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arXiv:1301.1012 · Journal of the Physical Society of Japan

Spontaneous Fermi Surface Deformation in the Three-Band Hubbard Model: A Variational Monte Carlo Study

Xiao-Jun Zheng, Zhongbing Huang, Liang‐Jian Zou

Published Jan 15, 2014• 4 citations
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Abstract

We perform a variational Monte Carlo study on spontaneous d-wave form Fermi surface deformation ($d$FSD) within the three-band Hubbard model. It is found that the variational energy of a projected Fermi sea is lowered by introducing an anisotropy between the hopping integrals along the x and y directions. Our results show that the $d$FSD state has the strongest tendency at half-filling in the absence of magnetism, and disappears as the hole concentration increases to $n_h\approx 1.15$. This is qualitatively in agreement with the mean field analysis and the exact diagonalization calculation for the one-band models, and provides a qualitative explanation to the "intra-unit-cell" electronic nematicity revealed by the scanning tunneling microscopy. An analysis of the dependence of $d$FSD on the parameters of the three-band model indicates that the copper on-site Coulomb interaction, the nearest-neighbor copper-oxygen repulsion, and the charge-transfer energy have a remarkable positive effect on $d$FSD.

DOI
10.7566/jpsj.83.024705

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We perform a variational Monte Carlo study on spontaneous d-wave form Fermi surface deformation (dddFSD) within the three-band Hubbard model. It is found that the variational energy of a projected Fermi sea is lowered by introducing an anisotropy between the hopping integrals along the x and y directions. Our results show that the dddFSD state has the strongest tendency at half-filling in the absence of magnetism, and disappears as the hole concentration increases to nh≈1.15n_h\approx 1.15nh​≈1.15. This is qualitatively in agreement with the mean field analysis and the exact diagonalization calculation for the one-band models, and provides a qualitative explanation to the "intra-unit-cell" electronic nematicity revealed by the scanning tunneling microscopy. An analysis of the dependence of dddFSD on the parameters of the three-band model indicates that the copper on-site Coulomb interaction, the nearest-neighbor copper-oxygen repulsion, and the charge-transfer energy have a remarkable positive effect on dddFSD.
We present a variational Monte Carlo (VMC) study of spontaneous Fermi-surface symmetry breaking in the $t\text{\ensuremath{-}}J$ model. We find that the variational energy of a Gutzwiller projected Fermi sea is lowered by allowing for a finite asymmetry between the xxx and the yyy directions. However, the best variational state remains a pure superconducting state with ddd-wave symmetry, as long as the underlying lattice is isotropic. Our VMC results are in good overall agreement with slave boson mean field theory (SBMFT) and renormalized mean field theory (RMFT), although apparent discrepancies do show up in the half-filled limit, revealing some limitations of mean field theories. VMC and complementary RMFT calculations also confirm the SBMFT predictions that many-body interactions can enhance any anisotropy in the underlying crystal lattice. Thus, our results may be of consequence for the description of strongly correlated superconductors with an anisotropic lattice structure.
The Fermi surface of the two-dimensional t- J model is studied using the variational Monte Carlo method. We study the Gutzwiller-projected d-wave superconducting state with an additional variational parameter t(')(v) corresponding to the next-nearest-neighbor hopping term. It is found that the finite t(')(v)<0 gives the lowest variational energy in the wide range of hole-doping rates. The obtained momentum distribution function shows that the Fermi surface deforms spontaneously. It is also shown that the Van Hove singularity is always located very close to the Fermi energy. Using the Gutzwiller approximation, we show that this deformation is due to the Gutzwiller projection operator or the strong correlation.
