Spin-Orbital Quantum Liquid on the Honeycomb Lattice

Corboz, Philippe; Lajkó, Miklós; Läuchli, Andreas M.; Penc, Karlo; Mila, Frédéric

doi:10.1103/physrevx.2.041013

Cited by 181 publications

(261 citation statements)

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“…In this study, we formulate the iPEPS ansatz on the honeycomb lattice by mapping it onto a brick-wall lattice in which the connectivity of the honeycomb lattice is reproduced exactly by introducing a trivial index on each tensor [26]. We have studied wave functions made of up to 2 × 2 unit cells with all four (rank-5) tensors being independent (see Fig.…”

Section: A Ansatzmentioning

confidence: 99%

“…By now, two decades after its development, MPS (or the DMRG) have become the golden standard for the simulation of 1D lattice models. Furthermore, their two-dimensional (2D) generalizations known as projected entangled-pair states (PEPS) [20,21] (and their thermodynamic limit version infinite PEPS or iPEPS) [22,23] have been successfully used to study both fermionic systems as well as frustrated magnets [24][25][26][27][28], with a notable example being the lowest variational energies for the t-J model available to date for large systems [29].…”

Section: Introductionmentioning

confidence: 99%

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Probing the stability of the spin-liquid phases in the Kitaev-Heisenberg model using tensor network algorithms

2014

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Probing the stability of the spin liquid phases in the Kitaev-Heisenberg model using tensor network algorithms Iregui, J.O.; Corboz, P.R.; Troyer, M. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. We study the extent of the spin liquid phases in the Kitaev-Heisenberg model using infinite projected entangledpair states tensor network ansatz wave functions directly in the thermodynamic limit. To assess the accuracy of the ansatz wave functions, we perform benchmarks against exact results for the Kitaev model and find very good agreement for various observables. In the case of the Kitaev-Heisenberg model, we confirm the existence of six different phases: Néel, stripy, ferromagnetic, zigzag, and two spin liquid phases. We find finite extents for both spin liquid phases and discontinuous phase transitions connecting them to symmetry-broken phases.

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Section: A Ansatzmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Probing the stability of the spin-liquid phases in the Kitaev-Heisenberg model using tensor network algorithms

2014

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“…For example numerical investigations of the SU(3)-Heisenberg model in a triangular lattice predict a perfectly ordered three-sublattice state [131]. On a honeycomb lattice, the SU (3) case has been shown to have a dimerized,magnetically ordered state [132][133][134], and it has been also predicted that the SU(6) case becomes a ACSL using a large 1/N expansion [135,136]. Whether or not the ACSL remains the ground state in the experimentally relevant part of the phase diagram, k = N and n = 1 is not unknown and needs to be validated by experiments.…”

Section: Strong Coupling Limit: the Su(n ) Heisenberg Modelmentioning

confidence: 99%

Ultracold Fermi gases with emergent SU(N) symmetry

2014

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We review recent experimental and theoretical progress on ultracold alkaline-earth Fermi gases with emergent SU(N ) symmetry. Emphasis is placed on describing the ground-breaking experimental achievements of recent years. The latter include the cooling to below quantum degeneracy of various isotopes of ytterbium and strontium, the demonstration of optical Feshbach resonances and the optical Stern-Gerlach effect, the realization of a Mott insulator of 173 Yb atoms, the creation of various kinds of Fermi-Bose mixtures and the observation of many-body physics in optical lattice clocks. On the theory side, we survey the zoo of phases that have been predicted for both gases in a trap and loaded into an optical lattice, focusing on two and three-dimensional systems. We also discuss some of the challenges that lie ahead for the realization of such phases, such as reaching the temperature scale required to observe magnetic and more exotic quantum orders, and dealing with collisional relaxation of excited electronic levels.

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“…A D = 1 iPEPS simply corresponds to a sitefactorized wave function (a product state), and by increasing D quantum fluctuations can be systematically added to the state. A D = 2 iPEPS includes short-range quantum fluctuations and often qualitatively reproduces the results from linear spin-wave (or flavor-wave) theory [34][35][36]. Here we consider iPEPS with D up to 12, which enables us to represent highlyentangled states.…”

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confidence: 99%

Crystals of Bound States in the Magnetization Plateaus of the Shastry-Sutherland Model

2014

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Using infinite projected entangled-pair states (iPEPS), we show that the Shastry-Sutherland model in an external magnetic field has low-magnetization plateaus which, in contrast to previous predictions, correspond to crystals of bound states of triplets, and not to crystals of triplets. The first sizable plateaus appear at magnetization 1/8, 2/15 and 1/6, in agreement with experiments on the orthogonal-dimer antiferromagnet SrCu2(BO3)2, and they can be naturally understood as regular patterns of bound states, including the intriguing 2/15 one. We also show that, even in a confined geometry, two triplets bind into a localized bound state with Sz = 2. Finally, we discuss the role of competing domain-wall and supersolid phases as well as that of additional anisotropic interactions. PACS numbers: 75.10.Jm, 75.40.Mg, 75.10.Kt, Predicting the phases of frustrated spin systems is one of the major challenges in theoretical condensed matter physics [1]. A famous example is the Shastry-Sutherland model (SSM) [2], which is believed to accurately capture the physics of the orthogonal-dimer antiferromagnet SrCu 2 (BO 3 ) 2 . A big effort has been invested in understanding the appearance of various magnetization plateaus observed in experiments [3][4][5][6][7][8][9][10][11][12][13]. Early on it was found that the SSM has almost localized triplet excitations [5,14] which suggests that each plateau corresponds to a particular crystal of localized triplets. This viewpoint has been supported by many analytical and (approximate) numerical studies over the last 15 years [14][15][16][17][18][19][20][21][22][23][24][25].The SSM is given by the Hamiltonianwhere the i, j bonds with coupling strength J build an array of orthogonal dimers while the bonds with coupling J denote inter-dimer couplings, and h the strength of the external magnetic field. The main result of this Letter is that -in contrast to the standard belief -the plateaus are not crystals of S z = 1 triplets (see Fig. 1(a)), but of S z = 2 bound states of triplets, which form a pinwheel pattern as shown in Fig. 1(b), and which are shown to be stable even if they are localized. Bound states have previously been predicted to be relevant in the dilute limit of excitations [16,[26][27][28][29], but not for the formation of crystals. The only hint so far that bound states can form crystals was found in a one-dimensional analog -a SSM spin tube [30]. It is also shown that the crystals formed by the bound states naturally explain the sequence of magnetization plateaus observed in SrCu 2 (BO 3 ) 2 . In particular, the 2/15 plateau is made of a simple and regular pattern of bound states, in contrast to the more complicated patterns of triplets which were previously suggested [12,21,24].Method -Our results have been obtained with infinite projected entangled-pair states (iPEPS) -a variational tensornetwork ansatz to represent a two-dimensional wave function in the thermodynamic limit [31][32][33]. It consists of a cell of tensors which is periodically repeated on the lattice, where ...

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Spin-Orbital Quantum Liquid on the Honeycomb Lattice

Cited by 181 publications

References 59 publications

Probing the stability of the spin-liquid phases in the Kitaev-Heisenberg model using tensor network algorithms

Probing the stability of the spin-liquid phases in the Kitaev-Heisenberg model using tensor network algorithms

Ultracold Fermi gases with emergent SU(N) symmetry

Crystals of Bound States in the Magnetization Plateaus of the Shastry-Sutherland Model

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