We investigate ground state properties of the half-filled staggered-flux Hubbard model on a square lattice. Energy gaps to charge and spin excitations and magnetic as well as dimer orders are calculated as a function of interaction strength U/t by means of a constrained-path quantum Monte Carlo method. It is found that the system is a semimetal at U/t≲5.6 and a Mott insulator, with long-range antiferromagnetic order, at U/t≳6.6. In the range 5.6≲U/t≲6.6, the ground state is a correlated insulator where both magnetic and dimer orders are absent. Furthermore, spin excitation in the intermediate phase appears to be gapless, and the measured spin-spin correlation function exhibits power-law decaying behavior. The data suggest that the nonmagnetic ground state is a possible candidate for the putative algebraic spin liquid.
Unique features of the nonmagnetic insulator phase are revealed, and the phase diagram of the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$ Hubbard model containing the diagonal transfers ${t}^{\ensuremath{'}}$ on a square lattice is presented. Using the path-integral renormalization group method, we find an antiferromagnetic phase for small next-nearest-neighbor transfer ${t}^{\ensuremath{'}}$ and a stripe (or collinear) phase for large ${t}^{\ensuremath{'}}$ in the Mott insulating region of the strong on-site interaction
U. For intermediate ${t}^{\ensuremath{'}}∕t\ensuremath{\sim}0.7$ at large
U∕t>7, we find a longer-period antiferromagnetic-insulator phase with $2\ifmmode\times\else\texttimes\fi{}4$ structure. In the Mott insulating region, we also find a quantum spin liquid (in other words, a nonmagnetic insulator) phase near the Mott transition to paramagnetic metals for the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$ Hubbard model on the square lattice as well as on the anisotropic triangular lattice. Correlated electrons often crystallize to the Mott insulator usually with some magnetic orders, whereas the ``quantum spin liquid" has been a long-sought issue. We report numerical evidence that a nonmagnetic insulating phase gets stabilized near the Mott transition with remarkable properties: The two-dimensional Mott insulators on geometrically frustrated lattices contain a phase with gapless spin excitations and degeneracy of the ground state in the whole Brillouin zone of the total momentum. The obtained vanishing spin renormalization factor suggests that spin excitations do not propagate coherently in contrast to conventional phases, where there exist either magnons in symmetry-broken phases or particle-hole excitations in paramagnetic metals. It imposes a constraint on the possible pictures of quantum spin liquids and supports an interpretation for the existence of an unconventional quantum liquid. The present concept is useful in analyzing a variety of experimental results in frustrated magnets including organic BEDT-TTF compounds and
3He atoms adsorbed on graphite.
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 investigate the metal-insulator transition (MIT) and phase diagram of the half-filled Fermi Hubbard model with Rashba-type spin-orbit coupling (SOC) on a square optical lattice. The interplay between the atomic interactions and SOC results in distinctive features of the MIT. Significantly, in addition to the diverse spin ordered phases, a nonmagnetic insulating phase emerges in a considerably large regime of parameters near the Mott transition. This phase has a finite single-particle gap but vanishing magnetization and spin correlation exhibits a power-law scaling, suggesting a potential algebraic spin-liquid ground state. These results are confirmed by the non-perturbative cluster dynamical mean-field theory.
The Hubbard model encapsulates the physics of strongly correlated quantum systems in its most basic form. It has been studied intensively in the context of the high-temperature superconductivity. A number of novel phases were recently proposed for Hubbard-like models on the honeycomb lattice, the structure of graphene. We analyzed the Hubbard model of spin-
21 fermions on the honeycomb lattice at half-filling using large-scale quantum Monte Carlo simulations. We find that the weak coupling semimetal and the antiferromagnetic Mott insulator at strong interaction are separated by an extended gapped phase in an intermediate coupling regime. Exploring excitation gaps, various correlation functions as well as probing for flux quantization, we conclude that a quantum spin liquid, lacking any conventional order, emerges with local charge and spin correlations, best described by a resonating valence bonds state.
The nature of quantum spin liquids is studied for the spin-
1/2 antiferromagnetic Heisenberg model on a square lattice containing exchange interactions between nearest-neighbor sites,
J1, and those between next-nearest-neighbor sites,
J2. We perform variational Monte Carlo simulations together with the quantum-number-projection technique and clarify the phase diagram in the ground state together with its excitation spectra. We obtain the nonmagnetic phase in the region
0.4<J2/J1≤0.6 sandwiched by the staggered and stripe antiferromagnetic (AF) phases. Our direct calculations of the spin gap support the notion that the triplet excitation from the singlet ground state is gapless in the range of
0.4<J2/J1≤0.5, while the gapped valence-bond-crystal (VBC) phase is stabilized for
0.5<J2/J1≤0.6. The VBC order is likely to have the columnar symmetry with a spontaneous symmetry breaking of the
C4v symmetry. The power-law behaviors of the spin-spin and dimer-dimer correlation functions in the gapless region are consistent with the emergence of the algebraic quantum-spin-liquid phase (critical phase). The exponent of the spin correlation
⟨S(0)S(r)⟩∝1/rz+η at a long distance
r appears to increase from
z+η∼1 at
J2/J1∼0.4 toward the continuous transition to the VBC phase at
J1/J1∼0.5. Our results, however, do not fully exclude the possibility of a direct quantum transition between the staggered AF and VBC phases with a wide critical region and deconfined criticality.
We consider the exchanged Hamiltonian HST=−J∑〈rr′〉(2Sr⋅Sr′−12)(2Tr⋅Tr′−12), describing two isotropic spin-1/2 Heisenberg antiferromagnets coupled by a quartic term on equivalent bonds. The model is relevant for systems with orbital degeneracy and strong electron-vibron coupling in the large Hubbard repulsion limit. To investigate the ground state properties we use a Green’s Function Monte Carlo, calculating energy gaps and correlation functions, the latter through the forward walking technique. In one dimension we find that the ground state is a “crystal” of valence bond dimers. In two dimensions, the spin gap appears to remain finite in the thermodynamic limit, and, consistently, the staggered magnetization—signal of Néel long range order—seems to vanish. From the analysis of dimer–dimer correlation functions, however, we find no sign of a valance bond crystal. A spin liquid appears as a plausible scenario compatible with our findings.