Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session W41: Topological Order |
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Sponsoring Units: DCMP Chair: Tanmoy Das, Los Alamos National Laboratory Room: Mile High Ballroom 3C |
Thursday, March 6, 2014 2:30PM - 2:42PM |
W41.00001: The uses of Instantons for classifying Topological Phases Juven Wang, Xiao-Gang Wen A strategy of using instantons, zero modes and the index theorem for classifying topological phases is developed in this work. We argue that this approach is very powerful and can be applied to topological phases with or without a global symmetry in any (higher) dimensional spacetime. (this URL for a work summary: www.mit.edu/~juven/) [Preview Abstract] |
Thursday, March 6, 2014 2:42PM - 2:54PM |
W41.00002: Surface Theory of Topological Insulators Pak On Chan, Taylor Hughes, Shinsei Ryu, Eduardo Fradkin We discuss a hydrodynamic effective field theory description of 3+1 dimensional topological insulators. The effective field theory is a BF type topological field theory augmented with an axion (theta) term, which is obtained from the functional bosonization technique that introduces one form as well as two form gauge fields, the latter of which describes the conserved U(1) charge. We construct various kinds of non-local operators describing topological excitations in the bulk and study their algebraic properties thereof. Furthermore, we derive a hydrodynamic effective field theory for the gapless surface of 3+1 dimensional topological insulators. Such theory, which is essentially a BF-CS theory with a non-local Maxwell term, reproduces all the physical properties appeared in the bulk and is hence compatible to the bulk theory. Current-current correlation function is calculated and its transformation under modular transform is also discussed. [Preview Abstract] |
Thursday, March 6, 2014 2:54PM - 3:06PM |
W41.00003: Topological invariants and the ground state wavefunction of topological insulators Zhong Wang, Shou-Cheng Zhang We will talk about precise topological invariants defined in terms of the ground state wavefuntion. The Hall coefficients in even spatial dimensions and the magnetoelectric theta terms in odd spatial dimensions are expressed in terms of the ground state wavefunctions under generalized twisted-boundary conditions. This formulation is valid in the presence of arbitrary interaction and disorder, in particular, it is applicable to both integer and fractional topological insulators. ( arXiv:1308.4900) [Preview Abstract] |
Thursday, March 6, 2014 3:06PM - 3:18PM |
W41.00004: Topological order in correlated topological insulators Joseph Maciejko, Andreas R\"uegg, Victor Chua, Gregory A. Fiete Motivated by recent experiments on correlated transition-metal oxides, an important outstanding issue in the field of topological insulators is to understand the effect of electron-electron interactions beyond the relatively well-understood perturbative limit. Using the $Z_2$ slave-spin theory, we theoretically predict that interaction effects in a spinful Chern insulator (CI) can give rise to a novel strongly correlated topological state of matter, the CI*, which is distinct from both the weakly correlated CI and the recently studied fractional CI. In the CI* the Hall conductivity and the quasiparticle charge are integer, but the quasiparticle statistics are fractional (semionic). In a time-reversal invariant 3D topological insulator strong interactions can give rise to a novel strongly correlated topological state of matter, the TI*, that is distinct from both the weakly correlated TI and other recently proposed fractionalized phases such as the topological Mott insulator and the fractional TI. In the TI* the weak-field magnetoelectric response is quantized as in a weakly correlated TI, but the state is a symmetry-enriched topological phase, with eight degenerate ground states on the 3-torus and emergent particle and string-like excitations with nontrivial mutual statistics. [Preview Abstract] |
Thursday, March 6, 2014 3:18PM - 3:30PM |
W41.00005: The Role of Space Group Symmetries in Many Body Interacting Systems Rahul Roy The constraints placed by space group symmetries in two and three dimensions on the ground state degeneracies of a many body interacting system in the thermodynamic limit are studied. It is shown that the number of such degenerate ground states have a lower bound which depends on the details of the space group. These results may be seen as a generalization of some free fermionic band touching theorems to interacting systems and also provide guidance for the search for topological phases in interacting systems. [Preview Abstract] |
Thursday, March 6, 2014 3:30PM - 3:42PM |
