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Journal of Physics Conference Series

Quantum fluctuations in the one dimensional doped Hubbard model

Norikazu Tomita

Published Mar 1, 2009• 0 citations
Publisher

Abstract

Quantum fluctuations in the one dimensional (ID) doped Hubbard model are described by superposition of optimized non-orthogonal Slater determinants. It is explicitly shown that the spin and charge fluctuations are mostly separated as spinons and holons in the strong interaction regime, while the fluctuations due to the spin-charge pled states become important in the weak and intermediate interaction regimes

DOI
10.1088/1742-6596/150/4/042214

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Quantum fluctuations in the one dimensional (ID) doped Hubbard model are described by superposition of optimized non-orthogonal Slater determinants. It is explicitly shown that the spin and charge fluctuations are mostly separated as spinons and holons in the strong interaction regime, while the fluctuations due to the spin-charge pled states become important in the weak and intermediate interaction regimes
Electronic states in the one-dimensional (1D) doped Hubbard model are described by superposition of optimized nonorthogonal Slater determinants (S-dets). Analysis on the S-dets allows us to visualize quantum fluctuations. In the weak and intermediate interaction regimes, quantum fluctuations are described by translation and breathing motions of spin-charge coupled defects called polarons as well as spin-charge decoupled defects called holons and spinons. In the strong-interaction regime, on the other hand, spin and charge fluctuations are mostly separated as spinons and holons, especially in the lightly doped systems $(\ensuremath{\delta}=0.08)$. In the highly doped systems $(\ensuremath{\delta}=0.24)$, polarons also play an important role. Finally, it is shown that in the 1/3-filled systems, the concepts of holon, spinon, and polaron do not work anymore. The electronic structure is qualitatively described by mixtures of two different density waves having triple periodicity to the lattice. The domains of these different density waves make quantum fluctuations.
Quantum fluctuations (QF's) in the two-dimensional Hubbard model are visualized by superposition of optimized nonorthogonal Slater determinants. In the half-filled system, QF's consist of rotational and translational motions of spinon-antispinon pairs, while in the lightly doped systems (delta=0.96), those motions of polarons form the QF's. It is shown that an attractive interaction works between two polarons, in the framework of a projected Hartree-Fock picture. At about 10% doping, the ground state has a stripe structure and QF's due to deviations from the uniform stripe. The present method gives the ground state energies comparable or in some cases superior to the variational Monte Carlo method with a Gutzwiller projection parameter.
Quantum fluctuations (QFs) in the two-dimensional Hubbard model are visualized by using a resonating Hartree-Fock method. Wave functions of optimized multi-Slater determinants show that QFs in the half-filled system are described by vibration, translation, and rotation of spinon-antispinon pairs, while those motions of polarons constitute dominant QFs in the lightly doped systems. We show that an attractive interaction works between two polarons in the framework of a projected Hartree-Fock approximation. The ground states at about 10% doping have a stripe structure and Q’s due to deviations from a uniform stripe.
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.
We study the spin and charge fluctuations of the extended Hubbard model with on-site interaction UUU and first neighbor interaction VVV on the two-dimensional square lattice in the weak to intermediate coupling regime. We propose an extension of the two-particle self-consistent approximation that includes the effect of functional derivatives of the pair-correlation functions on irreducible spin and charge vertices. These functional derivatives were ignored in our previous work. We evaluate them assuming particle-hole symmetry. The resulting theory satisfies conservation laws and the Mermin-Wagner theorem. Our current results are in much better agreement with benchmark quantum Monte Carlo results. This theory allows us to reliably determine the crossover temperatures toward renormalized-classical regimes, and hence, the dominant instability as a function of UUU and VVV. We have considered fillings n=1n=1n=1 and n=0.75n=0.75n=0.75. Either spin or charge fluctuations can dominate. The wave vector is self-determined by the approach.
The spin-holon effective Hamiltonian proposed by Zou and Anderson (1988) is used to calculate the chemical potential and the self-energy correction of spinons. The authors' results show that the effect of spin-exchange interaction is to enlarge the spinon bandwidth. For low temperatures and fixed doping fraction delta , the renormalized bandwidth and the chemical potential are nearly independent of temperature, but both change rapidly with the doping fraction. In the superfluid phase, the effect of increasing the doping fraction or increasing the on-site Coulomb repulsion U is to increase the relative kinetic energy of spinons, leading to a decrease in the superfluid transition temperature T s ( delta ), which is sensitive to various choices of U and the band parameter t; the increase in U tends to shift the boundary of T s ( delta ) towards a lower doping fraction. The correction due to spin fluctuations is extremely important for small doping fractions, leading to modification of the results of Baskaran, Zou and Anderson (1987), and Ruckstein, Hirschfeld and Appel (1987). Moreover, in the region of delta <or=8t/ pi 2 U, the effect of paramagnon fluctuations renders the mean-field theory invalid. The authors also discuss the effects of holon fluctuations on the mean-field results.