Journal of Physics Conference Series

Competition between the Haldane insulator, superfluid and supersolid phases in the one-dimensional Bosonic Hubbard Model

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

Published Sep 28, 2015• 3 citations

Abstract

We use quantum Monte Carlo (QMC), density matrix renormalization group (DMRG) and time evolution block decimation (TEBD) to study the competition between several exotic quantum phases in the one-dimensional extended bosonic Hubbard model and map its phase diagram. Of particular interest is the Haldane insulating phase which we show to be present only for density p = 1. We also show that the supersolid phase is present for a wide range of parameters including commensurate densities.

DOI: 10.1088/1742-6596/640/1/012042

Related papers

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

G. G. Batrouni, Richard T. Scalettar, V. G. Rousseau +1 more

arXiv:1304.2120Physical Review LettersJun 28, 201351 citations

Competing phases, phase separation, and coexistence in the extended one-dimensional bosonic Hubbard model

G. G. Batrouni, V. G. Rousseau, R. T. Scalettar +1 more

arXiv:1405.5382Physical Review BNov 17, 201430 citations

Supersolid and solitonic phases in the one-dimensional extended Bose-Hubbard model

Tapan Mishra, Ramesh V. Pai, S. Ramanan +2 more

arXiv:0907.1258Physical Review AOct 19, 200945 citations

Excitation and dynamics in the extended Bose-Hubbard model

Benoît Grémaud, G. G. Batrouni

arXiv:1508.02114Physical review. B./Physical review. BJan 11, 201611 citations

Superfluid, phase-separation, supersolid and density wave phases in extended Bose-Hubbard model

Pallavi P. Gaude, Ananya Das, Ramesh V. Pai

AIP conference proceedingsJan 1, 20240 citations

Phase diagrams of extended Bose-Hubbard model in one dimension by Monte-Carlo simulation with stochastic-series expansion

Keima Kawaki, Yoshihito Kuno, Ikuo Ichinose

Jan 3, 20170 citations

Journal of Physics Conference Series

Competition between the Haldane insulator, superfluid and supersolid phases in the one-dimensional Bosonic Hubbard Model

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

Published Sep 28, 2015• 3 citations

Publisher

Abstract

DOI: 10.1088/1742-6596/640/1/012042

Related papers

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

G. G. Batrouni, Richard T. Scalettar, V. G. Rousseau +1 more

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.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.

arXiv:1304.2120Physical Review LettersJun 28, 201351 citations

Competing phases, phase separation, and coexistence in the extended one-dimensional bosonic Hubbard model

G. G. Batrouni, V. G. Rousseau, R. T. Scalettar +1 more

We study the phase diagram of the one-dimensional bosonic Hubbard model with contact $(U)$ and near neighbor $(V)$ interactions focusing on the gapped Haldane insulating (HI) phase which is characterized by an exotic nonlocal order parameter. The parameter regime $(U,V$ , 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 $(U,V)$ plane.We study the phase diagram of the one-dimensional bosonic Hubbard model with contact $(U)$ and near neighbor $(V)$ interactions focusing on the gapped Haldane insulating (HI) phase which is characterized by an exotic nonlocal order parameter. The parameter regime $(U,V$, 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 $(U,V)$ plane.

arXiv:1405.5382Physical Review BNov 17, 201430 citations

Supersolid and solitonic phases in the one-dimensional extended Bose-Hubbard model

Tapan Mishra, Ramesh V. Pai, S. Ramanan +2 more

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.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.

arXiv:0907.1258Physical Review AOct 19, 200945 citations

Excitation and dynamics in the extended Bose-Hubbard model

Benoît Grémaud, G. G. Batrouni

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 ( $U$ ) and near neighbor ( $V$ ) 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 $k=0$ , the supersolid phase exhibits gapless modes at a finite $k$ which depends on the filling.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 ($U$) and near neighbor ($V$) 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 $k=0$, the supersolid phase exhibits gapless modes at a finite $k$ which depends on the filling.

arXiv:1508.02114Physical review. B./Physical review. BJan 11, 201611 citations

Superfluid, phase-separation, supersolid and density wave phases in extended Bose-Hubbard model

Pallavi P. Gaude, Ananya Das, Ramesh V. Pai

We study the one-dimensional extended Bose-Hubbard model in incommensurate densities using the density matrix renormalization group with the mean-filed (CMFT+DMRG)and density matrix renormalization group (DMRG) methods. We focus on the region of the phase diagram where onsite interaction (U) is smaller than the nearest-neighbor interaction (V). We determine the superfluid and the density wave order parameters to identify superfluid, phase-separated, supersolid, density wave phases, and obtain the phase diagram in the density-onsite interaction(ρ, U) plane for fixed nearest-neighbor interaction. The supersolid and phase-separation phases exist for a wide range of densities. The density ranges for which the phase-separation is seen shrinking with theincrease in the onsite interaction.We study the one-dimensional extended Bose-Hubbard model in incommensurate densities using the density matrix renormalization group with the mean-filed (CMFT+DMRG)and density matrix renormalization group (DMRG) methods. We focus on the region of the phase diagram where onsite interaction (U) is smaller than the nearest-neighbor interaction (V). We determine the superfluid and the density wave order parameters to identify superfluid, phase-separated, supersolid, density wave phases, and obtain the phase diagram in the density-onsite interaction(ρ, U) plane for fixed nearest-neighbor interaction. The supersolid and phase-separation phases exist for a wide range of densities. The density ranges for which the phase-separation is seen shrinking with theincrease in the onsite interaction.

AIP conference proceedingsJan 1, 20240 citations

Phase diagrams of extended Bose-Hubbard model in one dimension by Monte-Carlo simulation with stochastic-series expansion

Keima Kawaki, Yoshihito Kuno, Ikuo Ichinose

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, $n_c$ , is also controllable parameter, and we found that the phase diagram depends on the value of $n_c$ . 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.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, $n_c$, is also controllable parameter, and we found that the phase diagram depends on the value of $n_c$. 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.

Jan 3, 20170 citations

We study the phase diagram of the one-dimensional bosonic Hubbard model with contact

(U)

and near neighbor

(V)

interactions focusing on the gapped Haldane insulating (HI) phase which is characterized by an exotic nonlocal order parameter. The parameter regime

(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)

plane.

U

) and near neighbor (

V

) 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=0

, the supersolid phase exhibits gapless modes at a finite

k

which depends on the filling.

n_c

, is also controllable parameter, and we found that the phase diagram depends on the value of

n_c

. 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.