Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userEffective Spin Couplings in the Mott Insulator of the Honeycomb Lattice Hubbard Model
340
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Motivated by the recent discovery of a spin liquid phase for the Hubbard model on the honeycomb lattice at half-filling, we apply both perturbative and non-perturbative techniques to derive effective spin Hamiltonians describing the low-energy physics of the Mott-insulating phase of the system. Exact diagonalizations of the so-derived models on small clusters are performed, in order to assess the quality of the effective low-energy theory in the spin-liquid regime. We show that six-spin interactions on the elementary loop of the honeycomb lattice are the dominant sub-leading effective couplings. A minimal spin model is shown to reproduce most of the energetic properties of the Hubbard model on the honeycomb lattice in its spin-liquid phase. Surprisingly, a more elaborate effective low-energy spin model obtained by a systematic graph expansion rather disagrees beyond a certain point with the numerical results for the Hubbard model at intermediate couplings.
rate research
Read More
We take advantage of recent improvements in the grand canonical Hybrid Monte Carlo algorithm, to perform a precision study of the single-particle gap in the hexagonal Hubbard model, with on-site electron-electron interactions. After carefully controlled analyses of the Trotter error, the thermodynamic limit, and finite-size scaling with inverse temperature, we find a critical coupling of $U_c/kappa=3.834(14)$ and the critical exponent $z u=1.185(43)$. Under the assumption that this corresponds to the expected anti-ferromagnetic Mott transition, we are also able to provide a preliminary estimate $beta=1.095(37)$ for the critical exponent of the order parameter. We consider our findings in view of the $SU(2)$ Gross-Neveu, or chiral Heisenberg, universality class. We also discuss the computational scaling of the Hybrid Monte Carlo algorithm, and possible extensions of our work to carbon nanotubes, fullerenes, and topological insulators.
Quantum phase transitions in the Hubbard model on the honeycomb lattice are investigated in the variational cluster approximation. The critical interaction for the paramagnetic to antiferromagnetic phase transition is found to be in remarkable agreement with a recent large-scale quantum Monte Carlo simulation. Calculated staggered magnetization increases continuously with $U$ and thus we find the phase transition is of a second order. We also find that the semimetal-insulator transition occurs at infinitesimally small interaction and thus a paramagnetic insulating state appears in a wide interaction range. A crossover behavior of electrons from itinerant to localized character found in the calculated single-particle excitation spectra and short-range spin correlation functions indicates that an effective spin model for the paramagnetic insulating phase is far from a simple Heisenberg model with a nearest-neighbor exchange interaction.
Electrons in artificial lattices enable explorations of the impact of repulsive Coulomb interactions in a tunable system. We have trapped two-dimensional electrons belonging to a gallium arsenide quantum well in a nanofabricated lattice with honeycomb geometry. We probe the excitation spectrum in a magnetic field identifying novel collective modes that emerge from the Coulomb interaction in the artificial lattice as predicted by the Mott-Hubbard model. These observations allow us to determine the Hubbard gap and suggest the existence of a novel Coulomb-driven ground state. This approach offers new venues for the study of quantum phenomena in a controllable solid-state system.
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.
We investigate the competition between charge-density-wave (CDW) states and a Coulomb interaction-driven topological Mott insulator (TMI) in the honeycomb extended Hubbard model. For the spinful model with on-site ($U$) and next-nearest-neighbor ($V_2$) Coulomb interactions at half filling, we find two peculiar six-sublattice charge-density-wave insulating states by using variational Monte Carlo simulations as well as the Hartree-Fock approximation. We observe that conventional ordered states always win with respect to the TMI. The ground state is given in the large-$V_2$ region by a CDW characterized by a 220200 (001122) charge configuration for smaller (larger) $U$, where 0, 1, and 2 denote essentially empty, singly occupied, and doubly occupied sites. Within the 001122-type CDW phase, we find a magnetic transition driven by an emergent coupled-dimer antiferromagnet on an effective square lattice of singly occupied sites. Possible realizations of the found states are discussed.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
