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Chomaz L, Ferrier-Barbut I, Ferlaino F, Laburthe-Tolra B, Lev BL, Pfau T. Dipolar physics: a review of experiments with magnetic quantum gases. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2022; 86:026401. [PMID: 36583342 DOI: 10.1088/1361-6633/aca814] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2022] [Accepted: 12/02/2022] [Indexed: 06/17/2023]
Abstract
Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the experimental investigation of ultracold gases made of highly magnetic atoms has blossomed. The field has yielded the observation of many unprecedented phenomena, in particular those in which long-range and anisotropic dipole-dipole interactions (DDIs) play a crucial role. In this review, we aim to present the aspects of the magnetic quantum-gas platform that make it unique for exploring ultracold and quantum physics as well as to give a thorough overview of experimental achievements. Highly magnetic atoms distinguish themselves by the fact that their electronic ground-state configuration possesses a large electronic total angular momentum. This results in a large magnetic moment and a rich electronic transition spectrum. Such transitions are useful for cooling, trapping, and manipulating these atoms. The complex atomic structure and large dipolar moments of these atoms also lead to a dense spectrum of resonances in their two-body scattering behaviour. These resonances can be used to control the interatomic interactions and, in particular, the relative importance of contact over dipolar interactions. These features provide exquisite control knobs for exploring the few- and many-body physics of dipolar quantum gases. The study of dipolar effects in magnetic quantum gases has covered various few-body phenomena that are based on elastic and inelastic anisotropic scattering. Various many-body effects have also been demonstrated. These affect both the shape, stability, dynamics, and excitations of fully polarised repulsive Bose or Fermi gases. Beyond the mean-field instability, strong dipolar interactions competing with slightly weaker contact interactions between magnetic bosons yield new quantum-stabilised states, among which are self-bound droplets, droplet assemblies, and supersolids. Dipolar interactions also deeply affect the physics of atomic gases with an internal degree of freedom as these interactions intrinsically couple spin and atomic motion. Finally, long-range dipolar interactions can stabilise strongly correlated excited states of 1D gases and also impact the physics of lattice-confined systems, both at the spin-polarised level (Hubbard models with off-site interactions) and at the spinful level (XYZ models). In the present manuscript, we aim to provide an extensive overview of the various related experimental achievements up to the present.
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Affiliation(s)
- Lauriane Chomaz
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
- Physikalisches Institut der Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
| | - Igor Ferrier-Barbut
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
- Université Paris-Saclay, Institut d'Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau, France
| | - Francesca Ferlaino
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria
| | - Bruno Laburthe-Tolra
- Université Sorbonne Paris Nord, Laboratoire de Physique des Lasers, F-93430 Villetaneuse, France
- CNRS, UMR 7538, LPL, F-93430 Villetaneuse, France
| | - Benjamin L Lev
- Departments of Physics and Applied Physics and Ginzton Laboratory, Stanford University, Stanford, CA 94305, United States of America
| | - Tilman Pfau
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
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Zhu X, Guo J, Breuckmann NP, Guo H, Feng S. Quantum phase transitions of interacting bosons on hyperbolic lattices. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:335602. [PMID: 34111850 DOI: 10.1088/1361-648x/ac0a1a] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2021] [Accepted: 06/10/2021] [Indexed: 06/12/2023]
Abstract
The effect of many-body interaction in curved space is studied based on the extended Bose-Hubbard model on hyperbolic lattices. Using the mean-field approximation and quantum Monte Carlo simulation, the phase diagram is explicitly mapped out, which contains the superfluid, supersolid and insulator phases at various fillings. Particularly, it is revealed that the sizes of the Mott lobes shrink and the supersolid is stabilized at smaller nearest-neighbor interaction asqin the Schläfli symbol increases. The underlying physical mechanism is attributed to the increase of the coordination number, and hence the kinetic energy and the nearest-neighbor interaction. The results suggest that the hyperbolic lattices may be a unique platform to study the effect of the coordination number on quantum phase transitions, which may be relevant to the experiments of ultracold atoms in optical lattices.
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Affiliation(s)
- Xingchuan Zhu
- Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
- Center for Basic Teaching and Experiment, Nanjing University of Science and Technology, Jiangyin 214443, People's Republic of China
| | - Jiaojiao Guo
- School of Physics, Beihang University, Beijing 100191, People's Republic of China
| | - Nikolas P Breuckmann
- Department of Physics and Astronomy, University College London, WC1E 6BT London, United Kingdom
| | - Huaiming Guo
- School of Physics, Beihang University, Beijing 100191, People's Republic of China
| | - Shiping Feng
- Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
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Prestipino S. Ultracold Bosons on a Regular Spherical Mesh. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E1289. [PMID: 33287057 PMCID: PMC7712534 DOI: 10.3390/e22111289] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/22/2020] [Revised: 11/08/2020] [Accepted: 11/11/2020] [Indexed: 11/19/2022]
Abstract
Here, the zero-temperature phase behavior of bosonic particles living on the nodes of a regular spherical mesh ("Platonic mesh") and interacting through an extended Bose-Hubbard Hamiltonian has been studied. Only the hard-core version of the model for two instances of Platonic mesh is considered here. Using the mean-field decoupling approximation, it is shown that the system may exist in various ground states, which can be regarded as analogs of gas, solid, supersolid, and superfluid. For one mesh, by comparing the theoretical results with the outcome of numerical diagonalization, I manage to uncover the signatures of diagonal and off-diagonal spatial orders in a finite quantum system.