W41.00006: Topological order in lattice models of strongly interacting electrons Stefanos Kourtis, Titus Neupert, Claudio Chamon, Christopher Mudry Fractional Chern insulators are a class of strongly interacting topological states of electronic matter. So far, the paradigm of fractional Chern insulators was that they appear when interacting electrons with frozen spin degree of freedom populate relatively flat topological bands, with the interaction strength being smaller than the gap to other bands. In this talk, it will be shown that this limit is adiabatically connected to the opposite one, in which the interaction strength goes to infinity, thus exceeding the gap to other bands. Electrons then become extended hard-core particles, the notion of bands becomes meaningless and the connection to Landau-level physics of the fractional quantum-Hall effect is much less obvious. We also find fractional Chern-insulator states to be extremely robust in this hardcore limit, reaching up to, or possibly beyond, the noninteracting topological phase transition. [Preview Abstract] |
Thursday, March 6, 2014 3:42PM - 3:54PM |
W41.00007: Topological non-symmorphic crystalline insulators Chaoxing Liu, Ruixing Zhang, Brian Vanleeuwen In this talk, we will describe a new class of Z2 topological insulator protected by non-symmorphic crystalline symmetry, dubbed a ``topological non-symmorphic crystalline insulator.'' We construct a concrete tight-binding model with the non-symmorphic space group pmg and confirm the topological nature of this model by directly calculating topological surface states. In analog to ``Kramers' pairs'' due to time reversal symmetry, we introduce the ``doublet pairs'' originating from non-symmorphic symmetry to define the corresponding Z2 topological invariant for this phase. Based on the projective representation theory, we extend our discussion to other non-symmorphic space groups that allows to host topological non-symmorphic crystalline insulators. [Preview Abstract] |
Thursday, March 6, 2014 3:54PM - 4:06PM |
W41.00008: Topology of Symmetry Protected Gapless Modes in Insulators and Superconductors Masatoshi Sato There has been much recent interest in topological insulators and superconductors. Whereas the recent developments are based on topological classifications using the general symmetries of time-reversal and charge conjugation, systems often have other symmetries specific to their structures such as point group symmetries . Interestingly, additional symmetries can give rise to a nontrivial topology of the bulk wave functions and gapless states on the boundaries. Although these specific symmetries are microscopically sensitive to a small disturbance, recent studies of topological crystalline insulators have shown that if the symmetries are preserved on average, then the existence of gapless boundary states is rather robust. Therefore, it is expected that the symmetry-protected topological phase can provide an alternative platform of topological materials. Here we argue symmetry protected gapless modes in topological insulators and superconductors. We consider topological objects described by non-interacting Bloch and Bogoliubov de Gennes Hamiltonians that support an additional spatial symmetry, besides any of ten classes of symmetries defined by time-reversal and charge conjugation. Varoius symmetry protected gapless modes will be discussed in a uniform manner. [Preview Abstract] |
Thursday, March 6, 2014 4:06PM - 4:18PM |
W41.00009: (3 + 1)-dimensional BF theory from a tight-binding model of interacting spinless fermions Mauro Cirio, Giandomenico Palumbo, Jiannis K. Pachos Currently, there is much interest in discovering analytically tractable (3 + 1)-dimensional models that describe interacting fermions with emerging topological properties. Towards that end we present a three-dimensional tight-binding model of spinless interacting fermions that reproduces, in the low energy limit, the (3 + 1)-dimensional Abelian BF topological theory. We first consider the non- interacting case. By employing a mechanism equivalent to the Haldane's Chern insulator we can turn the model into a (3 + 1)-dimensional chiral topological insulator. We then isolate energetically one of the two Fermi points of the lattice model. In the presence of fermionic interactions we can map the system to a generalised version of the (3 + 1)-dimensional Thirring model with low energy behaviour that is faithfully described by the BF theory. This approach directly establishes the presence of (2 + 1)-dimensional BF theory at the boundary of the lattice and it provides an observable for the topological order of the model through fermionic density measurements. [Preview Abstract] |
Thursday, March 6, 2014 4:18PM - 4:30PM |
