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Continuous Mott Transition in the Hubbard Model on the 1/5-Depleted Square Lattice

K. Ueda Group

Metal-insulator (MI) transition is a central problem of the physics of strongly correlated electron systems. In the simplest case of the square lattice Hubbard model, it has been established that the ground state at half-filling is always a Mott insulating state with the antiferromagnetic long range order. Under the assumption of paramagnetic phase it is widely believed that the transition from the paramagnetic metallic phase to the paramagnetic insulating phase takes place through a discontinuous transition. One can ask the question how general is the first order nature of various MI transitions.

Fig. 1. Phase diagram of the Hubbard model on the 1/5-depleted square lattice. On the dimer side where the intra-dimer hopping, t2, is bigger than the intra-plaquette hopping, t1, the MI transition from the semi-metallic phase to the dimer-insulating one is a continuous transition.

In particular, nature of MI transitions in non-Bravais lattices seems to be non-trivial and interesting. We study the MI transition in the one-fifth depleted square lattice Hubbard model. The unit cell contains four lattice sites which form a square. The square plaquettes are connected by dimer bonds. The 1/5-depleted square lattice does not have any effect of the geometrical frustration. However, the Heisenberg model on this lattice shows quantum phase transitions from the dimer singlet phase to the antiferromagnetic ordered phase and then onto the plaquette singlet phase. Since the Heisenberg model is an effective Hamiltonian of the Hubbard model in the strong correlation limit, it is an interesting problem to look at the nature of MI transition of the Hubbard model.

In the present study we investigate the MI transition of the Hubbard model on the 1/5-depleted square lattice in the paramagnetic phase by using the cellular dynamical mean field theory. When the intra-plaquette hopping, t1, is smaller than the intra-dimer hopping, t2, the MI transition is continuous. This time we use the eight-site cluster to check the finite-size effect of the cellular DMFT. This continuous MI transition is characterized by the Lifshitz transition which is associated with the appearance or annihilation of the pair of electron and hole pockets in different bands. New feature found in this study is that the Lifshitz transition is triggered not only by changing a one-body parameter, t1/t2, but also by changing the magnitude of the Coulomb interaction, U. One can see these features clearly by studying the self-energies corresponding to the dimer bonds and the plaquette bonds.


References
  • [1] Y. Yanagi and K. Ueda, Phys. Rev. B90, 085113 (2014).
Authors
  • Y. Yanagia, and K. Ueda
  • aTokyo University of Science