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Affiliation(s)
- Santi Prestipino
- Dipartimento di Scienze Matematiche ed Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy
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Wang HY, Zheng Z, Zhuang L, Tai YH, Shi JS, Liu WM. Topological supersolidity of dipolar Fermi gases in a spin-dependent optical lattice. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:235701. [PMID: 32079005 DOI: 10.1088/1361-648x/ab7871] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We investigate the topological supersolid states of dipolar Fermi gases trapped in a spin-dependent 2D optical lattice. Our results show that topological supersolid states can be achieved via the combination of topological superfluid states with the stripe order. Different from the general held belief that supersolid state in fermionic system can only survive with simultaneous coexistence of the repulsive and attractive dipolar interaction. We demonstrate that it can be maintained when the dipolar interaction is attractive in both x and y direction. By adjusting the ratio of hopping amplitude between different directions and dipolar interaction strength U, the system will undergo a phase transition among p x + ip y superfluid state, p y -wave superfluid state, and the topological supersolid state. The supersolid state in the attractive environment is proved to be stable by the positive sign of the inverse compressibility. We also design an experimental protocol to realize the staggered next-next-nearest-neighbor hopping via the laser assisted tunneling technique, which is the key to simulate the spin-dependent potential.
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Affiliation(s)
- Huan-Yu Wang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China. School of Physical Sciences, University of Chinese Academy of Sciences, Beijing100190, People's Republic of China
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Abstract
We study the ground state phase diagram of a two dimensional mixed-spin system of coupled alternating spin-1 and 1/2 chains with a stripe supersolid phase. Utilizing different analytical and numerical approaches such as mean field approximation, cluster mean field theory and linear spin wave theory, we demonstrate that our system displays a rich ground state phase diagram including novel stripe supersolid, solids with different fillings and super-counterfluid phases, in addition to a stripe solid with half filling, superfluid and Mott insulating phases. In order to find a minimal mixed-spin model for stripe supersolidity, in the second part of the paper we consider two kinds of mixed-spin system of coupled alternating spin-1 and 1/2 chains with (i) anisotropic nearest neighbor interactions, (ii) anisotropic hoppings and study their ground state phase diagrams. We demonstrate that, for the systems with uniform hoppings, the repulsive intra-chains interactions are necessary for stripe supersolidity. In this case the minimal two dimensional mixed-spin model is a system of spin-1 and spin-1/2 XXZ chains, interacting via Ising Hamiltonian. In the case of anisotropic hoppings, a system of coupled Ising chains is the minimal model.
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Lin F, Maier TA, Scarola VW. Disordered Supersolids in the Extended Bose-Hubbard Model. Sci Rep 2017; 7:12752. [PMID: 28986536 PMCID: PMC5630629 DOI: 10.1038/s41598-017-13040-9] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2017] [Accepted: 09/12/2017] [Indexed: 11/17/2022] Open
Abstract
The extended Bose-Hubbard model captures the essential properties of a wide variety of physical systems including ultracold atoms and molecules in optical lattices, Josephson junction arrays, and certain narrow band superconductors. It exhibits a rich phase diagram including a supersolid phase where a lattice solid coexists with a superfluid. We use quantum Monte Carlo to study the supersolid part of the phase diagram of the extended Bose-Hubbard model on the simple cubic lattice. We add disorder to the extended Bose-Hubbard model and find that the maximum critical temperature for the supersolid phase tends to be suppressed by disorder. But we also find a narrow parameter window in which the supersolid critical temperature is enhanced by disorder. Our results show that supersolids survive a moderate amount of spatial disorder and thermal fluctuations in the simple cubic lattice.
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Affiliation(s)
- Fei Lin
- Department of Physics, Virginia Tech, Blacksburg, Virginia, 24061, USA
| | - T A Maier
- Computational Science and Engineering Division and Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee, 37831, USA
| | - V W Scarola
- Department of Physics, Virginia Tech, Blacksburg, Virginia, 24061, USA.
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Weber M, Assaad FF, Hohenadler M. Directed-Loop Quantum Monte Carlo Method for Retarded Interactions. PHYSICAL REVIEW LETTERS 2017; 119:097401. [PMID: 28949554 DOI: 10.1103/physrevlett.119.097401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2017] [Indexed: 06/07/2023]
Abstract
The directed-loop quantum Monte Carlo method is generalized to the case of retarded interactions. Using the path integral, fermion-boson or spin-boson models are mapped to actions with retarded interactions by analytically integrating out the bosons. This yields an exact algorithm that combines the highly efficient loop updates available in the stochastic series expansion representation with the advantages of avoiding a direct sampling of the bosons. The application to electron-phonon models reveals that the method overcomes the previously detrimental issues of long autocorrelation times and exponentially decreasing acceptance rates. For example, the resulting dramatic speedup allows us to investigate the Peierls quantum phase transition on chains of up to 1282 sites.
