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arXiv:cond-mat/0010165 · Physical review. B, Condensed matter

Spatially homogeneous ground state of the two-dimensional Hubbard model

Federico Becca, Massimo Capone, Sandro Sorella

Published Nov 15, 2000• 56 citations
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Abstract

We investigate the stability with respect to phase separation or charge-density-wave formation of the two-dimensional Hubbard model for various values of the local Coulomb repulsion and electron densities using Green-function Monte Carlo techniques. The well known sign problem is particularly serious in the relevant region of small hole doping. We show that the difference in accuracy for different doping makes it very difficult to probe the phase separation instability using only energy calculations, even in the weak-coupling limit $(U=4t)$ where reliable results are available. By contrast, the knowledge of the charge correlation functions allows us to provide clear evidence of a spatially homogeneous ground state up to $U=10t.$

DOI
10.1103/physrevb.62.12700

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We investigate the stability with respect to phase separation or charge-density-wave formation of the two-dimensional Hubbard model for various values of the local Coulomb repulsion and electron densities using Green-function Monte Carlo techniques. The well known sign problem is particularly serious in the relevant region of small hole doping. We show that the difference in accuracy for different doping makes it very difficult to probe the phase separation instability using only energy calculations, even in the weak-coupling limit (U=4t)(U=4t)(U=4t) where reliable results are available. By contrast, the knowledge of the charge correlation functions allows us to provide clear evidence of a spatially homogeneous ground state up to U=10t.U=10t.U=10t.
Using recent advances in auxiliary-field quantum Monte Carlo techniques and the phaseless approximation to control the sign/phase problem, we determine the equation of state in the ground state of the two-dimensional repulsive single-band Hubbard model at intermediate interactions. Shell effects are eliminated and finite-size effects are greatly reduced by boundary-condition integration. Spin-spin correlation functions and structure factors are also calculated. In lattice sizes up to $16\ifmmode\times\else\texttimes\fi{}16$, the results show signals for phase separation. Upon doping, the system separates into one phase of density n=1n=1n=1 (hole free) and the other at density nc{n}_{c}nc​ $(\ensuremath{\sim}0.9)$. The long-range antiferromagnetic order is coupled to this process and is lost below nc{n}_{c}nc​.
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.
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We have studied the $t\ensuremath{-}J$ model using the Green function Monte Carlo technique. We have obtained accurate energies well converged in the thermodynamic limit by performing simulations for up to 242242242 lattice sites. By studying the energy as a function of hole doping we conclude that there is no phase separation in the physical region relevant for high- Tc{T}_{c}Tc​ superconductors. This finding is further supported by the hole-hole correlation function calculation. Remarkably, near the phase separation instability, for ${J}_{c}/t\ensuremath{\sim}0.5$ this function displays enhanced fluctuations at incommensurate wave vectors that scale linearly with the doping, in agreement with experimental findings.
Fixed-node Green's-function Monte Carlo calculations have been performed for very large 16x16 two-dimensional Hubbard lattices, large interaction strengths U=10,20, and 40, and many (15 similar to 20) densities between empty and half-filling. The nodes were fixed by a simple Slater-Gutzwiller trial wave function. For each value of U we obtained a sequence of ground-state energies which is consistent with the possibility of a phase separation close to half-filling, with a hole density in the hole-rich phase which is a decreasing function of U. The energies suffer, however, from a fixed-node bias: more accurate nodes are needed to confirm this picture. Our extensive numerical results and their test against size, shell, shape, and boundary-condition effects also suggest that phase separation is quite a delicate issue, on which simulations based on smaller lattices than considered here are unlikely to give reliable predictions. RI Capone, Massimo/A-7762-2008; Guidoni, Leonardo/G-3759-2011
We investigate the ground-state properties of the two-dimensional Hubbard model, based on the off-diagonal wave function variational Monte Carlo method. We use an optimized wave function that is improved from an initial one-body wave function by multiplying by multiple correlation operators that are given by the form of exp(−S-S−S)-type where SSS is a suitable operator. We examine the inhomogeneous ground state at near 1/8 doping in the strongly correlated region where the on-site Coulomb interaction is larger than the bandwidth. The ddd-wave superconductivity with a spatially oscillating gap function can coexist with the charge ordering in the ground state without magnetic ordering, and superconducting condensation energy increases by this coexistence. We also show the ddd-wave pair correlation function as a function of lattice sites. The correlation function indicates that the long-range superconducting order indeed exists, and also that the strong electron correlation suppresses the pair correlation function.