Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session D54: Construction and detection of topological orders |
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Sponsoring Units: DCMP Chair: Daniel Bulmash, University of Maryland, College Park Room: Mile High Ballroom 2A |
Monday, March 2, 2020 2:30PM - 2:42PM |
D54.00001: A defect TQFT approach to fractons David Aasen, Daniel Bulmash, Abhinav Prem, Kevin Slagle, Dominic Williamson We explore fracton phases from the perspective of topological quantum field theories. We argue that type I and type II gapped fracton models can be realized by a network of defects embedded into various 3+1D topological quantum field theories. The idea is that subdimensional excitations characteristic of fracton phases can appear due to mobility restrictions imposed by the defect network. We explicitly construct many well known examples of fracton phases and a few new models using the defect construction. As a byproduct the defect construction provides a generalized membrane-net condensate picture of fracton phases. |
Monday, March 2, 2020 2:42PM - 2:54PM |
D54.00002: Anomalous surfaces of fracton phases Thomas Schuster, Nathanan Tantivasadakarn, Ashvin Vishwanath, Norman Yao Fractons are three-dimensional phases distinguished by the restricted mobility of their quasiparticles, and share many similarities to topological order in two dimensions. In this talk, we demonstrate that boundaries of well-known fracton models feature anomalous constraints arising from the emergent conservation laws that govern the bulk fracton order, in a manner similar to 2D topological orders such as the toric code. These constraints restrict the allowed boundary operators to those that commute with certain subsystem symmetry operations, determined both by the bulk fracton order and the direction of boundary termination. The constraints are anomalous in the sense that they cannot arise in any 2D local theory; we demonstrate this from a microscopic perspective, showing that the boundary operators' anticommutation relations are inconsistent with the constraints in any such theory. This gives rise to a rich phase diagram for the boundary theory, in correspondence with that of local 2D subsystem-symmetric systems. |
Monday, March 2, 2020 2:54PM - 3:06PM |
D54.00003: Multipole gauge theory for fracton phases Andrey Gromov I will describe an effective field theory approach to the fracton order. In particular I will show how to construct a U(1) version of the Haah code from the principles of symmetry and gauge invariance. |
Monday, March 2, 2020 3:06PM - 3:18PM |
D54.00004: Geodesic string condensation from symmetric tensor gauge theory: a unifying framework of holographic toy models Han Yan In this talk we reason that there is a universal picture for several different holographic toy model constructions, and a gravity-like bulk field theory that gives rise it. First, we observe that the perfect tensor-networks and hyperbolic fracton models are both equivalent to the even distribution of bit-threads on geodesics in the AdS space. Such picture is also a natural "leading-order" approximation to the holographic entanglement properties. Then, we argue that the rank-2 U(1) theory with linearized diffeomorphism as its gauge symmetry, also known as a case of Lifshitz gravity, is the bulk field theory behind such picture. The Gauss' laws and spatial curvature require the electric field lines along the geodesics to be the fundamental dynamical variables, which lead to geodesic string condensation. These results provide an intuitive way to understand the entanglement structure of gravity in AdS/CFT. |
Monday, March 2, 2020 3:18PM - 3:30PM |
D54.00005: Localized representation and surface signature of Hopf insulators. Aleksandra Nelson, Aris Alexandradinata, Alexey Soluyanov The Hopf insulator is a 3D topological insulator that can’t be described in terms of a 10-fold classification. It also differs from fragile topological insulators. The main requirement for its existence is a two-rank Hamiltonian. In case when Hopf Hamiltonian has a trivial first Chern class, it obeys Z classification. |
Monday, March 2, 2020 3:30PM - 3:42PM |
D54.00006: Lattice models that realize Zn-1-symmetry protected topological states for even n Lokman Tsui, Xiao-Gang Wen We study the lattice model of Zn-1-symmetry protected topological states (1-SPT) in 3+1D for even n. We write down an exactly soluble lattice model and study its boundary transformation. On the boundary, we show the existence of anyons with non-trivial self-statistics. For the n=2 case, where the bulk classification is given by an integer m mod 4, we show that the boundary can be gapped with double semion topological order for m=1 and toric code for m=2. The bulk ground state wavefunction amplitude is given in terms of the linking numbers of loops in the dual lattice. Our construction can be generalized to arbitrary 1-SPT protected by finite unitary symmetry. |
Monday, March 2, 2020 3:42PM - 3:54PM |
D54.00007: Strong 3D planar subsystem symmetry-protected topological phases and their dual fracton orders Trithep Devakul, Wilbur Shirley, Juven C Wang We classify subsystem symmetry-protected topological (SSPT) phases in 3+1D protected by planar subsystem symmetries: short-range entangled phases which are dual to long-range entangled abelian fracton topological orders via a generalized `gauging' duality. We distinguish between weak SSPTs, which can be constructed by stacking 2+1D SPTs, and strong SSPTs, which cannot. We identify signatures of strong phases, and show by explicit construction that such phases exist. A classification of strong phases is presented for an arbitrary finite abelian group. Finally, we show that fracton orders realizable via p-string condensation are dual to weak SSPTs, while those dual to strong SSPTs do not admit such a realization. |
