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Journal of Physics Condensed Matter

Properties of a weakly interacting electronic system under a staggered magnetic field

Jin An, Chang-De Gong

Published Aug 8, 2000• 0 citations
Publisher

Abstract

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.

DOI
10.1088/0953-8984/12/34/305

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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 a systematic study of the anisotropic spin-1/2 Heisenberg model in staggered magnetic fields in two dimensions. To mimic real materials, we consider a system of coupled, antiferromagnetic chains, whose interchain interaction can be either ferro- or antiferromagnetic. When the staggered field is commensurate with the magnetic interactions, an energy gap opens immediately and follows a power law as a function of the applied field, similar to the situation in one dimension. When the field competes with the interactions, a quantum phase transition (QPT) occurs from a gapless, magnetically ordered phase at low fields to a gapped, disordered regime. We use a continuous-time Monte Carlo method to compute the staggered moment of the ordered phases and the spin gap of the disordered phases. We deduce the phase diagrams as functions of the anisotropy ratio and the applied field, and calculate the scaling behavior of the models in both quantities. We show that in the competitive case, the staggered field acts to maintain a regime of quasi-1D behavior around the QPT, and we discuss as a consequence the nature of the crossover from one-dimensional (1D) to 2D physics.
We investigate the doped two-dimensional Hubbard model at finite temperature using controlled diagrammatic Monte Carlo calculations allowing for the computation of spectral properties in the infinite-size limit and, crucially, with arbitrary momentum resolution. We show that three distinct regimes are found as a function of doping and interaction strength, corresponding to a weakly correlated metal with properties close to those of the non-interacting system, a correlated metal with strong interaction effects including a reshaping of the Fermi surface, and a pseudogap regime at low doping in which quasiparticle excitations are selectively destroyed near the antinodal regions of momentum space. We study the physical mechanism leading to the pseudogap and show that it forms both at weak coupling when the magnetic correlation length is large and at strong coupling when it is shorter. In both cases, we show that spin-fluctuation theory can be modified in order to account for the behavior of the non-local component of the self-energy. We discuss the fate of the pseudogap as temperature goes to zero and show that, remarkably, this regime extrapolates precisely to the ordered stripe phase found by ground-state methods. This handshake between finite temperature and ground-state results significantly advances the elaboration of a comprehensive picture of the physics of the doped Hubbard model.
The competition between the staggered flux state, or the d-density wave state, and the d-wave pairing state is analyzed in a two-dimensional $t\ensuremath{-}J$ model based on the U(1) slave boson mean-field theory. Not only staggered flux of spinons but also staggered flux of holons are considered. In this formalism, the hopping order parameter of physical electron is described by the product of hopping order parameters of spinons and holons. The staggered flux amplitude of electrons is the difference of staggered flux amplitude of spinons and that of holons. In the $\ensuremath{\pi}$-flux phase of spinons, staggered fluxes of spinons and holons cancel completely and the staggered flux order of electrons does not exist. However, in the staggered flux phase of spinons whose staggered flux amplitude is not $\ensuremath{\pi},$ fluxes does not cancel completely and the staggered flux amplitude of electron remains. Thus the phase transition between these two phases, the $\ensuremath{\pi}$-flux phase and the staggered flux phase of spinons, becomes a second-order transition in the physical electron picture. The order parameter which characterizes this transition is the staggered flux order parameter of electrons. A mean-field phase diagram is shown. It is proved analytically that there is no coexistence of staggered flux and d-wave pairing. The temperature dependence of Fermi surface and excitation gap at $(0,\ensuremath{\pi})$ are shown. These behaviors are consistent with angle-resolved photoemission spectroscopy experiments.
Long-wavelength spin fluctuations prohibit antiferromagnetic long-range order at finite temperature in two dimensions. Nevertheless, the correlation length starts to grow rapidly at a crossover temperature, leading to critical slowing down and to a renormalized-classical regime over a wide range of temperature, between a fraction of the mean-field transition temperature and the zero-temperature ordered state. This leads to a single-particle pseudogap of the kind observed in electron-doped cuprates. Very few theoretical methods can claim an accurate description of this regime. The challenge is that in this regime Fermi-liquid quasiparticles are already destroyed and new quasiparticles of the ordered state are not fully formed yet. Here, we study this problem for the two-dimensional Hubbard model by first generalizing the two-particle self-consistent approach. Using a special algorithm, spin fluctuations are treated in the thermodynamic limit even for large correlation lengths. The effects of Kanamori-Br\"uckner screening, of classical and of quantum fluctuations are taken into account. Results are presented at half filling for the one-band Hubbard model with nearest-neighbor hopping. They agree well with available benchmark diagrammatic quantum Monte Carlo at high temperature where the pseudogap opens up. In addition to temperature-dependent spectral properties, we find quantum corrections to the zero-temperature renormalized mean-field antiferromagnetic gap. Finally, analytic continuation of the Matsubara results for spectral functions show that the pseudogap opens up at significantly higher temperature than was previously identified based on the Matsubara data only.
The influence of spin and charge fluctuations on spectra of the two-dimensional fermionic Hubbard model is considered using the strong coupling diagram technique. Infinite sequences of diagrams containing ladder inserts, which describe the interaction of electrons with these fluctuations, are summed, and obtained equations are self-consistently solved for the ranges of Hubbard repulsions [Formula: see text], temperatures [Formula: see text] and electron concentrations [Formula: see text] with t the intersite hopping constant. For all considered U the system exhibits a transition to the long-range antiferromagnetic order at [Formula: see text]. At the same time no indication of charge ordering is observed. Obtained solutions agree satisfactorily with results of other approaches and obey moments sum rules. In the considered region of the U-T plane, the curve separating metallic solutions passes from [Formula: see text] at the highest temperatures to U = 2t at [Formula: see text] for half-filling. If only short-range fluctuations are allowed for the remaining part of this region is occupied by insulating solutions. Taking into account long-range fluctuations leads to strengthening of maxima tails, which transform a part of insulating solutions into bad-metal states. For low T, obtained results allow us to trace the gradual transition from the regime of strong correlations with the pronounced four-band structure and well-defined Mott gap for [Formula: see text] to the Slater regime of weak correlations with the spectral intensity having a dip along the boundary of the magnetic Brillouin zone due to an antiferromagnetic ordering for [Formula: see text]. For [Formula: see text] and [Formula: see text] doping leads to the occurrence of a pseudogap near the Fermi level, which is a consequence of the splitting out of a narrow band from a Hubbard subband. Obtained spectra feature waterfalls and Fermi arcs, which are similar to those observed in hole-doped cuprates.