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Affiliation(s)
- Manuel Weber
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, 97074 Würzburg, Germany
| | - Fakher F Assaad
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, 97074 Würzburg, Germany
| | - Martin Hohenadler
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, 97074 Würzburg, Germany
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Martin AM, Marchant NG, O'Dell DHJ, Parker NG. Vortices and vortex lattices in quantum ferrofluids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:103004. [PMID: 28145899 DOI: 10.1088/1361-648x/aa53a6] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The experimental realization of quantum-degenerate Bose gases made of atoms with sizeable magnetic dipole moments has created a new type of fluid, known as a quantum ferrofluid, which combines the extraordinary properties of superfluidity and ferrofluidity. A hallmark of superfluids is that they are constrained to rotate through vortices with quantized circulation. In quantum ferrofluids the long-range dipolar interactions add new ingredients by inducing magnetostriction and instabilities, and also affect the structural properties of vortices and vortex lattices. Here we give a review of the theory of vortices in dipolar Bose-Einstein condensates, exploring the interplay of magnetism with vorticity and contrasting this with the established behaviour in non-dipolar condensates. We cover single vortex solutions, including structure, energy and stability, vortex pairs, including interactions and dynamics, and also vortex lattices. Our discussion is founded on the mean-field theory provided by the dipolar Gross-Pitaevskii equation, ranging from analytic treatments based on the Thomas-Fermi (hydrodynamic) and variational approaches to full numerical simulations. Routes for generating vortices in dipolar condensates are discussed, with particular attention paid to rotating condensates, where surface instabilities drive the nucleation of vortices, and lead to the emergence of rich and varied vortex lattice structures. We also present an outlook, including potential extensions to degenerate Fermi gases, quantum Hall physics, toroidal systems and the Berezinskii-Kosterlitz-Thouless transition.
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Affiliation(s)
- A M Martin
- School of Physics, University of Melbourne, Victoria 3010, Australia
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9
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Jürgensen O, Sengstock K, Lühmann DS. Twisted complex superfluids in optical lattices. Sci Rep 2015; 5:12912. [PMID: 26345721 PMCID: PMC4642545 DOI: 10.1038/srep12912] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2015] [Accepted: 07/13/2015] [Indexed: 11/09/2022] Open
Abstract
We show that correlated pair tunneling drives a phase transition to a twisted superfluid with a complex order parameter. This unconventional superfluid phase spontaneously breaks the time-reversal symmetry and is characterized by a twisting of the complex phase angle between adjacent lattice sites. We discuss the entire phase diagram of the extended Bose-Hubbard model for a honeycomb optical lattice showing a multitude of quantum phases including twisted superfluids, pair superfluids, supersolids and twisted supersolids. Furthermore, we show that the nearest-neighbor interactions lead to a spontaneous breaking of the inversion symmetry of the lattice and give rise to dimerized density-wave insulators, where particles are delocalized on dimers. For two components, we find twisted superfluid phases with strong correlations between the species already for surprisingly small pair-tunneling amplitudes. Interestingly, this ground state shows an infinite degeneracy ranging continuously from a supersolid to a twisted superfluid.
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Affiliation(s)
- Ole Jürgensen
- Institut fϋr Laser-Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Klaus Sengstock
- Institut fϋr Laser-Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Dirk-Sören Lühmann
- Institut fϋr Laser-Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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10
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Dutta O, Gajda M, Hauke P, Lewenstein M, Lühmann DS, Malomed BA, Sowiński T, Zakrzewski J. Non-standard Hubbard models in optical lattices: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2015; 78:066001. [PMID: 26023844 DOI: 10.1088/0034-4885/78/6/066001] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Originally, the Hubbard model was derived for describing the behavior of strongly correlated electrons in solids. However, for over a decade now, variations of it have also routinely been implemented with ultracold atoms in optical lattices, allowing their study in a clean, essentially defect-free environment. Here, we review some of the vast literature on this subject, with a focus on more recent non-standard forms of the Hubbard model. After giving an introduction to standard (fermionic and bosonic) Hubbard models, we discuss briefly common models for mixtures, as well as the so-called extended Bose-Hubbard models, that include interactions between neighboring sites, next-neighbor sites, and so on. The main part of the review discusses the importance of additional terms appearing when refining the tight-binding approximation for the original physical Hamiltonian. Even when restricting the models to the lowest Bloch band is justified, the standard approach neglects the density-induced tunneling (which has the same origin as the usual on-site interaction). The importance of these contributions is discussed for both contact and dipolar interactions. For sufficiently strong interactions, the effects related to higher Bloch bands also become important even for deep optical lattices. Different approaches that aim at incorporating these effects, mainly via dressing the basis, Wannier functions with interactions, leading to effective, density-dependent Hubbard-type models, are reviewed. We discuss also examples of Hubbard-like models that explicitly involve higher p orbitals, as well as models that dynamically couple spin and orbital degrees of freedom. Finally, we review mean-field nonlinear Schrödinger models of the Salerno type that share with the non-standard Hubbard models nonlinear coupling between the adjacent sites. In that part, discrete solitons are the main subject of consideration. We conclude by listing some open problems, to be addressed in the future.
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Affiliation(s)
- Omjyoti Dutta
- Instytut Fizyki imienia Mariana Smoluchowskiego, Uniwersytet Jagielloński, Łojasiewicza 11, 30-348 Kraków, Poland
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11
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Murakami Y, Werner P, Tsuji N, Aoki H. Supersolid phase accompanied by a quantum critical point in the intermediate coupling regime of the Holstein model. PHYSICAL REVIEW LETTERS 2014; 113:266404. [PMID: 25615362 DOI: 10.1103/physrevlett.113.266404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2014] [Indexed: 06/04/2023]
Abstract
We reveal that electron-phonon systems described by the Holstein model on a bipartite lattice exhibit, away from half filling, a supersolid (SS) phase characterized by coexisting charge order (CO) and superconductivity (SC), and an accompanying quantum critical point (QCP). The SS phase, demonstrated by the dynamical mean-field theory with a quantum Monte Carlo impurity solver, emerges in the intermediate-coupling regime, where the peak of the Tc dome is located and the metal-insulator crossover occurs. On the other hand, in the weak- and strong-coupling regimes the CO-SC boundary is of first order with no intervening SS phases. The QCP is associated with the continuous transition from SS to SC and characterized by a reentrant behavior of the SS around it. We further show that the SS-SC transition is hallmarked by diverging charge fluctuations and a kink (peak) in the superfluid density.
