Metal-insulator Transition On A Half Filled Triangular Lattice

Metal insulator transition(MIT) is one of the most important research subjects in condensed matter physics.Recently much work has been done upon the ground state properties of a variety of organic compounds.In experiments,it has been found that many compounds have the triangular lattice structure and undergo quantum phase transition from insulating to metallic state under moderate static pressure,such asκ-(BEDT-TTF)₂X etc.In the framework of half-filled Hubbard model upon triangular lattice,it has been shown numerically that there happens a MIT for a finite critical interaction with(U/t)_c＞0,where U is on-site repulsive interaction and t is the nearest-neighbor hopping term.But for the square lattice,the MIT takes place at (U/t)_c=0,which means for any U/t＞0,the ground state is a Mott insulator.The essential difference between a triangular lattice and a square one is the frustration properties of the former.So frustration plays a significant role in understanding MIT.As we know,frustration can not only be provided by the triangular structure,but also can be brought about by the long-range interactions.Hence it is of great interest to investigate what will happen to MIT if the long-range interaction is included for the triangular lattice, which is readily modeled by the extended Hubbard model,where the long-range interaction is represented by the nearest-neighbour one denoted by V/t.To carry out the research,we make use of the real space renarmalization-group method,which has once been applied successfully in traditional Hubbard model on triangular lattice to study the MIT.Through extensive numerical calculations,we have found that when V/t is small, i.e.V/t＜4.2,there is only one MIT critical point.By increasing V/t,the number of critical points will become three(4.2＜V/t＜4.4) and two(4.4＜V/t＜8.4).Moreover, as V/t is large enough,i.e.V/t＞8.4,the system is an insulation state for all the value of U/t.To explore the underlying mchanism,the critical values of v and z at some critical points are also calculated,which show different values with respect to changing U/t or V/t.This implicitly demonstrates the different MIT mechanism caused by these two factors.It is generally believed that U/t tend to induce spin density wave (SDW),while V/t favors charge density wave(CDW).In order to discuss the competition effects from the SDW and CDW phases,we have also studied the charge order(CO) and spin order(SO) in the U/t-V/t plane by using a self-consistent mean-field theory based upon Hartree-fock approximations(HFA).The phase diagram of CO and SO has been obtained.Finally,for different phases,besides using the corresponding order parameters to describe the different phase transitions,we also investigate the behavior of single-site entanglement in the parameter region.It has been found that there is an extremum of its first derivative near the boundaries of different phases,and the result of HFA shows that there is a jump of average single-site entanglement along the phase boundaries.All these results tell us that the single-site entanglement also can be used as an order parameter to characterize the phase transition in our systems.