Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session J54: Bulk-Boundary Correspondence and Classification of Topological Phases |
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Sponsoring Units: DCMP Room: Mile High Ballroom 2A |
Tuesday, March 3, 2020 2:30PM - 2:42PM |
J54.00001: Realizing the bulk-boundary correspondence for anomalous symmetry-enriched topological phases Daniel Bulmash, Maissam Barkeshli We construct models of anomalous 2+1D symmetry-enriched topological phases (SETs) on the surfaces of 3+1D symmetry-protected topological phases, providing an explicit realization of the bulk-boundary correspondence for SETs. Our construction takes as input the symmetry fractionalization data and does not require a priori knowledge of the SET’s anomaly. Our method works for both non-permuting and anyon-permuting symmetry actions on both Abelian and non-Abelian topological orders. We discuss the extraction of the absolute anomaly using our construction. |
Tuesday, March 3, 2020 2:42PM - 2:54PM |
J54.00002: Bulk-boundary correspondence for (2+1)D symmetry protected topological phases Kyle Kawagoe, Michael Levin A universal property of symmetry protected topological (SPT) phases is that they have low energy boundary modes that are protected under the symmetry. This fact inspires an important problem in the theory of SPT phases: How does one identify a bulk SPT phase given a low energy theory of its boundary? This question is particularly challenging in the case of interacting SPT phases where band theory approaches are inapplicable. In this talk, we present a general method for solving this problem in the case of (2+1)D interacting bosonic systems with internal (non-spatial) symmetries. |
Tuesday, March 3, 2020 2:54PM - 3:06PM |
J54.00003: Correlated bulk-boundary correspondence of the higher-order topological insulator Koji Kudo, Tsuneya Yoshida, Yasuhiro Hatsugai In this talk, we propose a novel topological state which we call “higher-order topological Mott insulator” (HOTMI) [1]. It gives a distinct bulk-boundary correspondence from a conventional higher-order topological insulator; d-dimensional bulk topology of the HOTMI predicts the emergence of gapless states not in charge excitations but in spin excitations around (d−n)-dimensional boundaries with n = 2, ..., d. We numerically demonstrate that the Hubbard model on the kagome lattice gives the 2nd-order HOTMI states for d = 2. Specifically, the corner-Mott states appearing in the system under the open boundary condition, which is gapless only in the spin excitations, are predicted by the Z_{3} spin Berry phase calculated in the bulk system. |
Tuesday, March 3, 2020 3:06PM - 3:18PM |
J54.00004: Anomaly and symmetry fractionalization of mirror-symmetric fermionic topological orders Binbin Mao, Chenjie Wang We study symmetry fractionalization and quantum anomaly in general 2D fermionic topological orders with the mirror reflection symmetry. A set of constraints on mirror fractionalization and an explicit anomaly indicator formula are derived. Our derivation is based on the recently developed folding approach, which was originally proposed in bosonic topological orders. The anomalous mirror-symmetric topological orders can only live on the surface of 3D topological crystalline superconductors, and we establish a direct bulk-boundary correspondence. |
Tuesday, March 3, 2020 3:18PM - 3:30PM |
J54.00005: Computing the Classification of Fermionic Symmetry-Protected Topological States Yunqing Ouyang, Qing-Rui Wang, Zhengcheng Gu, Yang Qi The bosonic symmetry protected topological (SPT) states are classified by the cohomology groups of the symmetry group. However, for interacting fermionic systems, the classification is much more complicated. It was untill very recent that a breakthrough was maded on the classification and construction of fermionic SPT states based on the concept of equivalence class under finite-depth symmetric fermionic local transformations. However, though layers of data for classification and construction can be obtained theoretically, the formalism based on the bar resolution of symmetry groups (also known as the inhomogeneous cochains) makes it impossible for realistic computation due to high computational costs. To solve these problems, we first design reduced resolutions for general groups by group extension, then we apply the chain maps between the bar resolution and reduced resolution to solve the obstruction function to get the unobstructed layers of data. Meanwhile, to simplify the computation, we apply the technique of spectral sequence. Finally, we give a classification of fermionic SPTs protected by 2D wallpaper-group symmetries. |
Tuesday, March 3, 2020 3:30PM - 3:42PM |
