Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session K20: Topological Phases: Theory |
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Sponsoring Units: DCMP Chair: Wei Cheng Lee, SUNY Binghamton Room: 280 |
Wednesday, March 15, 2017 8:00AM - 8:12AM |
K20.00001: Floquet topological phases with symmetry in all dimensions Rahul Roy, Fenner Harper Dynamical systems can host a number of remarkable symmetry-protected phases that are qualitatively different from their static analogs. We consider the phase space of symmetry-respecting unitary evolutions in detail and identify several distinct classes of evolution that host novel dynamical order. Using ideas from group cohomology, we construct a set of interacting drives that generate Floquet symmetry-protected topological order for each nontrivial cohomology class in every dimension. We go on to discuss symmetry-protected drives that lie outside of the cohomology construction and drives that are protected by antiunitary symmetries. The notions of order we define may be applied to general time-dependent systems, including many-body localized phases or time crystals. [Preview Abstract] |
Wednesday, March 15, 2017 8:12AM - 8:24AM |
K20.00002: Floquet topological order in interacting systems of bosons and fermions Fenner Harper, Rahul Roy Periodically driven noninteracting systems may exhibit anomalous chiral edge modes, despite hosting bands with trivial topology. We show that these drives have surprising many-body analogs, applicable to generic systems of bosons, fermions or spins, which demonstrate anomalous transport of charge or information at the edge. We characterize systems of this kind by studying their edge behavior, defining a notion of dynamical topological order that may be applied to general time-dependent systems, including many-body localized phases or time crystals. We go on to discuss symmetry-protected generalizations of these drives. [Preview Abstract] |
Wednesday, March 15, 2017 8:24AM - 8:36AM |
K20.00003: Topological edge and dislocation modes in 3D Floquet systems Dominic Reiss, Fenner Harper, Rahul Roy Anomalous chiral edge modes are known to arise in both interacting and non-interacting periodically driven systems in two dimensions. We study three dimensional Floquet systems with translational symmetry which exhibit anomalous edge modes and show that dislocations in these systems can bind topological modes. We attempt a classification of such anomalous 3D drives and study a bulk-boundary correspondence in these systems. [Preview Abstract] |
Wednesday, March 15, 2017 8:36AM - 8:48AM |
K20.00004: Partial symmetry transformation to compute topological invariants of interacting fermionic SPTs Hassan Shapourian, Ken Shiozaki, Shinsei Ryu We present an approach to define and compute topological invariants of interacting fermionic symmetry-protected topological (SPT) phases, protected by an orientation-reversing symmetry, such as time-reversal or reflection symmetry. The topological invariants are given by partition functions on unoriented spacetime manifolds which as we show, can be computed for a given ground state wave function by considering a non-local operation, ``partial'' time-reversal or reflection. As an application of our scheme, we study the $\mathbb{Z}_8$ and $\mathbb{Z}_{16}$ classification of topological superconductors in one and three dimensions. Finally, we make a bridge between partial time-reversal transformation and the entanglement negativity in fermionic systems. [Preview Abstract] |
Wednesday, March 15, 2017 8:48AM - 9:00AM |
K20.00005: Exactly Solvable Models for Symmetry-Enriched Topological Phases Yang Qi, Meng Cheng, Zheng-Cheng Gu, Shenghan Jiang We construct fixed-point wave functions and exactly solvable commuting-projector Hamiltonians for a large class of bosonic symmetry-enriched topological (SET) phases, based on the concept of equivalent classes of symmetric local unitary transformations. We argue that for onsite unitary symmetries, our construction realizes all SETs free of anomaly, as long as the underlying topological order itself can be realized with a commuting-projector Hamiltonian. We further extend the construction to antiunitary symmetries (e.g. time-reversal symmetry), mirror-reflection symmetries, and to anomalous SETs on the surface of three-dimensional symmetry-protected topological phases. Mathematically, our construction naturally leads to a generalization of group extensions of unitary fusion category theory. [Preview Abstract] |
Wednesday, March 15, 2017 9:00AM - 9:12AM |
