Phase diagram of bosons in a two-dimensional optical lattice with infinite-range cavity-mediated interactions

Flottat, Thibaut; Parny, Laurent de Forges de; Hébert, F.; Rousseau, V. G.; Batrouni, G. G.

doi:10.1103/physrevb.95.144501

Cited by 51 publications

(60 citation statements)

References 33 publications

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“…To gain better control over the longrange terms in an experimental scenario, a suitable combination of interaction processes would be required, i.e multiple attractive and repulsive long-range interactions or a large enough g such that offsite contact terms are possible [8,39]. Alternatively a setup exploiting lightmatter processes to induce synthetic interactions [40][41][42][43][44][45] could potentially be more efficient. However, in order to understand the effects of each process individually in this work, we will consider the parameters of Hamiltonian (8) to be independent variables.…”

Section: Bose-hubbard Modelmentioning

confidence: 99%

Staggered ground states in an optical lattice

et al. 2019

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Non-standard Bose-Hubbard models can exhibit rich ground state phase diagrams, even when considering the one-dimensional limit. Using a self-consistent Gutzwiller diagonalisation approach, we study the mean-field ground state properties of a long-range interacting atomic gas in a onedimensional optical lattice. We first confirm that the inclusion of long-range two-body interactions to the standard Bose-Hubbard model introduces density wave and supersolid phases. However, the introduction of pair and density-dependent tunnelling can result in new phases with two-site periodic density, single-particle transport and two-body transport order parameters. These staggered phases are potentially a mean-field signature of the known novel twisted superfluids found via a DMRG approach [PRA 94, 011603(R) (2016)]. We also observe other unconventional phases, which are characterised by sign staggered order parameters between adjacent lattice sites.

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Section: Bose-hubbard Modelmentioning

confidence: 99%

Staggered ground states in an optical lattice

et al. 2019

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“…In the absence of disorder, with longrange interactions, the BHM exhibits a richer phase di-agram with additional density wave (DW) and supersolid (SS) phases [35][36][37][38]. The ground state phase diagram of the extended BHM with cavity-mediated longrange interactions has been investigated extensively with the help of mean-field theory [37,[39][40][41][42], Gutzwiller ansatz [38,43], quantum Monte Carlo [36,38,41], and Variational Monte-Carlo [44] methods in 1D, 2D, and 3D. The addition of disorder to the BHM with long-range interactions leads to additional phases.…”

Section: Introductionmentioning

confidence: 99%

The Effect of Disorder on the Phase Diagrams of Hard-Core Lattice Bosons With Cavity-Mediated Long-Range and Nearest-Neighbor Interactions

Zhang

Rieger

2020

Front. Phys.

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We use quantum Monte Carlo simulations with the worm algorithm to study the phase diagram of a two-dimensional Bose-Hubbard model with cavity-mediated long-range interactions and uncorrelated disorder in the hard-core limit. Our study shows the system is in a supersolid phase at weak disorder and a disordered solid phase at stronger disorder. Due to long-range interactions, a large region of metastable states exists in both clean and disordered systems. By comparing the phase diagrams for both clean and disordered systems, we find that disorder suppresses metastable states and superfluidity. We compare these results with the phase diagram of the extended Bose-Hubbard model with nearest-neighbor interactions. Here, the supersolid phase does not exist even at weak disorder. We identify two kinds of glassy phases: a Bose glass phase and a disordered solid phase. The glassy phases intervene between the density-wave and superfluid phases as the Griffiths phase of the Bose-Hubbard model. The disordered solid phase intervenes between the density-wave and Bose glass phases since both have a finite structure factor.

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“…The extreme case of infinite (global) range interactions corresponds to α = 0 and, also, receives a great amount of attention as evident from Refs. [1][2][3][4][5][6][7][8][9][10] . One can think of this limit as the opposite case of highly local nearest-neighbor (NN) interactions having α → ∞, or the limit where the lattice dimensionality and geometry become irrelevant.…”

Section: Introductionmentioning

confidence: 99%

Finding the ground states of symmetric infinite-dimensional Hamiltonians: explicit constrained optimizations of tensor networks

Saadatmand¹

2020

J. Phys.: Condens. Matter

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Understanding extreme non-locality in many-body quantum systems can help resolve questions in thermostatistics and laser physics. The existence of symmetry selection rules for Hamiltonians with non-decaying terms on infinite-size lattices can lead to finite energies per site, which deserves attention. Here, we present a tensor network approach to construct the ground states of nontrivial symmetric infinite-dimensional spin Hamiltonians based on constrained optimizations of their infinite matrix product states description, which contains no truncation step (offering a very simple mathematical structure) at the cost of slightly higher polynomial complexity in comparison to existing methods. Our proposed algorithm is in part equivalent to the more generic and wellestablished solvers of infinite density-matrix renormalization-group and variational uniform matrix product states, which are, in principle, capable of precisely representing the ground states of such infinite-range-interacting many-body systems. However, we employ some mathematical simplifications that only allow for efficient brute-force optimizations of tensor-network matrices for the specific cases of highly-symmetric infinite-size infinite-range models. As a toy-model example, we showcase the effectiveness and explain some features of our method by finding the ground state of the U(1)-symmetric infinite-dimensional antiferromagnetic XX Heisenberg model. arXiv:1910.10370v2 [cond-mat.str-el]

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Phase diagram of bosons in a two-dimensional optical lattice with infinite-range cavity-mediated interactions

Cited by 51 publications

References 33 publications

Staggered ground states in an optical lattice

Staggered ground states in an optical lattice

The Effect of Disorder on the Phase Diagrams of Hard-Core Lattice Bosons With Cavity-Mediated Long-Range and Nearest-Neighbor Interactions

Finding the ground states of symmetric infinite-dimensional Hamiltonians: explicit constrained optimizations of tensor networks

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