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

Mishra, Tapan; Pai, Ramesh V.; Ramanan, S.; Luthra, Meetu Sethi; Das, B. P.

doi:10.1103/physreva.80.043614

Cited by 49 publications

(54 citation statements)

References 39 publications

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“…Moreover, we find that at low U the region of low ζ significantly extends inside the CDW region. We identify this region with the apperance of a supersolid phase [27]. Interestingly, this region presents a peculiar L A dependence of the ES (Fig.…”

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confidence: 63%

Entanglement spectrum of one-dimensional extended Bose-Hubbard models

Deng

Santos

2011

Phys. Rev. B

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The entanglement spectrum provides crucial information about correlated quantum systems. We show that the study of the block-like nature of the reduced density matrix in number sectors and the partition dependence of the spectrum in finite systems leads to interesting unexpected insights, which we illustrate for the case of a 1D extended Hubbard model. We show that block symmetry provides an intuitive understanding of the spectral double degeneracy of the Haldane-insulator, which is remarkably maintained at low on-site interaction, where triple or higher site occupation is significant and particle-hole symmetry is broken. Moreover, surprisingly, the partition dependence of the spectral degeneracy in the Haldane-isulator, and of a partial degeneracy in the Mott-insulator, are directly linked to the, in principle unrelated, density-density correlations, and presents an intriguing periodic behavior in superfluid and supersolid phases.Ultra-cold gases in optical lattices [1,2] allow for the controlled study of Hubbard-like models [3], fundamental for the description of strongly correlated systems. Although until recently only on-site interactions have been relevant, inter-site interactions may play a crucial role in new experiments on gases with dipolar interactions [4]. Polar lattice gases may allow for the simulation of extended Hubbard models, which play an important role in e.g. the analysis of high-T c superconductivity [5], being the simplest models that capture the interplay between strong correlations and charge-ordering effects.Most remarkably, it has been recently shown that 1D polar lattice bosons, in addition to conventional locallyordered phases, may allow for the so-called Haldaneinsulator (HI) phase [6-8] (a Haldane-liquid phase has been recently proposed for polar fermions [9]). The HI lacks local order, but presents non-local string-like order [10], resembling to a large extent the Haldane phase in integer spin chains [11]. The Haldane phase is one of the paradigms of topological quantum phases, which due to the lack of local order parameter fall beyond the Landau paradigm of condensed-matter physics. Topological phases have attracted a growing interest in recent years, most relevantly their entanglement properties. In particular, topological phases present an anomalous entanglement entropy, characterized by a topology-dependent universal additive constant [12,13].The entanglement entropy is defined as the von Neumann entropy, S = −T rρ A log ρ A , associated to the reduced density matrix, ρ A , obtained after partitioning the system into two parts, A and B, and tracing out B. However, ρ A contains much more information than its mere entanglement entropy. In particular, it has been shown that the set of eigenvalues of ρ A , the so-called entanglement spectrum (ES), provides key insights concerning quantum correlations in many-body systems [14]. The intriguing properties of the ES in different physical systems have attracted recently a major interest [15][16][17][18]. Interestingly, it has been shown...

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confidence: 63%

Entanglement spectrum of one-dimensional extended Bose-Hubbard models

Deng

Santos

2011

Phys. Rev. B

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“…It has been proposed that a system of polar gases in optical lattices can give rise to a crystalline phase [4] due to the long range van der Waal type interaction. Under certain conditions, it is possible to stabilize the exotic supersolid phase [5][6][7][8][9][10][11][12][13]. The observation of chromium Bose-Einstein condensate (BEC) [14,15] followed by the realization of quantum gases in other highly-magnetic species, including dysprosium Bose and Fermi gases [16] and erbium condensate [17], experiments on polar molecules such as KRb [18] and the Rydberg gases [19] have opened up possibilities for manipulating the off-site interactions in optical lattices.…”

Section: Introductionmentioning

confidence: 99%

Quantum phases of attractive bosons on a Bose-Hubbard ladder with three-body constraint

et al. 2014

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We obtain the complete quantum phase diagram of bosons on a two-leg ladder in the presence of attractive onsite and repulsive interchain nearest neighbor interactions by imposing the onsite three body constraint. We find three distinct phases, namely, the atomic superfluid(ASF), dimer superfluid (DSF) and the dimer rung insulator (DRI). In the absence of the interchain nearest neighbor repulsion, the system exhibits a transition from the ASF to the DSF phase with increasing onsite attraction. However, the presence of the interchain nearest neighbor repulsion stabilizes a gapped DRI phase, which is flanked by the DSF phase. We also obtain the phase diagram of the system for different values of the interchain nearest neighbor interaction. By evaluating different order parameters, we obtain the complete phase diagram and the properties of the phase transitions using the self consistent cluster mean field theory.

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“…DMRG is able to take into account the full quantum behavior of the system and it has already given strong evidences of solitonic waves in spin chains [26] and in bosonic models with nearest neighbors interaction [27]. A crucial point in order to have accurate results by using DMRG is played by the size of the Hilbert space we set in our simulations.…”

Section: B Dmrg Approachmentioning

confidence: 99%

Quantum bright solitons in a quasi-one-dimensional optical lattice

Barbiero

Salasnich

2014

Phys. Rev. A

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We study a quasi-one-dimensional attractive Bose gas confined in an optical lattice with a super-imposed harmonic potential by analyzing the one-dimensional Bose-Hubbard Hamiltonian of the system. Starting from the three-dimensional many-body quantum Hamiltonian we derive strong inequalities involving the transverse degrees of freedom under which the one-dimensional Bose-Hubbard Hamiltonian can be safely used. In order to have a reliable description of the one-dimensional ground-state, that we call quantum bright soliton, we use the Density-MatrixRenormalization-Group (DMRG) technique. By comparing DMRG results with mean-field (MF) ones we find that beyond-mean-field effects become relevant by increasing the attraction between bosons or by decreasing the frequency of the harmonic confinement. In particular we find that, contrary to the MF predictions based on the discrete nonlinear Schrödinger equation, average density profiles of quantum bright solitons are not shape invariant. We also use the time-evolving-blockdecimation (TEBD) method to investigate dynamical properties of bright solitons when the frequency of the harmonic potential is suddenly increased. This quantum quench induces a breathing mode whose period crucially depends on the final strength of the super-imposed harmonic confinement.

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

Cited by 49 publications

References 39 publications

Entanglement spectrum of one-dimensional extended Bose-Hubbard models

Entanglement spectrum of one-dimensional extended Bose-Hubbard models

Quantum phases of attractive bosons on a Bose-Hubbard ladder with three-body constraint

Quantum bright solitons in a quasi-one-dimensional optical lattice

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