A recently proposed projection operator technique based on the introduction of cumulants is used to investigate the ground-state energy of the Hubbard model at half filling on a square lattice in two dimensions, in the antiferromagnetic phase. Our results in the intermediate and large regime of the ratio U/t are below those of variational Monte Carlo calculations, which set an upper bound for the energy. By including the most dominant spin-fluctuation processes, the present calculation also obeys the correct infinite U/t limit, where the Hubbard model at half filling reduces to the Heisenberg antiferromagnet. The relation of our approach to recent coupled-cluster calculations for the Hubbard model is also discussed. \textcopyright{} 1996 The American Physical Society.
We extend a Quantum Monte Carlo (QMC) algorithm to the Hubbard model containing bond-dependent off-diagonal hoppings, which describes the manganites and other similar systems, such as systems with spin-flip hoppings. To show correctness of this extension, we detect two simple examples of one-dimensional chains. The first one is half-filled and the hopping matrixes between arbitrary nearest neighboring pairs are uniform, i.e.,
ti,i+1=ti+1,i+2 (i=1,2,3,…). The other one is quarter-filled and the hopping matrixes alternate every four lattice constants with ${t}_{i,i+1}{=t}_{i+1,i+2}\ensuremath{\ne}{t}_{i+2,i+3}{=t}_{i+3,i+4}$
(i=1,5,9,…). Results of the two examples are reasonable.
We design a novel formalism of determinant quantum Monte Carlo method for the half-filled Hubbard model with on-site Hubbard interaction
U and nearest-neighbor density-density interaction
V on the square lattice. The formalism is free of sign problem for $|U|\ensuremath{\ge}4|V|$, and is achieved by introducing discrete auxiliary fields on the nearest-neighbor bonds alone. Based on this formalism, we study the ground-state phase diagram of the model systematically using the projector algorithm. Within the sign-problem free parameter space $|U|\ensuremath{\ge}4|V|$, we obtain antiferromagnetism for $U\ensuremath{\ge}4|V|>0$, charge density wave for $U<\ensuremath{-}4V$ and
V>0,s-wave superconductivity for
U<0 and small negative
V, and phase separation for
U<0 and a larger negative
V. We also obtain the single particle gap and spin excitation spectra, and by comparison to mean field results, as well as available literatures, we discuss the possible phase boundary beyond the sign-problem free region. The unbiased numerically exact results can be taken as benchmarks in future studies. Finally, we discuss possible extension for longer-range interactions in the model.
We investigate the phase diagram of the half-filled
SU(N) Hubbard-Heisenberg model with hopping
t, exchange
J, and Hubbard
U, on a two-dimensional square lattice. In the large-
N limit, and as a function of decreasing values of
t∕J, the model shows a transition from a
d-density wave state to a spin dimerized insulator. A similar behavior is observed at
N=6 whereas at
N=2 a spin density wave insulating ground state is stabilized. The
N=4 model, has a
d-density wave ground state at large values of
t∕J which as a function of decreasing values of
t∕J becomes unstable to an insulating state with no apparent lattice and spin broken symmetries. In this state, the staggered spin-spin correlations decay as a power law, resulting in gapless spin excitations at $\stackrel{P\vec}{q}=(\ensuremath{\pi},\ensuremath{\pi})$. Furthermore, low lying spin modes with small spectral weight are apparent around the wave vectors $\stackrel{P\vec}{q}=(0,\ensuremath{\pi})$ and $\stackrel{P\vec}{q}=(\ensuremath{\pi},0)$. This gapless spin liquid state is equally found in the SU(4) Heisenberg $(U∕t\ensuremath{\rightarrow}\ensuremath{\infty})$ model in the self-adjoint antisymmetric representation. An interpretation of this state in terms of a $\ensuremath{\pi}$-flux phase is offered. Our results stem from projective
(T=0) quantum Monte Carlo simulations on lattice sizes ranging up to $24\ifmmode\times\else\texttimes\fi{}24$.
The half-filled Hubbard model on the honeycomb lattice is investigated by numerically exact large-scale quantum Monte Carlo simulations for lattice sizes up to 2592 sites. By performing careful finite-size scaling for the spin-spin correlation functions, calculated with a high degree of accuracy, we find that the ground state is antiferromagnetically long-range ordered at U / t = 4, where U is the on-site Hubbard interaction and t is the nearest neighbor hopping. Our result is in sharp contrast to a recent report [Meng et al. , Nature 464, 847 (2010)], where instead strong evidence of spin liquid behavior is found.
We develop series expansions for the ground state properties of the Hubbard model by introducing an Ising anisotropy into the Hamiltonian. For the two-dimensional square lattice half-filled Hubbard model, the ground state energy, local moment, sublattice magnetization, uniform magnetic susceptibility, and spin stiffness are calculated as a function of U/t, where U is the Coulomb constant and t is the hopping parameter. Magnetic susceptibility data indicate a crossover around U\ensuremath{\approxeq}4 between spin density wave antiferromagnetism and Heisenberg antiferromagnetism. Comparisons with Monte Carlo simulations, random phase approximation result, and mean-field solutions are also made.