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      Dynamical time-reversal symmetry breaking and photo-induced chiral spin liquids in frustrated Mott insulators

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          Abstract

          The search for quantum spin liquids in frustrated quantum magnets recently has enjoyed a surge of interest, with various candidate materials under intense scrutiny. However, an experimental confirmation of a gapped topological spin liquid remains an open question. Here, we show that circularly polarized light can provide a knob to drive frustrated Mott insulators into a chiral spin liquid, realizing an elusive quantum spin liquid with topological order. We find that the dynamics of a driven Kagome Mott insulator is well-captured by an effective Floquet spin model, with heating strongly suppressed, inducing a scalar spin chirality S i · ( S j  ×  S k ) term which dynamically breaks time-reversal while preserving SU(2) spin symmetry. We fingerprint the transient phase diagram and find a stable photo-induced chiral spin liquid near the equilibrium state. The results presented suggest employing dynamical symmetry breaking to engineer quantum spin liquids and access elusive phase transitions that are not readily accessible in equilibrium.

          Abstract

          Exotic quantum phases like spin liquids have long been investigated theoretically but it is difficult to find materials that realize these states in equilibrium. Here the authors propose that optical driving could be used to induce chiral spin liquid behaviour in frustrated Mott insulators.

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          Experimental realisation of the topological Haldane model

          The Haldane model on the honeycomb lattice is a paradigmatic example of a Hamiltonian featuring topologically distinct phases of matter. It describes a mechanism through which a quantum Hall effect can appear as an intrinsic property of a band-structure, rather than being caused by an external magnetic field. Although an implementation in a material was considered unlikely, it has provided the conceptual basis for theoretical and experimental research exploring topological insulators and superconductors. Here we report on the experimental realisation of the Haldane model and the characterisation of its topological band-structure, using ultracold fermionic atoms in a periodically modulated optical honeycomb lattice. The model is based on breaking time-reversal symmetry as well as inversion symmetry. The former is achieved through the introduction of complex next-nearest-neighbour tunnelling terms, which we induce through circular modulation of the lattice position. For the latter, we create an energy offset between neighbouring sites. Breaking either of these symmetries opens a gap in the band-structure, which is probed using momentum-resolved interband transitions. We explore the resulting Berry-curvatures of the lowest band by applying a constant force to the atoms and find orthogonal drifts analogous to a Hall current. The competition between both broken symmetries gives rise to a transition between topologically distinct regimes. By identifying the vanishing gap at a single Dirac point, we map out this transition line experimentally and compare it to calculations using Floquet theory without free parameters. We verify that our approach, which allows for dynamically tuning topological properties, is suitable even for interacting fermionic systems. Furthermore, we propose a direct extension to realise spin-dependent topological Hamiltonians.
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            Equivalence of the resonating-valence-bond and fractional quantum Hall states.

            (1987)
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              Spin Liquid Ground State of the \(S=1/2\) Kagome Heisenberg Model

              Condensed matter physicists have long sought a realistic two-dimensional (2D) magnetic system whose ground state is a {\it spin liquid}---a zero temperature state in which quantum fluctuations have melted away any form of magnetic order. The nearest-neighbor \(S=1/2\) Heisenberg model on the kagome lattice has seemed an ideal candidate, but in recent years some approximate numerical approaches to it have yielded instead a valence bond crystal. We have used the density matrix renormalization group to perform very accurate simulations on numerous cylinders with circumferences up to 12 lattice spacings, finding instead of the valence bond crystal a singlet-gapped spin liquid with substantially lower energy that appears to have \(Z_2\) topological order. Our results, through a combination of very low energy, short correlation lengths and corresponding small finite size effects, a new rigorous energy bound, and consistent behavior on many cylinders, provide strong evidence that the 2D ground state of this model is a gapped spin liquid.
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                Author and article information

                Contributors
                mclaassen@stanford.edu
                tpd@stanford.edu
                Journal
                Nat Commun
                Nat Commun
                Nature Communications
                Nature Publishing Group UK (London )
                2041-1723
                30 October 2017
                30 October 2017
                2017
                : 8
                : 1192
                Affiliations
                [1 ]ISNI 0000000419368956, GRID grid.168010.e, Department of Applied Physics, Stanford University, ; Stanford, CA 94305 USA
                [2 ]ISNI 0000000419368956, GRID grid.168010.e, Stanford Institute for Materials and Energy Sciences, SLAC & Stanford University, ; Stanford, CA 94025 USA
                [3 ]ISNI 0000000419368956, GRID grid.168010.e, Geballe Laboratory for Advanced Materials, Stanford University, ; Stanford, CA 94305 USA
                Author information
                http://orcid.org/0000-0002-3747-8484
                Article
                876
                10.1038/s41467-017-00876-y
                5662750
                29084937
                39005bee-3733-4994-a467-ce5107a65e5f
                © The Author(s) 2017

                Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

                History
                : 27 January 2017
                : 1 August 2017
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