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Affiliation(s)
- Yuta Murakami
- Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033, Japan
| | - Philipp Werner
- Department of Physics, University of Fribourg, 1700 Fribourg, Switzerland
| | - Naoto Tsuji
- Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033, Japan
| | - Hideo Aoki
- Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033, Japan
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Rademaker L, Pramudya Y, Zaanen J, Dobrosavljević V. Influence of long-range interactions on charge ordering phenomena on a square lattice. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:032121. [PMID: 24125227 DOI: 10.1103/physreve.88.032121] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2013] [Revised: 08/01/2013] [Indexed: 06/02/2023]
Abstract
Usually complex charge ordering phenomena arise due to competing interactions. We have studied how such ordered patterns emerge from the frustration of a long-ranged interaction on a lattice. Using the lattice gas model on a square lattice with fixed particle density, we have identified several interesting phases, such as a generalization of Wigner crystals at low particle densities and stripe phases at densities between ρ=1/3 and 1/2. These stripes act as domain walls in the checkerboard phase present at half-filling. The phases are characterized at zero temperatures using numerical simulations, and mean field theory is used to construct a finite temperature phase diagram.
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Affiliation(s)
- Louk Rademaker
- Institute-Lorentz for Theoretical Physics, Leiden University, PO Box 9506, NL-2300 RA Leiden, The Netherlands
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13
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Batrouni GG, Scalettar RT, Rousseau VG, Grémaud B. Competing supersolid and Haldane insulator phases in the extended one-dimensional bosonic Hubbard model. PHYSICAL REVIEW LETTERS 2013; 110:265303. [PMID: 23848892 DOI: 10.1103/physrevlett.110.265303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2013] [Indexed: 06/02/2023]
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.
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Affiliation(s)
- G G Batrouni
- INLN, Université de Nice-Sophia Antipolis, CNRS, 1361 route des Lucioles, 06560 Valbonne, France
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14
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Wierschem K, Sengupta P. Columnar antiferromagnetic order and spin supersolid phase on the extended Shastry-Sutherland lattice. PHYSICAL REVIEW LETTERS 2013; 110:207207. [PMID: 25167448 DOI: 10.1103/physrevlett.110.207207] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2012] [Indexed: 06/03/2023]
Abstract
We use large scale quantum Monte Carlo simulations to study an extended version of the canonical Shastry-Sutherland model--including additional interactions and exchange anisotropy--over a wide range of interaction parameters and an applied magnetic field. The model is appropriate for describing the low energy properties of some members of the rare earth tetraborides. Working in the limit of large Ising-like exchange anisotropy, we demonstrate the stabilization of columnar antiferromagnetic order in the ground state at zero field and an extended magnetization plateau at 1/2 the saturation magnetization in the presence of an applied longitudinal magnetic field--qualitatively similar to experimentally observed low-temperature phases in ErB(4). Our results show that for an optimal range of exchange parameters, a spin supersolid ground state is realized over a finite range of an applied field between the columnar antiferromagnetic phase and the magnetization plateau. The full momentum dependence of the longitudinal and transverse components of the static structure factor is calculated in the spin supersolid phase to demonstrate the simultaneous existence of diagonal and off-diagonal long-range order. Our results provide crucial guidance in designing further experiments to search for the interesting spin supersolid phase in ErB(4).
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Affiliation(s)
- Keola Wierschem
- School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
| | - Pinaki Sengupta
- School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
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15
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Zhang XF, Sun Q, Wen YC, Liu WM, Eggert S, Ji AC. Rydberg polaritons in a cavity: a superradiant solid. PHYSICAL REVIEW LETTERS 2013; 110:090402. [PMID: 23496692 DOI: 10.1103/physrevlett.110.090402] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2012] [Indexed: 06/01/2023]
Abstract
We study an optical cavity coupled to a lattice of Rydberg atoms, which can be represented by a generalized Dicke model. We show that the competition between the atom-atom interaction and atom-light coupling induces a rich phase diagram. A novel superradiant solid (SRS) phase is found, where both the superradiance and crystalline orders coexist. Different from the normal second order superradiance transition, here both the solid-1/2 and SRS to SR phase transitions are first order. These results are confirmed by large scale quantum Monte Carlo simulations.