J54.00006: Non-Abelian reciprocal braiding of Weyl nodes and fragile topology Adrien Bouhon, QuanSheng Wu, Robert-Jan Slager, Tomas Bzdusek Weyl nodes trapped within C_{2}T symmetric planes (i.e. -crystalline rotation combined with time reversal) acquire a non-Abelian topological charge on top of their chirality. E.g. three-level systems realize the quaternion group [1]. The non-Abelian nature of Weyl nodes can alternatively be captured by the Euler class [2,3], which itself can be efficiently computed through the Wilson loop as the winding number of a Pfaffian [3]. These tools allow us (i) to design minimal experimental setups, and (ii) to search for material candidates. Furthermore, we show that additional crystalline symmetries can lead to the obstruction of the Euler class which naturally gives rise to nontrivial fragile topology. |
Tuesday, March 3, 2020 3:42PM - 3:54PM |
J54.00007: Topology of SO(5) monopoles and three dimensional Dirac semimetals Pallab Goswami, Alexander Tyner, Shouvik Sur The topological properties of Kramers degenerate band structures generally emerge from non-trivial textures of underlying SO(5) Berry’s vector potential. The linear touching between a pair of Kramers degenerate energy bands at isolated points of momentum space along an n-fold axis of rotation gives rise to three dimensional Dirac semimetals, where the Dirac points act as singularities of SO(5) gauge fields. Even though considerable progress has been made in recent years toward understanding the stability of Dirac points in the presence of parity, time reversal and discrete rotational symmetries, as of now there is no clear definition of topological invariants for Dirac points and any arbitrary momentum plane that is perpendicular to the direction of nodal separation. We will show how the implementation of global rotational symmetry causes an U(1) x U(1) abelian gauge fixing of SO(5) vector potential, allowing us to define monopole invariants and quantized ``spin Chern" numbers respectively for the Dirac points and the two dimensional planes perpendicular to the direction of nodal separation. We also demonstrate that generic form of Kramers degenerate Dirac semimetals do not support protected helical Fermi arcs. |
Tuesday, March 3, 2020 3:54PM - 4:06PM |
J54.00008: Duality between supercohomology fermionic SPT (symmetry-protected-topological) phases and higher-group bosonic SPT phases Yu-An Chen, Tyler Ellison, Nathanan Tantivasadakarn The first part of this talk will introduce generalized Jordan–Wigner transformation on arbitrary triangulation of any simply connected manifold in arbitrary dimensions. This gives a duality between any fermionic systems and a new class of Z_{2} lattice gauge theories. This map preserves the locality and has an explicit dependence on the second Stiefel–Whitney class and a choice of spin structure on the manifold. In the Euclidean picture, this mapping is exactly equivalent to adding topological terms, Steenrod square, to the spacetime action. The second part of the talk is the application of this boson-fermion duality on SPT phases. By the boson-fermion duality, we are able to show the equivalent between any supercohomology fermionic SPT and some higher-group bosonic SPT phase in arbitrary dimensions. Particularly in (3+1)D, we will show a unitary quantum circuit for any supercohomology fermionic SPT state with gapped boundary construction. |
Tuesday, March 3, 2020 4:06PM - 4:18PM |
J54.00009: Non-Abelian anomalies in multi-Weyl semimetals Renato M. A. Dantas, Francisco Pena-Benitez, Bitan Roy, Piotr Surowka We construct the effective field theory for time-reversal symmetry breaking multi-Weyl semimetals (mWSMs), composed of a single pair of Weyl nodes of (anti-)monopole charge $n$, with $n=1,2,3$ in crystalline environment. From both the continuum and lattice models, we show that a mWSM with $n>1$ can be constructed by placing $n$ flavors of linearly dispersing simple Weyl fermions in a bath of an $SU(2)$ non-Abelian static background gauge field. Such an $SU(2)$ field preserves certain crystalline symmetry (four-fold rotational or $C_4$ in our construction), but breaks the Lorentz symmetry, resulting in nonlinear band spectra. Consequently, the effective field theory displays $U(1) \times SU(2)$ non-Abelian anomaly, yielding anomalous Hall effect, its non-Abelian generalization, which we further substantiate by numerically computing the regular and ``isospin" densities from the lattice models of mWSMs. Altogether our findings unify the field theoretic descriptions of mWSMs of arbitrary monopole charge $n$ (featuring $n$ copies of the Fermi arc surface states), predict signatures of non-Abelian anomaly in table-top experiments, and pave the route to explore anomaly structures for multi-fold fermions, transforming under arbitrary half-integer or integer spin representations. |
Tuesday, March 3, 2020 4:18PM - 4:30PM |
