Quantum Monte Carlo Study Of SU(2N) Hubbard Model

Due to the high degree of control,the ultracold atomic systems in optical lattices are often used as quantum simulators.Recently,with the rapid development of experimental technologies,alkali earth atoms can be loaded in optical lattices to realize the quantum simulations of the SU(2N)Hubbard model.The success of experiments has made the pure theory of this model significantly important.We hope to build the bridge between experiments and pure theory further by numerical simulations.Based on the nonperturbative and unbiased determinantal quantum Monte Carlo method,we have studid the ground state properties and thermodynamic properties of the half-filled SU(2N)Hubbard model.At first,we have explored interaction-induced quantum phase transitions from the Dirac semimetals to the Mott insulating phases in the SU(4)and SU(6)cases.Both of these Mott insulating states are found to be columnar valence bond solid(cVBS)and to be absent of antiferromagnetic ordering and the current ordering.Inside the cVBS phases,the magnitude of order parameter is enhanced by increasing fermion components and behaves nonmonotonically as the interaction strength increases.Because of a cubic invariance possessed by the cVBS order,the transitions generally should be of first order.But due to the coupling between cVBS order and the gapless Dirac fermions,the transitions is second order at zero temperature and first order at finite temperature.Next,we have studied the ground state properties of ?-flux SU(4)Hubbard model on a square lattice.With increasing interaction,a Mott transition occurs from the semimetals to the valence bond solid,accompanied by the Z4 discrete symmetry breaking.Our simulations demonstrate the existence of a second-order phase transition,which confirms the Ginzburg-Landau analysis.The phase transition point and the critical exponent ? are also estimated.To account for the effect of a ? flux on the ordering in the strong-coupling regime,we analytically derive by the perturbation theory the ring-exchange term,which is the leading-order term that can reflect the difference between the ?-flux and zero-flux SU(4)Hubbard model.Finally,we have studied the thermodynamic properties of SU(2N)Hubbard model on a square lattice or a honeycomb lattice.We have calculated the entropy-temperature relation,isoentropy curve,and showed that the Pomeranchuk cooling effect can be enhanced by increasing fermion components.Especially,by analyzing the crossing point of entropy-temperature curves with different interactions,we have found the characteristic entropy to represent the onset of Pomeranchuk cooling regime.That characteristic entropy is related to the spin degree of freedom of the system,and has nothing to do with the lattice type.In order to connect our simulations to experimental observables,we have calculated the probability distribution of onsite occupation number and density compressibility,and we hope these simulations can shed light on the future experiments of large-hyperfine-spin ultracold fermions on optical lattices.