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arXiv:1304.2120 · Physical Review Letters

Competing Supersolid and Haldane Insulator Phases in the Extended One-Dimensional Bosonic Hubbard Model

G. G. Batrouni, Richard T. Scalettar, V. G. Rousseau, Benoît Grémaud

Published Jun 28, 2013• 51 citations
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Abstract

The Haldane insulator is a gapped phase characterized by an exotic nonlocal order parameter. The parameter regimes at which it might exist, and how it competes with alternate types of order, such as supersolid order, are still incompletely understood. Using the stochastic Green function quantum Monte Carlo algorithm and density matrix renormalization group, we study numerically the ground state phase diagram of the one-dimensional bosonic Hubbard model with contact and near neighbor repulsive interactions. We show that, depending on the ratio of the near neighbor to contact interactions, this model exhibits charge density waves, superfluid, supersolid, and the recently identified Haldane insulating phases. We show that the Haldane insulating phase exists only at the tip of the unit-filling charge density wave lobe and that there is a stable supersolid phase over a very wide range of parameters.

DOI
10.1103/physrevlett.110.265303

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The Haldane insulator is a gapped phase characterized by an exotic nonlocal order parameter. The parameter regimes at which it might exist, and how it competes with alternate types of order, such as supersolid order, are still incompletely understood. Using the stochastic Green function quantum Monte Carlo algorithm and density matrix renormalization group, we study numerically the ground state phase diagram of the one-dimensional bosonic Hubbard model with contact and near neighbor repulsive interactions. We show that, depending on the ratio of the near neighbor to contact interactions, this model exhibits charge density waves, superfluid, supersolid, and the recently identified Haldane insulating phases. We show that the Haldane insulating phase exists only at the tip of the unit-filling charge density wave lobe and that there is a stable supersolid phase over a very wide range of parameters.
We study the phase diagram of the one-dimensional bosonic Hubbard model with contact (U)(U)(U) and near neighbor (V)(V)(V) interactions focusing on the gapped Haldane insulating (HI) phase which is characterized by an exotic nonlocal order parameter. The parameter regime (U,V(U,V(U,V, and $\ensuremath{\mu})$ where this phase exists and how it competes with other phases, such as the supersolid (SS) phase, is incompletely understood. We use the stochastic Green function quantum Monte Carlo algorithm as well as the density matrix renormalization group to map out the phase diagram. Our main conclusions are that the HI exists only at $\ensuremath{\rho}=1$, the SS phase exists for a very wide range of parameters (including commensurate fillings), and displays power law decay in the one-body Green function. In addition, we show that at fixed integer density, the system exhibits phase separation in the (U,V)(U,V)(U,V) plane.
The one-dimensional extended bosonic Hubbard model has been shown to exhibit a variety of phases ranging from Mott insulator and superfluid to exotic supersolids and Haldane insulators depending on the filling and the relative value of the contact (UUU) and near neighbor (VVV) interaction strengths. In this paper we use the density matrix renormalization group and the time evolving block decimation numerical methods to study in detail the dynamics and excitation spectra of this model in its various phases. In particular, we study in detail the behavior of the charge and neutral gaps which characterize the Mott, charge density, and Haldane insulating phases. We also show that in addition to the gapless modes at k=0k=0k=0, the supersolid phase exhibits gapless modes at a finite kkk which depends on the filling.
We discuss the existence of a nontrivial topological phase in one-dimensional interacting systems described by the extended Bose-Hubbard model with a mean filling of one boson per site. Performing large-scale density-matrix renormalization group calculations we show that the presence of nearest-neighbor repulsion enriches the ground-state phase diagram of the paradigmatic Bose-Hubbard model by stabilizing a novel gapped insulating state, the so-called Haldane insulator, which, embedded into superfluid, Mott insulator, and density wave phases, is protected by the lattice inversion symmetry. The quantum phase transitions between the different insulating phases were determined from the central charge via the von Neumann entropy. The Haldane phase reveals a characteristic fourfold degeneracy of the entanglement spectrum. We finally demonstrate that the intensity maximum of the dynamical charge structure factor, accessible by Bragg spectroscopy, features the gapped dispersion known from the spin-1 Heisenberg chain.
In this paper, we study detailed phase diagrams of the extended Bose-Hubbard model (EBHM) in one dimension by means of the quantum Monte-Carlo (QMC) simulation using the stochastic-series expansion (SSE). In the EBHM, there exists a nearest-neighbor repulsion as well as the on-site repulsion. In the SSE-QMC simulation, the highest particle number at each site, ncn_cnc​, is also controllable parameter, and we found that the phase diagram depends on the value of ncn_cnc​. It is shown that in addition to the Mott insulator, superfluid, density wave, the phase so-called Haldane insulator and supersolid appear in the phase diagrams, and their locations in the phase diagrams are clarified.
We report our findings on the quantum phase transitions in cold bosonic atoms in a one-dimensional optical lattice using the finite-size density-matrix renormalization-group method in the framework of the extended Bose-Hubbard model. We consider wide ranges of values for the filling factors and the nearest-neighbor interactions. At commensurate fillings, we obtain two different types of charge-density wave phases and a Mott insulator phase. However, departure from commensurate fillings yields the exotic supersolid phase where both the crystalline and the superfluid orders coexist. In addition, we obtain the signatures for the solitary waves and the superfluid phase.