Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session H3: Symmetry Protected Topological Phases |
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Sponsoring Units: DCMP Chair: dong-Ling Deng, University of Maryland Room: 262 |
Tuesday, March 14, 2017 2:30PM - 2:42PM |
H3.00001: Symmetry protected valence bond solid states and strange correlator Shintaro Takayoshi, Pierre Pujol, Akihiro Tanaka We describe symmetry-protected topological (SPT) properties of quantum antiferromagnets using an effective field theory of nonlinear sigma models with topological Berry phase terms. We mainly focus on valence-bond-solid states on a two-dimensional square lattice, which has a spatially uniform ground state when the spin quantum number $S$ is an even integer. By representing the ground state wave functional through a path integral, SPT properties appear in temporal surface term of a field theory defined in a space whose dimensionality is reduced by one. This representation allows us to conclude that the ground state can be an SPT state for $S=2\times{\rm odd}$ integer while topologically trivial for $S=2\times{\rm even}$ integer. We also show that this temporal surface term in the ground state wave functional is equivalent to strange correlator, which is proposed as an indicator of SPT phases. [Preview Abstract] |
Tuesday, March 14, 2017 2:42PM - 2:54PM |
H3.00002: Topological mirror insulators in one dimension Alexander Lau, Jeroen van den Brink, Carmine Ortix In the context of novel topological states of matter protected by crystalline symmetries, we show that the presence of mirror symmetry leads to a new class of time-reversal invariant topological insulators in one dimension. These \textit{topological mirror insulators} are characterized by a nontrivial $\mathbb{Z}_2$ topological invariant defined in terms of the partial polarization, which we show to be quantized in the presence of a 1D mirror point. Their hallmark is an odd number of electronic integer end charges at the mirror-symmetric boundaries of the system. We check our findings against spin-orbit coupled Aubry-Andr\'e-Harper models which realize this novel topological state of matter. In particular, we determine the phase diagram, calculate energy spectra, and compute the values of the end charges. We also study the effect of weak on-site disorder to demonstrate the stability of the topolgical features. Furthermore, we draw conclusions for topological states in the two-dimensional Hofstadter model with spin-orbit coupling. The presented models could be realized, for instance, with cold-atomic Fermi gases loaded in periodic optical lattices. [Preview Abstract] |
Tuesday, March 14, 2017 2:54PM - 3:06PM |
H3.00003: Effective Models for Topological Phases R. Winkler, H. Deshpande Edge states in topological insulators (TIs) disperse near one of the time-reversal invariant momenta $\Lambda_i$ with a protected degeneracy at $\Lambda_i$. Commonly TIs are distinguished from trivial insulators by the values of one or multiple topological invariants that require an analysis of the bulk band structure across the Brillouin zone. We propose effective Hamiltonians based on a Taylor expansion about $\Lambda_i$ that provide an accurate description of the protected edge states though the concept of a Brillouin zone is not part of such effective models. Graphene has served as an archetype for TIs. We show that an expansion about the graphene $M$ point faithfully describes the protected edge states for both zigzag and armchair edges in graphene ribbons. We show that the edge states are determined by a band inversion local in $k$ space reflecting the boundary conditions at the edges of the TI. This allows one to select $\Lambda_i$ for the edge states. Our findings highlight the interplay between boundary conditions in real space and the location of edge states in reciprocal space. [Preview Abstract] |
Tuesday, March 14, 2017 3:06PM - 3:18PM |
H3.00004: The anisotropic Harper-Hofstadter-Mott model: supersolid, striped superfluid, and symmetry protected topological groundstates Dario H\"ugel, Hugo U. R. Strand, Philipp Werner, Lode Pollet We derive the reciprocal cluster mean-field method to study the strongly-interacting bosonic Harper-Hofstadter-Mott model. In terms of the hopping anisotropy and the chemical potential, the system exhibits a rich groundstate phase diagram featuring band insulating, striped superfluid, and supersolid phases. At finite anisotropy we additionally observe incompressible symmetry protected topological (SPT) phases, which are analyzed by a newly introduced measure for non-trivial many-body topological properties. The SPT phases at fillings $\nu=1,3$ exhibit the same symmetries and band fillings as the integer quantum Hall effect, in analog to non-interacting fermions. We further observe a new SPT phase at $\nu=2$, which has no fermionic counterpart, and belongs to the same symmetry class as the quantum spin Hall effect due to particle-hole symmetry. Incompressible metastable states at fractional filling are also observed, indicating competing fractional quantum Hall phases. The observed SPT phases are promising candidates for realizing strongly correlated topological phases using cold atoms. [Preview Abstract] |
