic ordered state. In absence of an external field, the system is in a stripe-ordered phase. In the presence of uniform and staggered fields, the uniform and staggered out-of-plane magnetizations appear while the stripe order remains in the xy plane, and a second-order quantum phase transition (QPT) at a critical staggered field is observed. The critical exponents of correlation length for QPTs induced by a staggered field for the cases with J>0, J^{'}<0 and J<0, J^{'}>0 are obtained to be ν=0.70046(1) and 0.7086(3), respectively, indicating that both cases belong to O(3) universality. The corresponding dynamic and susceptibility exponent z and γ/ν are fitted to be 1.006572(9), 1.9412(2) and 1.004615(8), 1.96121(9) for the two cases, respectively. The scaling behavior in a staggered field is analyzed, and the ground-state phase diagrams in the plane of coupling ratio and staggered field are presented for two cases. The temperature dependence of susceptibility and specific heat of both systems in external magnetic fields is also discussed. A Kosterlitz-Thouless phase transition is found for the present system in a uniform field.
The Hubbard model in a two-dimensional square lattice is studied within the unrestricted Hartree-Fock approximation. A wide variety of solutions are found, as a function of filling and value of the Coulomb repulsion. Their properties range from those of magnetic polarons to a behavior similar to electrons in an external magnetic field (flux phases). The main features of the vortex solution are studied. It is shown that its energy increases logarithmically with system size, and that it becomes more stable for high values of the Coulomb repulsion and doping levels. Also, multivortex configurations are shown to exist. The implications of our results in the qualitative behavior of the Hubbard model as function of doping and strength of the interaction are discussed.
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).
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.