K20.00006: Gapless Topological Order, Gravity, and Black Holes Alexander Rasmussen, Adam Jermyn, Gil Refael In recent years, there has been an intense theoretical effort to understand the low-energy properties of quantum mechanical systems where the emergent behavior has no classical analog. Systems with a bulk energy gap can exhibit topological order characterized by locally indistinguishable of states and degeneracy on manifolds with nonzero genus. Gapless systems, on the other hand, can arise out of systems without spontaneous symmetry breaking via emergent gauge structure. Seemingly unrelated, recent work by Strominger and others has related Weinberg's soft boson theorems to a new set of symmetries in both QED and linearized gravity. In this talk, we make an explicit connection between these new symmetries and the peculiar type of topological order present in the gapless pyrochlore U(1) spin liquid. This connection allows us to resolve the long-standing 1/L degeneracy splitting problem, and provides some insight into current issues with black holes. [Preview Abstract] |
Wednesday, March 15, 2017 9:12AM - 9:24AM |
K20.00007: Topological quantum paramagnet in a quantum spin ladder Darshan Joshi, Andreas Schnyder Recently, it has been shown that analogs of quantum Hall systems could be realized in quantum magnets. Most of these works have focused on the symmetry broken phases in magnetic systems. In this work, we consider the dimer-quantum-paramagnetic phase of a S$=1/2$ quantum spin ladder, which does not break any symmetry of the parent Hamiltonian. We show that in the presence of Dzyaloshinskii-Moriya interaction and external magnetic field the paramagnetic phase is actually split into a topologically trivial and a topologically non-trivial phase. We calculate the winding number and the end-states in this topologically non-trivial phase. The topological aspect is a consequence of the reflection symmetries present in the model and other models with similar properties may also realize the same physics. [Preview Abstract] |
Wednesday, March 15, 2017 9:24AM - 9:36AM |
K20.00008: Density Matrix Embedding Theory for Symmetry Protected Topological Systems Ushnish Ray, Garnet Chan Density Matrix Embedding Theory (DMET) presents a novel approach in capturing the physics of strongly correlated systems. It essentially describes finite fragments in the presence of environment while explicitly allowing quantum entanglement between both. DMET has been remarkably successful in studying systems ranging from molecules to solids and the paradigmatic Hubbard model. In this talk, we will present extensions of DMET to systems that are allowed to break SU(2) spin symmetry as well as U(1) particle number symmetry. This will enable us to study a range of broken symmetry phases such as topological superconductivity and, more interestingly, their interplay with strong correlations. [Preview Abstract] |
Wednesday, March 15, 2017 9:36AM - 9:48AM |
K20.00009: An one-dimensional spin-$\frac{1}{2}$ model realizing the time-reversal symmetry protected phase Wenjie Ji, Xiao-Gang Wen Symmetry protected topological (SPT) phases are one kind of phases beyond the classification described by Landau symmetry breaking paradigm. Topological insulators and spin-1 AKLT model are all familiar examples of SPT phases. Towards looking for more realistic SPT models, we consider the simplest bosonic case, i.e., one dimensional spin-$\frac{1}{2}$ model, with one of the smallest symmetry group, i.e., time-reversal symmetry. We present such a SPT model, called YZY model, of which the time-reversal symmetry operation $T$, has the property $T^2=1$. We show that it has four gapless edge modes realizing the projective representation of the symmetry and how the SPT phase is robust under any perturbation with respect to time-reversal symmetry alone. Moreover, the phase diagram of the hybrid model with both YZY and Heisenberg interaction is identified and analyzed both analytically by conformal field theory and numerically by tensor-network renormalization, giving an example of the phase transition between SPT phase and other kind of phases such trivial symmetric phase and gapless phase. [Preview Abstract] |
Wednesday, March 15, 2017 9:48AM - 10:00AM |
K20.00010: Weyl-Kondo semimetals in a non-centrosymmetric three-dimensional lattice Sarah Elaine Grefe, Hsin-Hua Lai, Silke Paschen, Qimiao Si The spin-orbit coupling and electron correlations of heavy fermion systems make them a rich playground for a variety of quantum phases, including those with topological characteristics. Motivated by the recent finding of a Dirac-Kondo semimetal phase in a two-dimensional model [1], we study the Anderson lattice model in an inversion-symmetry-breaking lattice in three dimensions. Both the weak coupling and strong coupling limits are analyzed. In both parameter regimes, we identify a Weyl-Kondo semimetal (WKSM) phase. In the strong coupling regime, the quasiparticles near the Weyl nodes have velocities that are strongly reduced by the interaction effects, corresponding to a narrow band, which will make them readily amenable to studies by thermodynamic and thermoelectric means. We also determine the surface states of the WKSM phase, and demonstrate how they manifest the correlation effects. [1] X.-Y. Feng, H. Zhong, J. Dai, Q. Si, ``Dirac-Kondo semimetals and topological Kondo insulators in the dilute carrier limit,'' arXiv:1605.02380 [Preview Abstract] |
Wednesday, March 15, 2017 10:00AM - 10:12AM |