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Affiliation(s)
- Xue-Feng Zhang
- Physics Department and Research Center OPTIMAS, University of Kaiserslautern, 67663 Kaiserslautern, Germany
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16
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Baranov MA, Dalmonte M, Pupillo G, Zoller P. Condensed Matter Theory of Dipolar Quantum Gases. Chem Rev 2012; 112:5012-61. [DOI: 10.1021/cr2003568] [Citation(s) in RCA: 480] [Impact Index Per Article: 40.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- M. A. Baranov
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
- Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
- RRC “Kurchatov Institute”,
Kurchatov Square 1, 123182, Moscow, Russia
| | - M. Dalmonte
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
- Dipartimento di Fisica dell’Università
di Bologna, via Irnerio 46, 40126 Bologna, Italy
| | - G. Pupillo
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
- Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
- ISIS (UMR 7006) and IPCMS (UMR
7504), Université de Strasbourg and CNRS, Strasbourg, France
| | - P. Zoller
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
- Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
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17
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Ohgoe T, Suzuki T, Kawashima N. Commensurate supersolid of three-dimensional lattice bosons. PHYSICAL REVIEW LETTERS 2012; 108:185302. [PMID: 22681086 DOI: 10.1103/physrevlett.108.185302] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/27/2011] [Indexed: 06/01/2023]
Abstract
Using an unbiased quantum Monte Carlo method, we obtain convincing evidence of the existence of a checkerboard supersolid at a commensurate filling factor 1/2 (a commensurate supersolid) in the soft-core Bose-Hubbard model with nearest-neighbor repulsions on a cubic lattice. In conventional cases, supersolids are realized at incommensurate filling factors by a doped-defect-condensation mechanism, where particles (holes) doped into a perfect crystal act as interstitials (vacancies) and delocalize in the crystal order. However, in the model, a supersolid state is stabilized even at the commensurate filling factor 1/2 without doping. By performing grand canonical simulations, we obtain a ground-state phase diagram that suggests the existence of a supersolid at a commensurate filling. To obtain direct evidence of the commensurate supersolid, we next perform simulations in canonical ensembles at a particle density ρ=1/2 and exclude the possibility of phase separation. From the obtained snapshots, we discuss its microscopic structure and observe that interstitial-vacancy pairs are unbound in the crystal order.
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Affiliation(s)
- Takahiro Ohgoe
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
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18
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Sowiński T, Dutta O, Hauke P, Tagliacozzo L, Lewenstein M. Dipolar molecules in optical lattices. PHYSICAL REVIEW LETTERS 2012; 108:115301. [PMID: 22540482 DOI: 10.1103/physrevlett.108.115301] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2011] [Indexed: 05/31/2023]
Abstract
We study the extended Bose-Hubbard model describing an ultracold gas of dipolar molecules in an optical lattice, taking into account all on-site and nearest-neighbor interactions, including occupation-dependent tunneling and pair tunneling terms. Using exact diagonalization and the multiscale entanglement renormalization ansatz, we show that these terms can destroy insulating phases and lead to novel quantum phases. These considerable changes of the phase diagram have to be taken into account in upcoming experiments with dipolar molecules.
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Affiliation(s)
- Tomasz Sowiński
- Institute of Physics of the Polish Academy of Sciences, Warsaw, Poland
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19
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Ng KK, Chen YC, Tzeng YC. Quarter-filled supersolid and solid phases in the extended Bose-Hubbard model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:185601. [PMID: 21393687 DOI: 10.1088/0953-8984/22/18/185601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We numerically study the ground state phase diagram of the two-dimensional hard-core Bose-Hubbard model with nearest-(V(1)) and next-nearest-neighbour (V(2)) repulsions. In particular, we focus on the quarter-filled phases where one supersolid and two solid phases are observed. Using both canonical and grand canonical quantum Monte Carlo (QMC) methods and a mean-field calculation, we provide evidence for the existence of a commensurate supersolid. Despite the two possible diagonal long-range orderings for the solid phase, only one kind of supersolid phase is found to be energetically stable. The competition between the two solid phases manifests itself as a first-order phase transition around 2V(2) ∼ V(1). The change of order parameters as a function of the chemical potential is also presented.
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Affiliation(s)
- Kwai-Kong Ng
- Department of Physics, Tunghai University, Taichung 40704, Taiwan
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20
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Pollet L, Picon JD, Büchler HP, Troyer M. Supersolid phase with cold polar molecules on a triangular lattice. PHYSICAL REVIEW LETTERS 2010; 104:125302. [PMID: 20366542 DOI: 10.1103/physrevlett.104.125302] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2009] [Revised: 08/11/2009] [Indexed: 05/29/2023]
Abstract
We study a system of heteronuclear molecules on a triangular lattice and analyze the potential of this system for the experimental realization of a supersolid phase. The ground state phase diagram contains superfluid, solid, and supersolid phases. At finite temperatures and strong interactions there is an additional emulsion region, in contrast with similar models with short-range interactions. We derive the maximal critical temperature T{c} and the corresponding entropy S/N=0.04(1) for supersolidity and find feasible experimental conditions for its realization.
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Affiliation(s)
- L Pollet
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
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21
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Capogrosso-Sansone B, Trefzger C, Lewenstein M, Zoller P, Pupillo G. Quantum phases of cold polar molecules in 2D optical lattices. PHYSICAL REVIEW LETTERS 2010; 104:125301. [PMID: 20366541 DOI: 10.1103/physrevlett.104.125301] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2009] [Revised: 02/22/2010] [Indexed: 05/29/2023]
Abstract
We study the quantum phases of hard-core bosonic polar molecules on a two-dimensional square lattice interacting via repulsive dipole-dipole interactions. In the limit of small tunneling, we find evidence for a devil's staircase, where Mott solids appear at rational fillings of the lattice. For finite tunneling, we establish the existence of extended regions of parameters where the ground state is a supersolid, obtained by doping the solids either with particles or vacancies. We discuss the effects of finite temperature and finite-size confining potentials as relevant to experiments.