J54.00010: Entanglement Entropy of Generalized Moore-Read Fractional Quantum Hall State Interfaces Ramanjit Sohal, Bo Han, Luiz Santos, Chi Yan Jeffrey Teo Topologically ordered phases of matter can be characterized by the presence of a universal, constant contribution to the entanglement entropy known as the topological entanglement entropy (TEE). The TEE can been calculated for Abelian phases via a "cut-and-glue" approach by treating the entanglement cut as a physical cut, coupling the resulting gapless edges with explicit tunneling terms, and computing the entanglement between the two edges. We provide a first step towards extending this methodology to non-Abelian topological phases, focusing on the generalized Moore-Read (MR) fractional quantum Hall states at filling fractions ν=1/q. We consider interfaces between different MR states and write down explicit tunneling terms, which we motivate using an anyon condensation picture. We compute the entanglement entropy for an entanglement cut lying along the interface. Our work provides new insight towards understanding the connections between anyon condensation, gapped interfaces of non-Abelian phases, and TEE. |
Tuesday, March 3, 2020 4:30PM - 4:42PM |
J54.00011: Majorana zero modes in the presence of many-body interactions Maciej Maska, Andrzej Wieckowski, Marcin Mierzejewski Recently, there has been substantial progress in methods of identifying local integrals of motion in interacting integrable models or in systems with many-body localization [1]. We show that one of these approaches can be utilized for constructing local, conserved, Majorana fermions in systems with an arbitrary many-body interaction [2]. Then, we discuss how the many-body interactions influence the spatial structure and the lifetime of the Majorana modes. Finally, we determine the regime for which the information stored in the Majorana correlators is also retained for arbitrarily long times at high temperatures. We show that it is included in the regime with topologically protected soft Majorana modes, but in some cases is significantly smaller. |
Tuesday, March 3, 2020 4:42PM - 4:54PM |
J54.00012: The Nieh-Yan Anomaly: Torsional Landau Levels, Central Charge and Anomalous Thermal Hall Effect Ze-Min Huang, Bo Han, Michael Stone The Nieh-Yan anomaly is the anomalous breakdown of the chiral U(1) symmetry caused by the interaction between torsion and fermions. We study this anomaly from the point of view of torsional Landau levels. It was found that the torsional Landau levels are gapless, while their contributions to the chiral anomaly are canceled, except those from the lowest torsional Landau levels. Hence, the dimension is effectively reduced from (3+1)d to (1+1)d. We further show that the coefficient of the Nieh-Yan anomaly is the free energy density in (1+1)d. Especially, at finite temperature, the thermal Nieh-Yan anomaly is proportional to the central charge. The anomalous thermal Hall conductance in Weyl semimetals is then shown to be proportional to the central charge, which is the experimental fingerprint of the thermal Nieh-Yan anomaly. |
Tuesday, March 3, 2020 4:54PM - 5:06PM |
J54.00013: Bulk-edge and bulk-hinge correspondence in inversion-symmetric insulators Ryo Takahashi, Yutaro Tanaka, Shuichi Murakami We show that a slab of a three-dimensional inversion-symmetric higher-order topological insulator (HOTI) in class A is a 2D Chern insulator, and that in class AII is a 2D Z_{2} topological insulator. We prove it by considering a process of cutting the three-dimensional inversion-symmetric HOTI along a plane, and study the spectral flow in the cutting process [1]. We show that the Z_{4} indicators, which characterize three-dimensional inversion-symmetric HOTIs in classes A and AII, are directly related to the Z_{2} indicators for the corresponding two-dimensional slabs with inversion symmetry, i.e. the Chern number parity and the Z_{2} topological invariant, for classes A and AII respectively [2]. The existence of the gapless hinge states is understood from the conventional bulk-edge correspondence between the slab system and its edge states. Moreover, we also show that the spectral-flow analysis leads to another proof of the bulk-edge correspondence in one-dimensional inversion-symmetric insulators. |
Tuesday, March 3, 2020 5:06PM - 5:18PM |
J54.00014: Surface Topological Order for Higher-Order Topological Phases of Matter Apoorv Tiwari, Minghao Li, Andrei Bernevig, Titus Neupert, Siddharth parameswaran We show that the chiral Dirac and Majorana hinge modes in three-dimensional higher-order topological insulators (HOTIs) and superconductors (HOTSCs) can be gapped while preserving the protecting C_{2n}T symmetry upon the introduction of non-Abelian surface topological order. In both cases, the topological order on a single side surface breaks time reversal symmetry, but appears with its time-reversal conjugate on alternating sides in a C_{2n}T preserving pattern. In the absence of the HOTI/HOTSC bulk, such a pattern necessarily involves gapless chiral modes on hinges between C_{2n}T-conjugate domains. However, using a combination of K-matrix and anyon condensation arguments, we show that on the boundary of a 3D HOTI/HOTSC these topological orders are fully gapped and hence `anomalous'. Our results suggest that new patterns of surface and hinge states can be engineered by selectively introducing topological order only on specific surfaces. |
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