Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session J18: Two Dimensional Topological Insulators: Theory |
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Sponsoring Units: DCMP Chair: Byounghak Lee, Texas State University Room: 320 |
Tuesday, March 19, 2013 2:30PM - 2:42PM |
J18.00001: Correlated effects in topological phase transitions Hsiang-Hsuan Hung, Lei Wang, Zheng-Cheng Gu, Gregory A. Fiete Correlation effects in topological phases have been a central topic of interest, yet elusive in experiment. In this talk, we present the results of a numerical study beyond mean-field theory of a phase transition between a two-dimensional Z2 topological insulator phase and a trivial insulator that is driven by correlation effects. In addition to the Z2 invariant, we find that certain features of the single-particle Green's functions (simpler to compute than the full Z2 invariant) carry important information that are strongly indicative of a non-trivial Z2 topological character. We observe that the fluctuations originating from correlations tend to move the topological phase transition boundary to larger values of interactions. [Preview Abstract] |
Tuesday, March 19, 2013 2:42PM - 2:54PM |
J18.00002: Topological insulators of interacting bosons in two dimensions: Classification, effective field theory and microscopic construction Yuan-Ming Lu, Ashvin Vishwanath While topological insulators of non-interacting fermions have been extensively studied, we know very little about topological insulators of bosons, whose realization necessitates strong interaction. In this work we apply Chern-Simons effective theory to classify and characterize interacting bosonic topological insulators in two spatial dimensions. These topological phases have a unique ground state on any closed manifold and no fractional excitations: yet they feature gapless edge states which are often protected by a symmetry. Examples include a bosonic analog of chiral superconductors, bosonic integer quantum Hall states (with Hall conductance quantized to even integers) and bosonic analog of the quantum spin Hall state. We show that these topological phases can be constructed in various ways: such as in arrays of coupled one-dimensional quantum wires. Our formulation also naturally applies to topological insulators of two-dimensional interacting fermions. [Preview Abstract] |
Tuesday, March 19, 2013 2:54PM - 3:06PM |
J18.00003: Topological parity invariant in interacting two-dimensional systems from quantum Monte Carlo Thomas C. Lang, Victor Gurarie, Andrew M. Essin, Stefan Wessel We report results on calculating the parity invariant from Green's functions in quantum Monte Carlo simulations of strongly interacting systems. The topological invariant is used to study the trivial- to topological-insulator transitions in the Kane-Mele-Hubbard model with an explicit bond dimerization. We explore accessibility and behavior of this invariant within quantum Monte Carlo simulations. [Preview Abstract] |
Tuesday, March 19, 2013 3:06PM - 3:18PM |
J18.00004: Rotating spin density wave and inverse spin pumping in quantum spin Hall edges Qinglei Meng, Taylor Hughes, Smitha Vishveshwara We explore interaction effects in quantum spin Hall (QSH) edges in the presence of a finite bias voltage. Using bosonization techniques, we show that repulsive interactions give rise to a spin density wave phase in which the transverse magnetization shows spatial rotation. The effect of a finite bias voltage on this phase is to give the rotation a temporal variation. Using spin transfer torque methods, we show that the system can induce an inverse spin pumping effect in which the magnetic moment of a ferromagnet placed in its proximity can be made to rotate. We demonstrate that this device is equivalent to an electric inductor and in principle can also emit microwave radiation, thus providing a unique ways of probing QSH properties. [Preview Abstract] |
Tuesday, March 19, 2013 3:18PM - 3:30PM |
J18.00005: Theory of correlated topological insulators with broken axial spin symmetry Stephan Rachel, Johannes Reuther, Ronny Thomale The two-dimensional Hubbard model defined for topological band structures exhibiting a quantum spin Hall effect poses fundamental challenges in terms of phenomenological characterization and microscopic classification. We consider weak, moderate, and strong interactions and argue that the resulting phase diagrams depend on the microscopic details of the spin orbit interactions which give rise to the non-trivial topology. In particular, it turns out that there is a crucial difference between models with broken and with conserved axial spin symmetry. These results suggest that there is a general framework for correlated 2D topological insulators with broken axial spin symmetry. [Preview Abstract] |
Tuesday, March 19, 2013 3:30PM - 3:42PM |
J18.00006: ABSTRACT WITHDRAWN |
Tuesday, March 19, 2013 3:42PM - 3:54PM |