Tuesday, March 14, 2017 3:18PM - 3:30PM |
H3.00005: Fingerprints of bosonic symmetry protected topological state in a quantum point contact Rui-Xing Zhang, Chao-Xing Liu In this work, we study the transport through a quantum point contact for two-channel interacting helical liquids that exist at the edge of a bilayer graphene under a strong magnetic field. We identify ``smoking gun'' transport signatures to distinguish bosonic symmetry protected topological (BSPT) state from fermionic two-channel quantum spin Hall (QSH) state in this system. In particular, a novel charge insulator/spin conductor phase is found for a weak repulsive interaction in the BSPT state, while either charge insulator/spin insulator or charge conductor/spin conductor phase is expected for the two-channel QSH state. In the strong interaction limit, shot noise measurement for the BSPT state is expect to reveal charge-2e instanton tunneling, in comparison with the charge-e tunneling in the two-channel QSH phase. [Preview Abstract] |
Tuesday, March 14, 2017 3:30PM - 3:42PM |
H3.00006: Multi-scale entanglement Renormalization Ansatz and chiral topological phases Zhi Li, Roger Mong We considered the question of applying the multi-scale entanglement renormalization ansatz (MERA) to describe chiral topological phases. We rigorously proved a theorem showing the trade-off between the number of orbitals per cell (which roughly corresponds to the bond dimension) and the correlation length. An interesting corollary is that the bond dimension should grow with the height. Specifically, we established a No-Go theorem stating that we won't approach a renormalization fixed point if we restricted the bond dimension. [Preview Abstract] |
Tuesday, March 14, 2017 3:42PM - 3:54PM |
H3.00007: Classification of topological band theories with magnetic wallpaper group symmetries in 2D Meng Hua, Syed Raza, Ching-Kai Chiu, Jeffrey C. Y. Teo Topological band theories (TBD) of the tenfold Altland-Zirnbauer (AZ) classes with time reversal, particle-hole or chiral symmetries were classified. On the other hand, crystalline symmetries in two dimensions were classified by the wallpaper group (WG), or the magnetic wallpaper group (MWG), for example, in an antiferromagnetic medium. In this work, we classify gapped TBD in the presence of both non-spatial AZ symmetries as well as spatial WG/MWG symmetries. This extends the classification of topological insulators and superconductors to combine non-symmorphic, symmorphic symmetries and time reversal symmetry. [Preview Abstract] |
Tuesday, March 14, 2017 3:54PM - 4:06PM |
H3.00008: Interaction effects on two-dimensional topological crystalline superconductors Bowen Shi, Yuan-Ming Lu We classify topological crystalline superconductors (TCSCs) of free fermions on two-dimensional square and triangular lattices, and discuss how the free-fermion classification is modified by strong electronic interactions. In particular we consider the C4v and C6v point groups of square and triangular lattices, and their associated magnetic point groups. A connection between free-fermion TCSCs and symmetry-enriched topological orders is established, which allows us to understand the interacting classification. [Preview Abstract] |
Tuesday, March 14, 2017 4:06PM - 4:18PM |
H3.00009: Glide symmetry protected topological phases in interacting bosons and fermions Fuyan Lu, Bowen Shi, Yuan-Ming Lu We classify and construct glide symmetry protected topological (GSPT) phases of interacting bosons and fermions in three dimensions. We focus on the systems with U(1) charge conservation and/or time reversal symmetry. Using a stacked plane construction, we also identify the anomalous surface topological orders of these GSPT phases, one example being the hourglass fermions in three-dimensional glide-protected topological insulator. [Preview Abstract] |
Tuesday, March 14, 2017 4:18PM - 4:30PM |
H3.00010: Symmetry Protected Topological Hopf Insulator and its Generalizations Farzan Vafa, Chunxiao Liu, Cenke Xu The 10-fold way classification has provided us the prototypes of topological insulators. The usual wisdom is that even the topological insulators with symmetries beyond the 10-fold way classification can also be understood as these prototypes enriched with other symmetries. The boundary states of all these prototypes should be either gapless Dirac fermion, Weyl fermion, or Majorana fermion. One important open question is, can these prototypes represent all possible topological insulators? We study a class of $3d$ topological insulators whose topological nature is characterized by the Hopf map and its multi-band as well as $4d$ generalizations. We identify the symmetry $C'$, a generalized particle-hole symmetry that gives the Hopf insulator a $\mathbb{Z}_2$ classification. We demonstrate that the minimal model of the $3d$ Hopf insulator must have a ``Fermi ring" on its boundary, instead of a massless Dirac fermion; though the more generic multi-band version of the Hopf insulator protected by the $C'$ symmetry still has a Dirac fermion on its boundary. Similar phenomena are found for the $4d$ analogue of the Hopf insulator. We also discuss the relation between the Hopf insulator and the Weyl and Dirac semimetals, which points the direction for its experimental realization. [Preview Abstract] |
