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Journal of Tianjin University of Commerce

Effects of Next-nearest-neighbor Hopping on the Phase Diagram of the Mott Insulating Phase in Optical Lattices

Yune Gao

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

The next-nearest-neighbor hopping is considered into a Bose-Hubbard model. The effects of the next-nearest-neighbor hopping on the phase diagram of the Mott insulating phase have been studied by perturbation theory and the mean field theory. The results show that the region of the Mott insulating phase on the phase space has been changed and those effects are greater as the absolute value of the next-nearest-neighbor hopping parameter increases.

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The next-nearest-neighbor hopping is considered into a Bose-Hubbard model. The effects of the next-nearest-neighbor hopping on the phase diagram of the Mott insulating phase have been studied by perturbation theory and the mean field theory. The results show that the region of the Mott insulating phase on the phase space has been changed and those effects are greater as the absolute value of the next-nearest-neighbor hopping parameter increases.
Introducing the next-nearest-neighbor hopping t′ into the Bose–Hubbard model, we study its effects on the phase diagram, on the ground-state energy, and on the quasiparticle and quasihole dispersion relations of the Mott insulating phase in optical lattices. We have found that a negative value of t′ enlarges the Mott-insulating region on the phase diagram, while a positive value of t′ acts oppositely. We have also found that the effects of t′ are dependent on the dimensionality of optical lattices with its effects largest in three-dimensional optical lattices.
We study an extended Bose-Hubbard model with next-nearest-neighbor (NNN) hopping in a shaken optical lattice. We show how mean-field phase diagram evolves with the change of NNN hopping amplitude t2{t}_{2}t2​, which can be easily tuned via shaking amplitude. As t2{t}_{2}t2​ increases, a Z2{Z}_{2}Z2​-symmetry-breaking superfluid (Z2SF)({Z}_{2}\mathrm{SF})(Z2​SF) phase emerges at the bottom of the Mott lobs. The tricritical points between normal superfluid, Z2SF{Z}_{2}\mathrm{SF}Z2​SF, and Mott insulator (MI) phases are identified. We further demonstrate the tricritical point can be tuned to the tip of the Mott lobe, in which case a new critical behavior has been predicted. Within random-phase approximation, excitation spectra in the three phases are obtained, which indicate how the phase transitions occur.
We investigate the ground-state phase diagram of the half-filled one-dimensional Hubbard model with next-nearest-neighbor hopping using the density-matrix renormalization-group technique as well as an unrestricted Hartree-Fock approximation. We find commensurate and incommensurate disordered magnetic insulating phases and a spin-gapped metallic phase in addition to the one-dimensional Heisenberg phase. At large on-site Coulomb repulsion U, we make contact with the phase diagram of the frustrated Heisenberg chain, which has spin-gapped phases for sufficiently large frustration. For weak U, sufficiently large next-nearest-neighbor hopping t2{t}_{2}t2​ leads to a band structure with four Fermi points rather than two, producing a spin-gapped metallic phase. As U is increased in this regime, the system undergoes a Mott-Hubbard transition to a frustrated antiferromagnetic insulator.
The single-particle spectral properties near the Mott transition in the two-dimensional Hubbard model with next-nearest-neighbor hopping are investigated by using cluster perturbation theory. Complicated spectral features of this model are simply interpreted, by considering how the next-nearest-neighbor hopping shifts the spectral weights of the two-dimensional Hubbard model. Various anomalous features observed in hole-doped and electron-doped cuprate high-temperature superconductors are explained in a unified manner as properties near the Mott transition in a two-dimensional system whose spectral weights are shifted by next-nearest-neighbor hopping.
The introduction of disorder in the extended Bose-Hubbard model gives rise to new glassy quantum phases, namely the Bose-glass and disordered solid phases. In this work, we present a rich phase diagram of interacting bosons in a disordered two-dimensional optical lattice, modeled by the disordered Bose-Hubbard model. We systematically probe the effect of long-range interaction truncated to the nearest neighbors and next-nearest neighbors on the phase diagram. We investigate the zero-temperature ground-state quantum phases using the single-site Gutzwiller mean-field theory. We also employ strong-coupling perturbative expansion to identify the nature of ground-state solid phases analytically. At sufficiently high disorder strength, we observe a quantum phase transition between the disordered solid and Bose-glass phases. We have investigated this transition in greater detail using cluster Gutzwiller mean-field theory to study the effect of intersite correlations which is absent in the single-site Gutzwiller mean-field theory. We have also studied this phase transition from the perspective of percolation theory.