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Affiliation(s)
- B Capogrosso-Sansone
- ITAMP, Harvard-Smithsonian Center of Astrophysics, Cambridge, Massachusetts 02138, USA
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22
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Danshita I, Sá de Melo CAR. Stability of superfluid and supersolid phases of dipolar bosons in optical lattices. PHYSICAL REVIEW LETTERS 2009; 103:225301. [PMID: 20366103 DOI: 10.1103/physrevlett.103.225301] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2008] [Revised: 11/03/2009] [Indexed: 05/29/2023]
Abstract
We perform a stability analysis of superfluid (SF) and supersolid (SS) phases of polarized dipolar bosons in two-dimensional optical lattices at high filling factors and zero temperature, and obtain the phase boundaries between SF, checkerboard SS (CSS), striped SS (SSS), and collapse. We show that the phase diagram can be explored through the application of an external field and the tuning of its direction with respect to the optical lattice plane. In particular, we find a transition between the CSS and SSS phases.
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Affiliation(s)
- Ippei Danshita
- Department of Physics, Waseda University, Shinjuku-ku, Tokyo 169-8555, Japan
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23
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Carleo G, Tarzia M, Zamponi F. Bose-Einstein condensation in quantum glasses. PHYSICAL REVIEW LETTERS 2009; 103:215302. [PMID: 20366050 DOI: 10.1103/physrevlett.103.215302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2009] [Revised: 10/10/2009] [Indexed: 05/29/2023]
Abstract
The role of geometrical frustration in strongly interacting bosonic systems is studied with a combined numerical and analytical approach. We demonstrate the existence of a novel quantum phase featuring both Bose-Einstein condensation and spin-glass behavior. The differences between such a phase and the otherwise insulating "Bose glasses" are elucidated.
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Affiliation(s)
- Giuseppe Carleo
- SISSA-Scuola Internazionale Superiore di Studi Avanzati and CNR-INFM DEMOCRITOS-National Simulation Center, via Beirut 2-4, I-34014 Trieste, Italy
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24
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Cherng RW, Demler E. Magnetoroton softening in Rb spinor condensates with dipolar interactions. PHYSICAL REVIEW LETTERS 2009; 103:185301. [PMID: 19905809 DOI: 10.1103/physrevlett.103.185301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2009] [Revised: 10/09/2009] [Indexed: 05/28/2023]
Abstract
Superfluids with a tendency towards periodic order have both phonon- and rotonlike spectra. We show that magnetoroton softening occurs in 87Rb spinor condensates. A rich variety of dynamical instabilities emerges as a function of the magnetic field orientation and strength of the quadratic Zeeman shift. These instabilities are driven by an effective dipolar interaction modified dramatically by quasi-two-dimensionality and rapid Larmor precession.
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Affiliation(s)
- R W Cherng
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
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25
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Trefzger C, Menotti C, Lewenstein M. Pair-supersolid phase in a bilayer system of dipolar lattice bosons. PHYSICAL REVIEW LETTERS 2009; 103:035304. [PMID: 19659292 DOI: 10.1103/physrevlett.103.035304] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2009] [Revised: 05/19/2009] [Indexed: 05/28/2023]
Abstract
The competition between tunneling and interactions in bosonic lattice models generates a whole variety of different quantum phases. While, in the presence of a single species interacting via on site interaction, the phase diagram presents only superfluid or Mott insulating phases, for long-range interactions or multiple species, exotic phases such as supersolid or pair-superfluid appear. In this Letter, we show for the first time that the coexistence of effective multiple species and long-range interactions leads to the formation of a novel pair-supersolid phase, namely, a supersolid of composites. We propose a possible implementation with dipolar bosons in a bilayer two-dimensional optical lattice.
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Affiliation(s)
- C Trefzger
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels, Barcelona, Spain
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26
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Schmidt KP, Dorier J, Läuchli AM. Solids and supersolids of three-body interacting polar molecules on an optical lattice. PHYSICAL REVIEW LETTERS 2008; 101:150405. [PMID: 18999578 DOI: 10.1103/physrevlett.101.150405] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2008] [Indexed: 05/27/2023]
Abstract
We study the physics of cold polar molecules loaded into an optical lattice in the regime of strong three-body interactions, as put forward recently by Büchler et al. [Nature Phys. 3, 726 (2007)]. To this end, quantum Monte Carlo simulations, exact diagonalization, and a semiclassical approach are used to explore hard-core bosons on the 2D square lattice which interact solely by long-ranged three-body terms. The resulting phase diagram shows a sequence of solid and supersolid phases. Our findings are directly relevant for future experimental implementations and open a new route towards the discovery of a lattice supersolid phase in experiment.
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Affiliation(s)
- Kai P Schmidt
- Lehrstuhl für theoretische Physik I, Otto-Hahn-Str. 4, TU Dortmund, D-44221 Dortmund, Germany.
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27
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Titvinidze I, Snoek M, Hofstetter W. Supersolid bose-fermi mixtures in optical lattices. PHYSICAL REVIEW LETTERS 2008; 100:100401. [PMID: 18352164 DOI: 10.1103/physrevlett.100.100401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2007] [Indexed: 05/26/2023]
Abstract
We study a mixture of strongly interacting bosons and spinless fermions with on-site repulsion in a three-dimensional optical lattice. For this purpose we develop and apply a generalized dynamical mean-field theory, which is exact in infinite dimensions and reliably describes the full range from weak to strong coupling. We restrict ourselves to half filling. For weak Bose-Fermi repulsion a supersolid forms, in which bosonic superfluidity coexists with charge-density wave order. For stronger interspecies repulsion the bosons become localized while the charge-density wave order persists. The system is unstable against phase separation for weak repulsion among the bosons.