W41.00010: Hopf insulators and their topologically protected surface states Sheng-Tao Wang, Dong-Ling Deng, Chao Shen, Lu-Ming Duan Three-dimensional (3D) topological insulators in general need to be protected by certain kinds of symmetries other than the presumed $U(1)$ charge conservation. A peculiar exception is the Hopf insulators which are 3D topological insulators characterized by an integer Hopf index. To demonstrate the existence and physical relevance of the Hopf insulators, we construct a class of tight-binding model Hamiltonians which realize all kinds of Hopf insulators with arbitrary integer Hopf index. These Hopf insulator phases have topologically protected surface states and we numerically demonstrate the robustness of these topologically protected states under general random perturbations without any symmetry other than the $U(1)$ charge conservation that is implicit in all kinds of topological insulators. [Preview Abstract] |
Thursday, March 6, 2014 4:30PM - 4:42PM |
W41.00011: 3D topological states - layer construction, surface topological order and surface symmetry Chao-Ming Jian, Xiao-Liang Qi 3D topological states can be constructed by stacking layers of 2D topological states and introducing coupling between them. The coupling between layers can effectively drive condensation of anyons in the stacked 2D systems. In the talk, we shall discuss a general layer construction of 3D topological states using the anyon condensation technique for Abelian topologically ordered states in each layer. For the finite size 3D system constructed this way, the emergent surface topological order (including that at the top/bottom and side surfaces) can also be described using the same technique. Extra symmetries can be cooperated into this construction to obtain 3D SPT phases with the symmetries realized in an anomalous way on the gapped surface states. We propose a general criterion to distinguish the symmetry operations that can be realized in a purely two-dimensional topological state from those that can only be realized anomalously on the surface of a higher dimensional state. [Preview Abstract] |
Thursday, March 6, 2014 4:42PM - 4:54PM |
W41.00012: Combined topological and Landau order from strong correlations in Chern bands Maria Daghofer, Stefanos Kourtis In recent years, topologically nontrivial and nearly dispersionless bands have attracted attention as hosts for states analogous to fractional quantum-Hall states, but without a magnetic field. Indeed, such fractional Chern insulators were found and connections to fractional quantum-Hall states in Landau levels were established. We discuss here aspects where fractional Chern insulators differ from Landau levels. In particular, we present a class of states where both topological order and symmetry breaking arise spontaneously: the states show both fractional Hall conductivity and charge order. This coexistence of topological and conventional Landau order relies on the geometric frustration of the underlying lattice and consequently goes qualitatively beyond physics found in continuous Landau levels with their weak lattice. [1] S. Kourtis, J. W. F. Venderbos and M. Daghofer, PRB {\bf 86}, 235118 (2012);S. Kourtis and M. Daghofer, arXiv:1305.6948. [Preview Abstract] |
Thursday, March 6, 2014 4:54PM - 5:06PM |
W41.00013: Symmetry-protected topological phases and orbifolds: Generalized Laughlin's argument Olabode Sule, Xiao Chen, Shinsei Ryu We consider non-chiral symmetry-protected topological phases of matter in two spatial dimensions protected by a discrete symmetry such as $Z_K$ or $Z_K \times Z_K $ symmetry. We argue that modular invariance/noninvariance of the partition function of the one-dimensional edge theory can be used to diagnose whether, by adding a suitable potential, the edge theory can be gapped or not without breaking the symmetry. By taking bosonic phases described by Chern-Simons K-matrix theories and fermionic phases relevant to topological superconductors as an example, we demonstrate explicitly that when the modular invariance is achieved, we can construct an interaction potential that is consistent with the symmetry and can completely gap out the edge. [Preview Abstract] |
Thursday, March 6, 2014 5:06PM - 5:18PM |
W41.00014: Interactions and Bosonization for Topological Insulators David Schmeltzer The time reversal symmetry $ T^2=-1$ imposes restriction on the eigenvectors when transported in the Brillouin Zone, resulting in momentum dependent vector potentials which is sensitive to obstructions. The study of electron-electron interactions is done using the Hubbard Stratonovici field which are treated similarly to external electromagnetic fields. The integration of the fermion field is done using the gauge fields in momentum space, which obey special gauge imposed by the eigenvectors. The effect of the interaction is similar to the magnetoelectric response, due to the Hubbard Stratoonovici field we find that the magnetoelectric response is controlled by a fractional topological angle. Using the time reversal time reversal symmetry $ T^2=-1$ we construct the Bosonization for one and two dimensions and use the formulation to study interactions. [Preview Abstract] |
Thursday, March 6, 2014 5:18PM - 5:30PM |
W41.00015: ABSTRACT WITHDRAWN |
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