J18.00007: Band geometry of fractional topological insulators Rahul Roy Recent numerical simulations of flat band models with interactions which show clear evidence of fractionalized topological phases in the absence of a net magnetic field have generated a great deal of interest. We provide an explanation for these observations by showing that the physics of these systems is the same as that of conventional fractional quantum Hall phases in the lowest Landau level under certain ideal conditions which can be specified in terms of the Berry curvature and the Fubini study metric of the topological band. In particular, we show that when these ideal conditions hold, the density operators projected to the topological band obey the celebrated $W_{\infty}$ algebra. Our approach provides a quantitative way of testing the suitability of topological bands for hosting fractionalized phases. [Preview Abstract] |
Tuesday, March 19, 2013 3:54PM - 4:06PM |
J18.00008: An effective theory of two-dimensional fractional topological insulators Predrag Nikolic A generic spin-orbit coupling in 2D electron systems can be represented by an SU(2) gauge field with a non-trivial SU(2) flux. This makes it possible to stabilize novel non-Abelian incompressible quantum liquids by appropriate interactions (perhaps useful in quantum computing). We will discuss a generalization of the Chern-Simons Lagrangian to an arbitrary SU(N) symmetry group that describes such liquids. This effective field theory contains a Landau-Ginzburg part, which identifies the low energy fluctuations near any putative second-order quantum phase transition between conventional phases. Whenever an incompressible quantum liquid intervenes in such a phase transition, the fractional statistics of its quasiparticles is governed by the topological term of this theory and determined by the low energy dynamics. Commuting external gauge fields reduce the topological term to a Chern-Simons or BF form appropriate for fractional quantum (spin) Hall states, but the generic non-commuting gauge fields are expected to yield new classifiable topological orders without a quantum Hall analogue. We will discuss the possible non-Abelian fractional states in topological insulator quantum wells shaped by the Rashba spin-orbit coupling. [Preview Abstract] |
Tuesday, March 19, 2013 4:06PM - 4:18PM |
J18.00009: Exactly soluble lattice models for abelian topological phases Chien-Hung Lin, Michael Levin We construct exactly soluble bosonic lattice models that realize a large class of abelian topological phases. These models are a generalization of the ``string-net'' models of Ref. [1], but unlike the original construction, we find that our models can realize phases with broken time reversal symmetry. We analyze the braiding statistics of the quasiparticle excitations and show that they are described by nonchiral $U(1) \times U(1) \times \cdots \times U(1)$ Chern-Simons theories(i.e. equal numbers of left and right moving edge modes).\\[4pt] [1] M. Levin and X.-G. Wen, Phys. Rev. B 71, 045110 (2005) [Preview Abstract] |
Tuesday, March 19, 2013 4:18PM - 4:30PM |
J18.00010: Topological Phases in gapped edges of fractionalized systems Frank Pollmann, Johannes Motruk, Erez Berg, Ari Turner We present an extension of the classification scheme for topological phases in interacting one-dimensional fermionic systems to parafermionic chains. We find that the parafermions support both topological as well as symmetry broken phases in which the parafermions condense. In a series of recent works an experimental way of creating parafermions had been proposed: they can arise on the edge of a two-dimensional fractional topological insulator when coupled to superconducting and ferromagnetic domains. The low-energy edge degrees of freedom are described by a chain of coupled parafermions. As a concrete example of our classification we consider the $\nu=1/3$ fractional topological insulator for which we calculate the phase diagram and study the entanglement spectra. We furthermore discuss a concrete physical realization which allows us to tune between the different topological phases. [Preview Abstract] |
Tuesday, March 19, 2013 4:30PM - 4:42PM |
J18.00011: Quantum Geometry of the ``Fuzzy-Lattice'' Hubbard Model and the Fractional Chern Insulator Sagar Vijay, F.D.M. Haldane Recent studies of interacting particles on tight-binding lattices with broken time-reversal symmetry reveal ``zero-field'' fractional quantum Hall (FQH) phases (fractional Chern insulators, FCI). In a partially-filled Landau level, the non-commutative guiding-centers are the residual degrees of freedom, requiring a ``quantum geometry'' Hilbert-space description (a real-space Schr\"odinger description can only apply in the ``classical geometry'' of unprojected coordinates). The continuum description does not apply on a lattice, where we describe emergence of the FCI from a non-commutative quantum lattice geometry. We define a ``fuzzy lattice'' by projecting a one-particle bandstructure (with more than one orbital per unit cell) into a single band, and then renormalize the orbital on each site to unit weight. The resulting overcomplete basis of local states is analogous to a basis of more than one coherent state per flux quantum in a Landau level. The overlap matrix characterizes ``quantum geometry'' on the ``fuzzy lattice'', defining a ``quantum distance'' measure and Berry fluxes through elementary lattice triangles. We study quantum geometry at transitions between topologically-distinct instances of a fuzzy lattice, as well as $N$-body states with local Hubbard interactions. [Preview Abstract] |
