We establish the ground-state phase diagram of a spinless fermion model with the nearest and next-nearest-neighbor repulsions via the density-matrix-renormalization-group method. The bond-order (BO) correlation function and its static structure factor can be employed to accurately determine the BO phase boundaries. The first derivative of the charge-density wave (CDW) structure factor and the second derivative of the energy are expect to diverge at the 2k(F)-CDW-BO transition point, which indicates that a second-order transition occurs. We determine the metallic-4k(F)-CDW boundary by analyzing the decay behavior of the charge correlation function near the transition point.
We use the mean-field method, the Quantum Monte-carlo method and the Density matrix renormalization group method to study the trimer superfluid phase and the quantum phase diagram of the Bose-Hubbard model in an optical lattice, with explicit trimer tunneling term. Theoretically, we derive the explicit trimer hopping terms, such as a 3 † i a 3 j , by the Schrieffer-Wolf transformation. In practice, the trimer superfluid described by these terms is driven by photoassociation. The phase transition between the trimer superfluid phase and other phases are also studied. Without the on-site interaction, the phase transition between the trimer superfluid phase and the Mott Insulator phase is continuous. Turning on the on-site interaction, the phase transitions are first order with Mott insulators of atom filling 1 and 2. With nonzero atom tunneling, the phase transition is first order from the atom superfluid to the trimer superfluid. In the trimer superfluid phase, the winding numbers can be divided by three without any remainders. In the atom superfluid and pair superfluid, the vorticities are 1 and 1/2, respectively. However, the vorticity is 1/3 for the trimer superfluid. The power law decay exponents is 1/2 for the non diagonal correlation a †3 i a 3 j , i.e. the same as the exponent of the correlation a † i aj in hardcore bosons. The density dependent atom-tunneling term n 2 i a † i aj and pair tunneling term nia †2 i a 2 j are also studied. With these terms, the phase transition from the empty phase to atom superfluid is first order and different from the cases without the density dependent terms. The phase transition is still first order from the trimer superfluid phase to the atom superfluid. The effects of temperature are studied. Our results will be helpful in realizing the trimer superfluid by a cold atom experiment.
In this paper, combined with infinite time-evolving block decimation (iTEBD) algorithm and Belltype inequalities, we investigate multi-partite quantum nonlocality in an infinite one-dimensional quantum spin-1 2 XXZ system. High hierarchy of multipartite nonlocality can be observed in the gapless phase of the model, meanwhile only the lowest hierarchy of multipartite nonlocality is observed in most regions of the gapped anti-ferromagnetic phase. Thereby, Bell-type inequalities disclose different correlation structures in the two phases of the system. Furthermore, at the infinite-order QPT (or Kosterlitz-Thouless QPT) point of the model, the correlation measures always show a local minimum value, regardless of the length of the subchains. It indicates that relatively low hierarchy of multi-partite nonlocality would be observed at the infinite-order QPT point in a Belltype experiment. The result is in contrast to the existing results of the second-order QPT in the one-dimensional XY model, where multi-partite nonlocality with the highest hierarchy has been observed. Thus, multi-partite nonlocality provides us an alternative perspective to distinguish between these two kinds of QPTs. Reliable clues for the existence of tripartite quantum entanglement have also been found.
We study the phase diagram of a half-filled one-dimensional superlattice Hubbard model with an alternating orbital energy ± ϵ/2 and on-site Coulomb repulsion U(A) and U(B) using the density-matrix renormalization group and finite-size scaling analysis. For U(A) >> U(B), we observe an incommensurate charge correlation phase. For U(B) = 0, we find a transition from the band insulating phase to the correlated metallic phase at the critical point ϵ = U(A)/2. For U(B) > 0, we find three insulating phases as in the ionic Hubbard model. In the gapless region, the correlation functions exhibit the asymptotic behavior of power-law decay as in the Tomonaga-Luttinger liquid.
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