K20.00011: A bilayer Double Semion Model with Symmetry-Enriched Topological Order Laura Ortiz, Miguel Angel Martin-Delgado We construct a new model of two-dimensional quantum spin systems that combines intrinsic topological orders and a global symmetry called flavour symmetry. It is referred as the bilayer Doubled Semion model (bDS) and is an instance of symmetry-enriched topological order. A honeycomb bilayer lattice is introduced to combine a Double Semion Topolgical Order with a global spin-flavour symmetry to get the fractionalization of its quasiparticles. The bDS model exhibits non-trival braiding self-statistics of excitations and its dual model constitutes a Symmetry-Protected Topological Order with novel edge states. This dual model gives rise to a bilayer Non-Trivial Paramagnet that is invariant under the flavour symmetry and the well-known spin flip symmetry. [Preview Abstract] |
Wednesday, March 15, 2017 10:12AM - 10:24AM |
K20.00012: Symmetry enriched string-nets: Exactly solvable models for SET phases Lukasz Fidkowski, Chris Heinrich, Fiona Burnell, Michael Levin We construct exactly solvable models for a wide class of symmetry enriched topological (SET) phases. Our construction applies to 2D bosonic SET phases with finite unitary onsite symmetry group G and we conjecture that our models realize every phase in this class that can be described by a commuting projector Hamiltonian. In particular, our construction realizes onsite the ${\mathbb Z}_2$ exchange symmetry of the charge and flux excitations in a model with toric code topological order. More generally, our construction makes use of a correspondence between so-called G-extensions of a fusion category $C$ and the braided G-crossed extensions of its quantum double. [Preview Abstract] |
Wednesday, March 15, 2017 10:24AM - 10:36AM |
K20.00013: Continuum models for the quantum Hall effect in the absence of Landau levels David Bauer, Fenner Harper, Rahul Roy We study a family of topologically nontrivial Hamiltonians in two dimensions distinct from both Chern insulator and Landau level models to elucidate the role of single-particle bands in the formation of quantum Hall states. We use reciprocal space geometry to quantify deviations of these bands from Landau level behavior and and draw connections with other geometric properties of the bands, including the Hall viscosity. We predict a range of experimental parameters in two-dimensional lattice systems for which quantum Hall states are stable yet non-Landau level behavior may be observed. [Preview Abstract] |
Wednesday, March 15, 2017 10:36AM - 10:48AM |
K20.00014: A Route to Dirac Liquid Theory: A Fermi Liquid Description for Dirac Materials Matthew Gochan, Kevin Bedell Since the pioneering work developed by L.V. Landau sixty years ago, Fermi Liquid Theory has seen great success in describing interacting Fermi systems. While much interest has been generated over the study of non-Fermi Liquid systems, Fermi Liquid theory serves as a formidable model for many systems and offers a rich amount of of results and insight. The recent classification of Dirac Materials, and the lack of a unifying theoretical framework for them, has motivated our study. Dirac materials are a versatile class of materials in which an abundance of unique physical phenomena can be observed. Such materials are found in all dimensions, with the shared property that their low-energy fermionic excitations behave as massless Dirac fermions and are therefore governed by the Dirac equation. The most popular Dirac material, graphene, is the focus of this work. We present our Fermi Liquid description of Graphene. We find many interesting results, specifically in the transport and dynamics of the system. Additionally, we expand on previous work regarding the Virial Theorem and its impact on the Fermi Liquid parameters in graphene. Finally, we remark on viscoelasticity of Dirac Materials and other unusual results that are consequences of AdS-CFT. [Preview Abstract] |
Wednesday, March 15, 2017 10:48AM - 11:00AM |
K20.00015: Diagnosis of Interaction-driven Topological Phase via Exact Diagonalization Chen Fang, Hanqing Wu, Yuanyao He, Zi Yang Meng, Zhongyi Lu We propose a general scheme for diagnosing interaction-driven topological phases in weak interaction regime using exact diagonalization (ED). The scheme comprises the analysis of eigenvalues of the point-group operators for the many-body eigenstates and the correlation functions for physical observables to extract the symmetries of the order parameters and the topological numbers of the underlying ground states at the thermodynamic limit from a relatively small size system afforded by ED. As a concrete example, we investigate the interaction effects on the half-filled spinless fermions on the checkerboard lattice with a quadratic band crossing point. Numerical results support the existence of a spontaneous quantum anomalous Hall phase purely driven by a nearest-neighbor weak repulsive interaction, separated from a nematic Mott insulator phase at strong repulsive interaction by a first-order phase transition. [Preview Abstract] |
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