We nonperturbatively investigate the ground state magnetic properties of the 2D half-filled SU(2N) Hubbard model in the square lattice by using the projector determinant quantum Monte Carlo simulations combined with the method of local pinning fields. Long-range Néel orders are found for both the SU(4) and SU(6) cases at small and intermediate values of U. In both cases, the long-range Néel moments exhibit nonmonotonic behavior with respect to U, which first grow and then drop as U increases. This result is fundamentally different from the SU(2) case in which the Néel moments increase monotonically and saturate. In the SU(6) case, a transition to the columnar dimer phase is found in the strong interaction regime.
We perform large-scale projector determinant quantum Monte Carlo simulations to study the insulating states of the half-filled SU(6) Hubbard model on the square lattice. The transition from the antiferromagnetic state to the valence bond solid state occurs as increasing the Hubbard
U. In contrast, in the SU(2) and SU(4) cases antiferromagnetism persists throughout the entire interaction range. In the SU(6) case, antiferromagnetism starts to develop in the weak interacting regime based on the Slater mechanism of Fermi surface nesting. As
U passes a crossover value ${U}^{*}/t\ensuremath{\approx}9$, the single-particle gap scales linearly with
U, marking the onset of Mott physics. In the Mott regime, antiferromagnetism becomes to be suppressed as
U increases and vanishes after
U passes the critical value ${U}_{\mathrm{AF},\mathrm{c}}/t=13.3\ifmmode\pm\else\textpm\fi{}0.05$. The critical exponents are obtained via critical scalings as ${\ensuremath{\nu}}_{\mathrm{AF}}=0.60\ifmmode\pm\else\textpm\fi{}0.02$ and ${\ensuremath{\eta}}_{\mathrm{AF}}=0.44\ifmmode\pm\else\textpm\fi{}0.03$. As
U further increases, the valence bond solid ordering appears exhibiting the anomalous dimension ${\ensuremath{\eta}}_{\mathrm{VBS}}=0.98\ifmmode\pm\else\textpm\fi{}0.01$.
The Hubbard model has been widely used to describe magnetism due to itinerant electrons. However, except for the one-dimensional case, no exact solution of the model exists. We have studied the two-dimensional Hubbard model on a square lattice using a Monte Carlo simulation technique. Simulations were performed on lattices of up to 8×8 in spatial size. We will discuss results for thermodynamic properties and correlation functions as a function of temperature and interaction strength. For the half-filled band case, our results indicate that the system exhibits long-range antiferromagnetic order in the ground state for any nonzero interaction, although substantially reduced from the classical Néel state due to both charge and spin fluctuations. For the non-half-filled band case, our results suggest that no long-range magnetic order exists. We also don’t find any indication of short-ranged ferromagnetic correlations in the parameter range studied. We have also studied the predictions of various approximate treatments for this model, particularly the static approximation and the coherent potential approximation (CPA). By comparison with the Monte Carlo results, we discuss the validity of these schemes. Finally, we discuss the effect of changing the band structure on the magnetic properties of the system.
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 $24\ifmmode\times\else\texttimes\fi{}24$.
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.
Magnetic properties of the two-dimensional Hubbard-model are inferred from results of Monte Carlo simulations. Lattice sizes up to 8\ifmmode\times\else\texttimes\fi{}8 and temperatures down to
T=20t (
t=hopping) were studied. The half-filled system is found to exhibit antiferromagnetic long-range order for all values of the Coulomb repulsion
U. The low-temperature magnetic properties are found to be well described by spin-wave theory with renormalized local moment and spin-wave velocity. Numerical evidence presented suggests that when doped the system loses the long-range order immediately away from half filling.