The Gutzwiller wave function for the three-band Hubbard model on a two-dimensional CuO2{\mathrm{CuO}}_{2}CuO2​ plane is studied by using the variational Monte Carlo (VMC) method in the limit Ud{\mathit{U}}_{\mathit{d}}Ud​\ensuremath{\rightarrow}\ensuremath{\infty}, where Ud{\mathit{U}}_{\mathit{d}}Ud​ is the Coulomb repulsion between holes on a Cu site. The VMC results for the energy and the fraction of d holes are compared with those of the Rice-Ueda type Gutzwiller approximation (GA). The difference between the VMC and the GA results are most pronounced at half-filling, and away from half-filling the two results agree well in both the hole-doped and the electron-doped cases. The doping dependence of the momentum distribution function is also studied.
We calculate the single-particle Green's function for a contact interaction with nearest-neighbor hopping on a square lattice as a function of chemical potential $\ensuremath{\mu}.$ This allows us to investigate the dependence of the leading Fermi-liquid dependencies on the band structure as the Fermi surface evolves from a circle at $\ensuremath{\mu}\ensuremath{\sim}\ensuremath{-}4t$ to a square at $\ensuremath{\mu}=0.$ The form of the single-particle self-energy $\ensuremath{\Sigma}(\stackrel{\ensuremath{\rightarrow}}{p},E)$ is determined by the density-density correlation function $\ensuremath{\chi}(\stackrel{\ensuremath{\rightarrow}}{q},\ensuremath{\omega})$ which develops two peaks for $\ensuremath{\mu}\ensuremath{\gtrsim}\ensuremath{-}2.5t$ unlike the parabolic band case. Near half-filling, $\ensuremath{\chi}(\stackrel{\ensuremath{\rightarrow}}{q},\ensuremath{\omega})$ becomes independent of $\ensuremath{\omega},$ one-dimensional behavior, at intermediate values of $\ensuremath{\omega},$ which leads to the one-dimensional behavior in $\ensuremath{\Sigma}(\stackrel{\ensuremath{\rightarrow}}{p},E).$ However, with $\ensuremath{\mu}<~\ensuremath{-}0.1t$ there is no influence on the Fermi-liquid dependencies from the spin-density wave instability. We find that throughout the doping region $\ensuremath{\Sigma}(\stackrel{\ensuremath{\rightarrow}}{p},E)$ remains qualitatively the same as for the isotropic Fermi surface with quantitative differences. The strong $\stackrel{\ensuremath{\rightarrow}}{p}$ and E dependence of the off-shell self-energy $\ensuremath{\Sigma}(p,E)$ found earlier for the parabolic band is recovered for $\ensuremath{\mu}\ensuremath{\lesssim}\ensuremath{-}t$ but deviates from this develop for $\ensuremath{\mu}\ensuremath{\gtrsim}\ensuremath{-}0.1t.$ The resonance peak width of the spectral function $A(\stackrel{\ensuremath{\rightarrow}}{p}E),$ has a linear dependence in ${\ensuremath{\xi}}_{\stackrel{\ensuremath{\rightarrow}}{p}}$ due to the E dependence of the imaginary part of $\ensuremath{\Sigma}(\stackrel{\ensuremath{\rightarrow}}{p},E).$ We point out that an accurate detailed form for $\ensuremath{\Sigma}(\stackrel{\ensuremath{\rightarrow}}{p},E)$ would be very difficult to recover from angle-resolved photoemission spectroscopy data for the spectral density. Since the leading corrections are determined by the long wavelength particle-hole excitations, the results found here for the Hubbard model carry over to Hamiltonians with finite range interactions.
On the basis of quantum Monte Carlo simulations we study the influence of "breathing" lattice distortions on the two-dimensional Hubbard model. In the half-filled band case the system remains stable against the formation of a charge-density wave already for intermediate values (U=4tU=4tU=4t) of the electronic interaction. However, the addition of holes allows for a charge-density-wave state. Thus, the structural instability is not driven by nesting of the Fermi surface, but by the combined effect of doping and Coulomb correlation. The influence of the distortion on the various pairing correlation functions is calculated.
Mechanisms of Mott transitions and d x 2 Ày 2 -wave superconductivity (SC) are studied in the half-filledband Hubbard model on square lattices with a diagonal hopping term (t 0 ), using an optimization (or correlated) variational Monte Carlo method.In the trial wave functions, a doublon-holon binding effect is introduced in addition to the onsite Gutzwiller projection.We mainly treat a d-wave singlet state and a projected Fermi sea.In both wave functions, first-order Mott transitions without direct relevance to magnetic orders occur at U ¼ U c , which is approximately the bandwidth, for arbitrary t 0 =t.These transitions originate in the binding or unbinding of a doublon to a holon.d-wave SC appears in a narrow range immediately below U c .The robust d-wave superconducting correlation is necessarily accompanied by enhanced antiferromagnetic correlation; the strength of SC decreases, as t 0 =t increases.