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Affiliation(s)
- I Titvinidze
- Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität, 60438 Frankfurt am Main, Germany
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28
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Sengupta P, Batista CD. Spin supersolid in an anisotropic spin-one Heisenberg chain. PHYSICAL REVIEW LETTERS 2007; 99:217205. [PMID: 18233248 DOI: 10.1103/physrevlett.99.217205] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2007] [Indexed: 05/25/2023]
Abstract
We consider an S=1 Heisenberg chain with strong exchange (Delta=J(z)/J(perpendicular)) and single-ion uniaxial anisotropy (D) in a magnetic field (B) along the symmetry axis. The low-energy spectrum is described by an effective S=1/2 XXZ model that acts on two different low-energy sectors for a finite range of fields. The vacuum of each sector exhibits Ising-like antiferromagnetic ordering coexisting with the finite spin stiffness obtained from the exact solution of the XXZ model. In this way, we demonstrate the existence of a spin supersolid phase. We also compute the full Delta-B quantum phase diagram using a quantum Monte Carlo method.
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Affiliation(s)
- P Sengupta
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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29
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Menotti C, Trefzger C, Lewenstein M. Metastable states of a gas of dipolar bosons in a 2D optical lattice. PHYSICAL REVIEW LETTERS 2007; 98:235301. [PMID: 17677913 DOI: 10.1103/physrevlett.98.235301] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2006] [Revised: 04/04/2007] [Indexed: 05/16/2023]
Abstract
We investigate the physics of dipolar bosons in a two-dimensional optical lattice. It is known that due to the long-range character of dipole-dipole interaction, the ground state phase diagram of a gas of dipolar bosons in an optical lattice presents novel quantum phases, like checkerboard and supersolid phases. In this Letter, we consider the properties of the system beyond its ground state, finding that it is characterized by a multitude of almost degenerate metastable states, often competing with the ground state. This makes dipolar bosons in a lattice similar to a disordered system and opens possibilities of using them as quantum memories.
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Affiliation(s)
- C Menotti
- ICFO - Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
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30
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Sengupta P, Batista CD. Field-induced supersolid phase in spin-one Heisenberg models. PHYSICAL REVIEW LETTERS 2007; 98:227201. [PMID: 17677874 DOI: 10.1103/physrevlett.98.227201] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2006] [Revised: 03/26/2007] [Indexed: 05/16/2023]
Abstract
We use numerical methods to demonstrate that the phase diagram of S=1 Heisenberg models with uniaxial anisotropy contains an extended supersolid phase. We show that this Hamiltonian is a particular case of a more general and ubiquitous model that describes the low-energy spectrum of some isotropic and frustrated spin-dimer systems. This result is crucial for finding a spin supersolid state in real magnets.
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Affiliation(s)
- P Sengupta
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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31
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Ueltschi D. Relation between Feynman cycles and off-diagonal long-range order. PHYSICAL REVIEW LETTERS 2006; 97:170601. [PMID: 17155456 DOI: 10.1103/physrevlett.97.170601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2006] [Indexed: 05/12/2023]
Abstract
The usual order parameter for Bose-Einstein condensation involves the off-diagonal correlation function of Penrose and Onsager, but an alternative is Feynman's notion of infinite cycles. We present a formula that relates both order parameters. We discuss its validity with the help of rigorous results and heuristic arguments. The conclusion is that infinite cycles do not always represent the Bose condensate.
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Affiliation(s)
- Daniel Ueltschi
- Department of Mathematics, University of Arizona, Tucson, Arizona 85721, USA
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32
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Ng KK, Lee TK. Supersolid phase in spin dimer XXZ systems under a magnetic field. PHYSICAL REVIEW LETTERS 2006; 97:127204. [PMID: 17025995 DOI: 10.1103/physrevlett.97.127204] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2006] [Indexed: 05/12/2023]
Abstract
Using the quantum Monte Carlo method, we study, under external magnetic fields, the ground state phase diagram of the two-dimensional spin S=1/2 dimer model with an anisotropic intraplane antiferromagnetic coupling. With the anisotropy 4 greater/approximately Delta greater/approximately 3, a supersolid phase characterized by a nonuniform Bose condensate density that breaks translational symmetry is found. The rich phase diagram also contains a checkerboard solid, an antiferromagnet in the z axis, and a superfluid phase formed by S(z)= +1 spin triplets which has a finite staggered magnetization in the in-plane direction. As we show, the model can be realized as a consequence of including the next nearest neighbor coupling among dimers and our results suggest that spin dimer systems may be an ideal model system to study the supersolid phase.
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Affiliation(s)
- Kwai-Kong Ng
- Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan
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33
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Batrouni GG, Hébert F, Scalettar RT. Supersolid phases in the one-dimensional extended soft-core bosonic Hubbard model. PHYSICAL REVIEW LETTERS 2006; 97:087209. [PMID: 17026334 DOI: 10.1103/physrevlett.97.087209] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2006] [Indexed: 05/12/2023]
Abstract
We present results of quantum Monte Carlo simulations for the soft-core extended bosonic Hubbard model in one dimension exhibiting the presence of supersolid phases similar to those recently found in two dimensions. We find that in one and two dimensions, the insulator-supersolid transition has dynamic critical exponent z = 2 whereas the first order insulator-superfluid transition in two dimensions is replaced by a continuous transition with z = 1 in one dimension. We present evidence that this transition is in the Kosterlitz-Thouless universality class and discuss the mechanism behind this difference. The simultaneous presence of two types of quasi-long-range order results in two solitonlike dips in the excitation spectrum.