Tuesday, March 19, 2013 4:42PM - 4:54PM |
J18.00012: Series of Abelian and Non-Abelian States in C$>$1 Fractional Chern Insulators Antoine Sterdyniak, C\'ecile Repellin, Bogdan Bernevig, Nicolas Regnault We report the observation of a new series of abelian and non-abelian topological states in fractional Chern insulators (FCI). The states appear at bosonic filling nu= k/(C+1) (k, C integers) in a wide variety of lattice models, in fractionally filled bands of Chern numbers C $\geq$ 1 subject to on-site Hubbard interactions. We show strong evidence that the $k=1$ series is abelian while the k $>$ 1 series is non-abelian. The energy spectrum at both ground-state filling and upon the addition of quasiholes shows a low-lying manifold of states whose total degeneracy and counting matches, at the appropriate size, that of the Fractional Quantum Hall (FQH) SU(C) (color) singlet k-clustered states (including Halperin, non-abelian spin singlet(NASS) states and their generalizations). The ground-state momenta are correctly predicted by the FQH to FCI lattice folding. However, the counting of FCI states also matches that of a spinless FQH series, preventing a clear identification just from the energy spectrum. The entanglement spectrum lends support to the identification of our states as SU(C) color-singlets but offers new anomalies in the counting for C $>$ 1, possibly related to dislocations that call for the development of new counting rules of these topological states. [Preview Abstract] |
Tuesday, March 19, 2013 4:54PM - 5:06PM |
J18.00013: Rydberg-Atom Quantum Simulation and Chern Number Characterization of a Topological Mott Insulator Alexandre Dauphin, Markus Mueller, Miguel-Angel Martin-Delgado In this talk we consider a system of spinless fermions with nearest and next-to-nearest neighbor repulsive Hubbard interactions on a honeycomb lattice within the mean-field treatment, and propose and analyze a realistic scheme for analog quantum simulation of this model with cold atoms in a two-dimensional hexagonal optical lattice. Besides a semi-metallic and a charge-density-wave ordered phase, the system exhibits a quantum anomalous Hall phase, which is generated dynamically, i.e. purely as a result of the repulsive fermionic interactions and in the absence of any external gauge fields. We establish the topological nature of this dynamically created Mott insulating phase by the numerical calculation of a Chern number, and study the possibility of coexistence of this phase with the other phases characterized by local order parameters. Based on the knowledge of the mean-field phase diagram, we then discuss in detail how the interacting Hamiltonian can be engineered effective ly by state-of-the-art experimental techniques for laser-dressing of cold fermionic ground-state atoms with electronically excited Rydberg states that exhibit strong dipolar interactions.\\[4pt] [1] A. Dauphin, M. Mueller, and M. A. Martin-Delgado, arXiv:1207.6373. Submitted to PRA and accepted on Sep 26, 2012. [Preview Abstract] |
Tuesday, March 19, 2013 5:06PM - 5:18PM |
J18.00014: Spin-orbit interactions in a helical Luttinger liquid with a Kondo impurity Erik Eriksson We study the transport properties of a helical Luttinger liquid with a Kondo impurity and spin-orbit interactions. Such a system, which may be realized at the edge of a quantum spin Hall insulator with a gate-induced electric field, provides a mechanism to electrically control the conductance. A Rashba spin-orbit interaction may even change the nature of the Kondo screening [Eriksson et al., Phys. Rev. B 86, 161103(R) (2012)]. Considering other types of spin-orbit interactions, together with an extended non-equilibrium analysis, we further improve the understanding of these phenomena. [Preview Abstract] |
Tuesday, March 19, 2013 5:18PM - 5:30PM |
J18.00015: Manipulating Majorana Fermions in Quantum Nanowires with Broken Inversion Symmetry Alejandro M. Lobos, Xiong-Jun Liu We study a Majorana-carrying quantum wire, driven into a trivial phase by breaking the spatial inversion symmetry with a tilted external magnetic field. Interestingly, we predict that a supercurrent applied in the proximate superconductor is able to restore the topological phase and therefore the Majorana end-states. Using Abelian bosonization, we further confirm this result in the presence of electron-electron interactions and show an insightful connection of this phenomenon to the physics of a one-dimensional doped Mott-insulator. The present results have important applications in e.g., realizing a supercurrent assisted braiding of Majorana fermions, which proves highly useful in topological quantum computation with realistic Majorana networks. [Preview Abstract] |
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