We study the effects of a periodically varying electric field on the Hubbard model at half filling on a triangular lattice. The electric field is incorporated through the phase of the nearest-neighbor hopping amplitude via the Peierls prescription. When the on-site interaction
U is much larger than the hopping, the effective Hamiltonian
Heff describing the spin sector can be found using a Floquet perturbation theory. To third order in the hopping,
Heff is found to have the form of a Heisenberg antiferromagnet with three different nearest-neighbor couplings $({J}_{\ensuremath{\alpha}},{J}_{\ensuremath{\beta}},{J}_{\ensuremath{\gamma}})$ on bonds lying along the different directions. Remarkably, when the periodic driving does not have time-reversal symmetry,
Heff can also have a chiral three-spin interaction in each triangle, with the coefficient
C of the interaction having opposite signs on up- and down-pointing triangles. Thus periodic driving which breaks time-reversal symmetry can simulate the effect of a perpendicular magnetic flux which is known to generate such a chiral term in the spin sector, even though our model does not have a magnetic flux. The four parameters $({J}_{\ensuremath{\alpha}},{J}_{\ensuremath{\beta}},{J}_{\ensuremath{\gamma}},C)$ depend on the amplitude, frequency, and direction of the oscillating electric field. We then study the spin model as a function of these parameters using exact diagonalization and find a rich phase diagram of the ground state with seven different phases consisting of two kinds of ordered phases (collinear and coplanar) and disordered phases. Thus periodic driving of the Hubbard model on the triangular lattice can lead to an effective spin model whose couplings can be tuned over a range of values thereby producing a variety of interesting phases.
Magnetic exchange couplings can be tuned by coupling to periodic light, where the frequency and amplitude are typically varied: a process known as Floquet engineering. The polarization of the light is also important, and in this paper, we show how different polarizations, including several types of unpolarized light, can tune the exchange couplings in distinct ways. Using unpolarized light, for example, it is possible to tune the material without breaking either time-reversal or any lattice symmetries. To illustrate these effects generically, we consider single-band Hubbard models at half-filling on the honeycomb, square and triangular lattices. We derive the effective Heisenberg spin models to fourth order in perturbation theory for arbitrary fixed polarizations, and several types of unpolarized light that preserve time-reversal and lattice symmetries. Coupling these models to periodic light tunes first, second, and third neighbor exchange couplings, as well as ring exchange terms on the square and triangular lattices. Circularly polarized light induces chiral fields for the honeycomb and triangular lattices, which favors noncoplanar magnetism and potential chiral spin liquids. We discuss how to maximize the enhancement of the couplings without inducing heating.
We study Mott transition in the two-dimensional Hubbard model on an anisotropic triangular lattice. We use the Lanczos exact diagonalization of finite-size clusters up to eighteen sites, and calculate Drude weight, charge gap, double occupancy and spin structure factor. We average these physical quantities over twisted boundary conditions in order to reduce finite-size effects. We find a signature of the Mott transition in the dependence of the Drude weight and/or charge gap on the system size. We also examine the possibility of antiferromagnetic order from the spin structure factor. Combining these information, we propose a ground-state phase diagram which has a nonmagnetic insulating phase between a metallic phase and an insulating phase with antiferromagnetic order. Finally, we compare our results with those reported in the previous theoretical studies, and discuss the possibility of an unconventional insulating state.
We study the quantum phase transition of an
S=21 anisotropic $\ensuremath{\alpha}$ $(\ensuremath{\equiv}{J}_{z}/{J}_{xy})$ Heisenberg antiferromagnet on a triangular lattice. We calculate the sublattice magnetization and the long-range helical order parameter and their Binder ratios on finite systems with $N\ensuremath{\le}36$ sites. The
N dependence of the Binder ratios reveals that the classical ${120}^{\ensuremath{\circ}}$ N\'eel state occurs for $\ensuremath{\alpha}\ensuremath{\lesssim}0.55$, whereas a critical collinear state occurs for $1/\ensuremath{\alpha}\ensuremath{\lesssim}0.6$. This result is at odds with a widely held belief that the ground state of a Heisenberg antiferromagnet is the ${120}^{\ensuremath{\circ}}$ N\'eel state, but it also provides a possible mechanism explaining experimentally observed spin liquids.
We show that the spin-liquid phase of the half-filled Hubbard model on the triangular lattice can be described by a pure spin model. This is based on a high-order strong coupling expansion (up to order 12) using perturbative continuous unitary transformations. The resulting spin model is consistent with a transition from three-sublattice long-range magnetic order to an insulating spin-liquid phase, and with a jump of the double occupancy at the transition. Exact diagonalizations of both models show that the effective spin model is quantitatively accurate well into the spin-liquid phase, and a comparison with the Gutzwiller projected Fermi sea suggests a gapless spectrum and a spinon Fermi surface.
Based on exact diagonalization and density matrix renormalization group method, we show that an anisotropic triangular lattice Heisenberg spin model has three distinct quantum phases. In particular, a spin-liquid phase is present in the weak interchain coupling regime, which is characterized by an anisotropic spin structure factor with an exponential-decay spin correlator along the weaker coupling direction, consistent with the
Cs2CuCl4 compounds. In the obtained phase diagram, the spin-liquid phase is found to persist up to a relatively large critical anisotropic coupling ratio ${J}^{\ensuremath{'}}∕J=0.78$, which is stabilized by strong quantum fluctuations, with a parity symmetry distinct from two magnetic ordered states in the stronger coupling regime.