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Affiliation(s)
- G G Batrouni
- Institut Non-Linéaire de Nice, UMR 6618 CNRS, Université de Nice-Sophia Antipolis, 1361 route des Lucioles, 06560 Valbonne, France
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34
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Wessel S, Troyer M. Supersolid hard-core bosons on the triangular lattice. PHYSICAL REVIEW LETTERS 2005; 95:127205. [PMID: 16197105 DOI: 10.1103/physrevlett.95.127205] [Citation(s) in RCA: 68] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2005] [Indexed: 05/04/2023]
Abstract
We determine the phase diagram of hard-core bosons on a triangular lattice with nearest-neighbor repulsion, paying special attention to the stability of the supersolid phase. Similar to the same model on a square lattice we find that for densities rho<1/3 or rho>2/3 a supersolid phase is unstable and the transition between a commensurate solid and the superfluid is of first order. At intermediate fillings 1/3<rho<2/3 we find an extended supersolid phase even at half filling rho=1/2. The emergence of the supersolid on the triangular lattice reflects a novel and interesting way for a quantum system to avoid classical frustration, similar to an order-by-disorder mechanism. It also offers an exciting possibility of realizing such phenomena in ultracold atoms on optical lattices.
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Affiliation(s)
- Stefan Wessel
- Institut für Theoretische Physik III, Universität Stuttgart, 70550 Stuttgart, Germany
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35
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Heidarian D, Damle K. Persistent supersolid phase of hard-core bosons on the triangular lattice. PHYSICAL REVIEW LETTERS 2005; 95:127206. [PMID: 16197106 DOI: 10.1103/physrevlett.95.127206] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2005] [Indexed: 05/04/2023]
Abstract
We study hard-core bosons with unfrustrated hopping (t) and nearest neighbor repulsion (U) (spin S=1/2 XXZ model) on the triangular lattice. At half filling, the system undergoes a zero temperature (T) quantum phase transition from a superfluid phase at small U to a supersolid at Uc approximately 4.45 in units of 2t. This supersolid phase breaks the lattice translation symmetry in a characteristic sqrt[3] x square root of 3 pattern, and is remarkably stable--indeed, a smooth extrapolation of our results indicates that the supersolid phase persists for arbitrarily large U/t.
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Affiliation(s)
- Dariush Heidarian
- Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
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36
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Melko RG, Paramekanti A, Burkov AA, Vishwanath A, Sheng DN, Balents L. Supersolid order from disorder: hard-core bosons on the triangular lattice. PHYSICAL REVIEW LETTERS 2005; 95:127207. [PMID: 16197107 DOI: 10.1103/physrevlett.95.127207] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2005] [Indexed: 05/04/2023]
Abstract
We study the interplay of Mott localization, geometric frustration, and superfluidity for hard-core bosons with nearest-neighbor repulsion on the triangular lattice. For this model at half filling, we demonstrate that superfluidity survives for arbitrarily large repulsion, and that diagonal solid order emerges in the strongly correlated regime from an order-by-disorder mechanism. This is thus an unusual example of a stable supersolid phase of hard-core lattice bosons at a commensurate filling.
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Affiliation(s)
- R G Melko
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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37
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Bendjama R, Kumar B, Mila F. Absence of single-particle Bose-Einstein condensation at low densities for bosons with correlated hopping. PHYSICAL REVIEW LETTERS 2005; 95:110406. [PMID: 16196986 DOI: 10.1103/physrevlett.95.110406] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2005] [Indexed: 05/04/2023]
Abstract
Motivated by the physics of mobile triplets in frustrated quantum magnets, the properties of a two-dimensional model of bosons with correlated hopping are investigated. A mean-field analysis reveals the presence of a pairing phase without single-particle Bose-Einstein condensation (BEC) at low densities for sufficiently strong correlated hopping, and of an Ising quantum phase transition towards a BEC phase at larger density. The physical arguments supporting the mean-field results and their implications for bosonic and quantum spin systems are discussed.
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Affiliation(s)
- Rachel Bendjama
- Institute of Theoretical Physics, Ecole Polytechnique Fédérale de Lausanne, CH 1015 Lausanne, Switzerland
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38
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Scarola VW, Das Sarma S. Quantum phases of the extended Bose-Hubbard hamiltonian: possibility of a supersolid state of cold atoms in optical lattices. PHYSICAL REVIEW LETTERS 2005; 95:033003. [PMID: 16090740 DOI: 10.1103/physrevlett.95.033003] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2005] [Indexed: 05/03/2023]
Abstract
Cold atom optical lattices typically simulate zero-range Hubbard models. We discuss the theoretical possibility of using excited states of optical lattices to generate extended range Hubbard models. We find that bosons confined to higher bands of optical lattices allow for a rich phase diagram, including the supersolid phase. Using Gutzwiller, mean-field theory we establish the parameter regime necessary to maintain metastable states generated by an extended Bose-Hubbard model.
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Affiliation(s)
- V W Scarola
- Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, MD 20742-4111, USA
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