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Register a new userPhase diagram and topological phases in the triangular lattice Kitaev-Hubbard model
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We study the half-filled Hubbard model on the triangular lattice with spin-dependent Kitaev-like hopping. Using the variational cluster approach, we identify five phases: a metallic phase, a non-coplanar chiral magnetic order, a $120^circ$ magnetic order, a nonmagnetic insulator (NMI), and an interacting Chern insulator (CI) with a nonzero Chern number. The transition from CI to NMI is characterized by the change of the charge gap from an indirect band gap to a direct Mott gap. Based on the slave-rotor mean-field theory, the NMI phase is further suggested to be a gapless Mott insulator with a spinon Fermi surface or a fractionalized CI with nontrivial spinon topology, depending on the strength of Kitaev-like hopping. Our work highlights the rising field that interesting phases emerge from the interplay of band topology and Mott physics.
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Two-dimensional density-matrix renormalization group method is employed to examine the ground state phase diagram of the Hubbard model on the triangular lattice at half filling. The calculation reveals two discontinuities in the double occupancy with increasing the repulsive Hubbard interaction U at Uc1 = 7.55 t and Uc2 = 9.65 t (t being the hopping integral), indicating that there are three phases separated by first order transitions. The absence of any singularity in physical quantities for 0 < U < Uc1 implies that this phase corresponds to a metallic phase. The local spin density induced by an applied pinning magnetic field for U > Uc2 exhibits a three sublattice feature, which is compatible with the Neel ordered state realized in the strong coupling limit. For Uc1 < U < Uc2, a response to the applied pinning magnetic field is comparable to that in the metallic phase but a relatively large spin correlation length is found with neither valence bond nor chiral magnetic order, suggesting a paramagnetic nature which resembles gapless spin liquid. The calculation also finds that the pair- ing correlation function monotonically decreases with increasing U and thus the superconductivity is unlikely in the intermediate phase.
The Hubbard model and its strong-coupling version, the Heisenberg one, have been widely studied on the triangular lattice to capture the essential low-temperature properties of different materials. One example is given by transition metal dichalcogenides, as 1T$-$TaS$_2$, where a large unit cell with $13$ Ta atom forms weakly-coupled layers with an isotropic triangular lattice. By using accurate variational Monte Carlo calculations, we report the phase diagram of the $t-t^prime$ Hubbard model on the triangular lattice, highlighting the differences between positive and negative values of $t^prime/t$; this result can be captured only by including the charge fluctuations that are always present for a finite electron-electron repulsion. Two spin-liquid regions are detected: one for $t^prime/t<0$, which persists down to intermediate values of the electron-electron repulsion, and a narrower one for $t^prime/t>0$. The spin-liquid phase appears to be gapless, though the variational wave function has a nematic character, in contrast to the Heisenberg limit. We do not find any evidence for non-magnetic Mott phases in the proximity of the metal-insulator transition, at variance with the predictions (mainly based upon strong-coupling expansions in $t/U$) that suggest the existence of a weak-Mott phase that intrudes between the metal and the magnetically ordered insulator.
We investigate the evolution of the Mott insulators in the triangular lattice Hubbard Model, as a function of hole doping $delta$ in both the strong and intermediate coupling limit. Using the density matrix renormalization group (DMRG) method, at light hole doping $deltalesssim 10%$, we find a significant difference between strong and intermediate couplings. Notably, at intermediate coupling an unusual metallic state emerges, with short ranged spin correlations but long ranged spin-chirality order. Moreover, no clear Fermi surface or wave-vector is observed. These features disappear on increasing interaction strength or on further doping. At strong coupling, the 120 degree magnetic order of the insulating magnet persists for light doping, and produces hole pockets with a well defined Fermi surface. On further doping, $delta approx 10%sim 20%$ SDW order and coherent hole Fermi pockets are found at both strong and intermediate coupling. At even higher doping $delta gtrsim 20%$, the SDW order is suppressed and the spin-singlet Cooper pair correlations are simultaneously enhanced. We interpret this as the onset of superconductivity on suppressing magnetic order. We also briefly comment on the strong particle hole asymmetry of the model, and contrast electron versus hole doping.
The fractional quantum Hall (FQH) effect illustrates the range of novel phenomena which can arise in a topologically ordered state in the presence of strong interactions. The possibility of realizing FQH-like phases in models with strong lattice effects has attracted intense interest as a more experimentally accessible venue for FQH phenomena which calls for more theoretical attention. Here we investigate the physical relevance of previously derived geometric conditions which quantify deviations from the Landau level physics of the FQHE. We conduct extensive numerical many-body simulations on several lattice models, obtaining new theoretical results in the process, and find remarkable correlation between these conditions and the many-body gap. These results indicate which physical factors are most relevant for the stability of FQH-like phases, a paradigm we refer to as the geometric stability hypothesis, and provide easily implementable guidelines for obtaining robust FQH-like phases in numerical or real-world experiments.
The interplay between the Kondo effect and magnetic ordering driven by the Ruderman-Kittel-Kasuya-Yosida interaction is studied within the two-dimensional Hubbard-Kondo lattice model. In addition to the antiferromagnetic exchange interaction, $J_perp$, between the localized and the conduction electrons, this model also contains the local repulsion, $U$, between the conduction electrons. We use variational cluster approximation to investigate the competition between the antiferromagnetic phase, the Kondo singlet phase, and a ferrimagnetic phase on square lattice. At half-filling, the Neel antiferromagnetic phase dominates from small to moderate $J_perp$ and $UJ_perp$, and the Kondo singlet elsewhere. Sufficiently away from half-filling, the antiferromagnetic phase first gives way to a ferrimagnetic phase (in which the localized spins order ferromagnetically, and the conduction electrons do likewise, but the two mutually align antiferromagnetically), and then to the Kondo singlet phase.
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