Tuesday, March 14, 2017 4:30PM - 4:42PM |
H3.00011: Symmetry-protected topological insulator and its symmetry-enriched topologically ordered boundary Juven Wang, Xiao-Gang Wen, Edward Witten We propose a mechanism for achieving symmetry-enriched topologically ordered boundaries for symmetry-protected topological states, including those of topological insulators. Several different boundary phases and their phase transitions are considered, including confined phases, deconfined phases, symmetry-breaking, gapped and gapless phases. [Preview Abstract] |
Tuesday, March 14, 2017 4:42PM - 4:54PM |
H3.00012: Topological Electromagnetic Responses of Bosonic Quantum Hall, Topological Insulator, and Chiral Semi-Metal phases in All Dimensions Matthew Lapa, Chao-Ming Jian, Peng Ye, Taylor Hughes We calculate the topological part of the electromagnetic response of Bosonic Integer Quantum Hall (BIQH) phases in odd (spacetime) dimensions, and Bosonic Topological Insulator (BTI) and Bosonic chiral semi-metal (BCSM) phases in even dimensions. To do this we use the Nonlinear Sigma Model description of bosonic symmetry-protected topological (SPT) phases and the method of gauged Wess-Zumino actions. We find the surprising result that for BIQH states in dimension $2m-1$ ($m=1,2,\dots$), the bulk response to an electromagnetic field $A_{\mu}$ is characterized by a Chern-Simons term for $A_{\mu}$ with a level quantized in integer multiples of $m!$ (factorial). We also show that BTI states (which have an extra $\mathbb{Z}_2$ symmetry) can exhibit a $\mathbb{Z}_2$ breaking Quantum Hall effect on their boundaries, with this boundary Quantum Hall effect described by a Chern-Simons term at level $\frac{m!}{2}$. We explain the factor of $m!$ using a gauge invariance argument, and we also use this argument to characterize the electromagnetic and gravitational responses of fermionic SPT phases with $U(1)$ symmetry in all odd dimensions. We then go on to consider several additional applications of our results to the study of the BTI boundary and to BCSM states in even dimensions. [Preview Abstract] |
Tuesday, March 14, 2017 4:54PM - 5:06PM |
H3.00013: Many body topological invariants in topological phases with point group symmetry Ken Shiozaki, Hassan Shapourian, Shinsei Ryu A way to detect topological phases from a given short-range entangled state is discussed. Many body topological invariants are defined as partition functions of topological quantum field theory (TQFT) on space-time manifolds, for example, real projective spaces. It is expected that by translating TQFT partition functions to the operator formalism one can get a definition of many body topological invariants made from ground state wave functions and symmetry operations. We propose that a kind of non-local operator, the "partial point group transformation", on a short-range entangled state is a unified measure to detect topologically nontrivial phases with point group symmetry. In this talk, I introduce (i) the partial rotations on (2$+$1)d chiral superconductors, and (ii) the Z16 invariant from the partial inversion on (3$+$1)d superconductors. These partial point group transformations can be analytically calculated from the boundary theory. We confirmed that analytical results from the boundary theory match with direct numerical calculations on bulk. [Preview Abstract] |
Tuesday, March 14, 2017 5:06PM - 5:18PM |
H3.00014: Surface field theories of point group symmetry protected topological phases Sheng-Jie Huang, Michael Hermele We identify various field theories which can be realized on the surface of three-dimensional point group symmetry protected topological (pgSPT) phases. There exist several parent field theories which can be realized on the surface of different kinds of three-dimensional pgSPT phases, depending on how the microscopic point group symmetry is embedded in the symmetry group of the field theory. The anomalies of the surface theories can be found by a dimensional reduction argument. We illustrate this idea by means of some examples, including topological crystalline insulators with $U(1) \times Z_{2}^{P}$ symmetry, and bosonic pgSPT phases with $C_{2v}$ symmetry. [Preview Abstract] |
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