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Register a new userStudy of the superconducting order parameter in the negative-$U$ 2D-Hubbard model by grand-canonical twist-averaged boundary conditions
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By using variational Monte Carlo and auxiliary-field quantum Monte Carlo methods, we perform an accurate finite-size scaling of the $s$-wave superconducting order parameter and the pairing correlations for the negative-$U$ Hubbard model at zero temperature in the square lattice. We show that the twist-averaged boundary conditions (TABCs) are extremely important to control finite-size effects and to achieve smooth and accurate extrapolations to the thermodynamic limit. We also show that TABCs is much more efficient in the grand-canonical ensemble rather than in the standard canonical ensemble with fixed number of electrons. The superconducting order parameter as a function of the doping is presented for several values of $|U|/t$ and is found to be significantly smaller than the mean-field BCS estimate already for moderate couplings. This reduction is understood by a variational ansatz able to describe the low-energy behaviour of the superconducting phase, by means of a suitably chosen Jastrow factor including long-range density-density correlations.
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We apply recently developed smooth boundary conditions to the quantum Monte Carlo simulation of the two-dimensional Hubbard model. At half-filling, where there is no sign problem, we show that the thermodynamic limit is reached more rapidly with smooth rather than with periodic or open boundary conditions. Away from half-filling, where ordinarily the simulation cannot be carried out at low temperatures due to the existence of the sign problem, we show that smooth boundary conditions allow us to reach significantly lower temperatures. We examine pairing correlation functions away from half-filling in order to determine the possible existence of a superconducting state. On a $10times 10$ lattice for $U=4$, at a filling of $langle n rangle = 0.87$ and an inverse temperature of $beta=10$, we did find enhancement of the $d$-wave correlations with respect to the non-interacting case, a possible sign of $d$-wave superconductivity.
Fixed-node Greens function Monte Carlo calculations have been performed for very large 16x6 2D Hubbard lattices, large interaction strengths U=10,20, and 40, and many (15-20) densities between empty and half filling. The nodes were fixed by a simple Slater-Gutzwiller trial wavefunction. 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.
The two-dimensional Hubbard model with a bimodal distribution of on-site interactions, P(U_i) = (1-f)delta(U_i-U) + fdelta(U_i), is studied using a finite temperature quantum Monte Carlo technique and dynamical mean-field theory. We find long range antiferromagnetic order off half-filling is stabilized by the disorder, due to localization of the dopants on the U=0 sites. Whereas in the clean model there is a single gap at n=1, for nonzero f we find the compressibility and density of states exhibit gaps at two separate fillings.
Two-dimensional Hubbard model is very important in condensed matter physics. However it has not been resolved though it has been proposed for more than 50 years. We give several methods to construct eigenstates of the model that are independent of the on-site interaction strength $U$.
We investigate melting of stripe phases in the overdoped regime x>0.3 of the two-dimensional t-t-U Hubbard model, using a spin rotation invariant form of the slave boson representation. We show that the spin and charge order disappear simultaneously, and discuss a mechanism stabilizing bond-centered and site-centered stripe structures.
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