Monday, March 2, 2020 3:54PM - 4:06PM |
D54.00008: Coupled wire constructions of 3D topological phases Joseph Sullivan
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Monday, March 2, 2020 4:06PM - 4:18PM |
D54.00009: Modeling Electron Fractionalization with Unconventional Fock Spaces Emilio Cobanera It is shown that certain fractionally-charged quasiparticles can be modeled on D−dimensional lattices in terms of unconventional yet simple Fock algebras of creation and annihilation operators. These unconventional Fock algebras are derived from the usual fermionic algebra by taking roots (the square root, cubic root, etc) of the usual fermionic creation and annihilation operators. If the fermions carry non-Abelian charges like spin, then this approach fractionalizes the Abelian charges only. In particular, the mth-root of a spinful fermion is an operator that carries charge e/m and spin 1/2. While the exclusion statics is fixed by the root operation, there are several possible choices of quantum exchange statistics for fermion-root quasiparticles. These choices are tied to the dimensionality D = … 1, 2, 3, of the lattice and the exchange statistics between fermions and fractionalized fermions. As an application of potential mesoscopic interest, I investigate numerically the hybridization of Majorana and parafermion zero-energy edge modes caused by fractionalizing but charge-conserving tunneling. |
Monday, March 2, 2020 4:18PM - 4:30PM |
D54.00010: Fractionalization and Anomalies in Symmetry-Enriched U(1) Gauge Theories Liujun Zou, Shang-Qiang Ning, Meng Cheng We classify symmetry fractionalization and anomalies in a 3+1d U(1) gauge theory enriched by a global symmetry group G. We find that, in general, a symmetry-enrichment pattern is specified by 4 pieces of data: ρ, a map from G to the duality symmetry group of this U(1) gauge theory, ν∈H2ρ[G, UT(1)], p∈H1[G, ZT], and a torsor n over H3ρ[G, Z]. However, certain choices of (ρ, ν, p, n) are not physically realizable, i.e., they are anomalous. There are two levels of anomalies. The first level of anomalies, deconfinement anomalies, obstruct fractional excitations being deconfined. States with these anomalies can be realized on the boundary of a 4+1d long-range entangled state. In the absence a deconfinement anomaly, there can still be the more familiar 't Hooft anomaly, which forbids certain types of symmetry fractionalization patterns to be implemented in an on-site manner. States with these anomalies can live on the boundary of a 4+1d short-range entangled state. We apply our results to some interesting physical examples. |
Monday, March 2, 2020 4:30PM - 4:42PM |
D54.00011: Coupled Wire Model of Z2 × Z2 Orbifold Quantum Hall States Pok Man Tam, Yichen Hu, Charles L Kane We construct a coupled wire model for a sequence of non-Abelian quantum Hall states occurring at filling factors ν=2/(2M+q) with integers M and even(odd) integers q for fermionic(bosonic) states. They are termed Z2 × Z2 orbifold states, which have a topological order with a neutral sector described by the c=1 orbifold conformal field theory (CFT) at radius R2=p/2 with even integers p. When p=2, the state can be viewed as two decoupled layers of Moore-Read (MR) state, whose neutral sector is described by the Ising × Ising CFT and contains a Z2 × Z2 fusion subalgebra. We demonstrate that orbifold states with p > 2, also containing a Z2 × Z2 fusion algebra, can be obtained by coupling an array of MR × MR wires together through local interactions. The corresponding charge spectrum of quasiparticles is also examined. The orbifold states constructed here are complementary to the Z4 orbifold states, whose neutral edge theory is described by orbifold CFT with odd integer p and contains a Z4 fusion algebra. |
Monday, March 2, 2020 4:42PM - 4:54PM |
D54.00012: Properties of the Dice-Lattice and its Ribbons Rahul Soni, Nitin Kaushal, Elbio Dagotto, Satoshi Okamoto Previous theoretical studies established the existence of nearly flat bands with non-zero Chern numbers in the dice lattice using non-interacting electrons in the presence of spin-orbit coupling and magnetic field [1]. To pave the way towards the introduction of Hubbard |
Monday, March 2, 2020 4:54PM - 5:06PM |
D54.00013: Anyonic partial transpose Hassan Shapourian, Roger Mong, Shinsei Ryu A basic diagnostic of entanglement in mixed quantum states is known as the positive partial transpose and the corresponding entanglement measure is called the logarithmic negativity. Despite the great success of logarithmic negativity in characterizing bosonic many-body systems, generalizing the partial transpose to fermionic systems remained a technical challenge until recently when a new definition that accounts for the Fermi statistics has been put forward. In this talk, I will present our attempts to generalize partial transpose to anyons with fractional statistics. It turns out that there is a connection between the partial transpose and braiding statistics. As an application, I will show how the braiding matrix can be used to reproduce many-body topological invariants of 1D time-reversal symmetric topological superconductors. |
Monday, March 2, 2020 5:06PM - 5:18PM |
D54.00014: Detecting Topological Order at Finite Temperature Using Entanglement Negativity Tsung-Cheng Lu, Timothy Hsieh, Tarun Grover We propose a scheme to diagnose finite temperature topological order using the long-range component of entanglement negativity, dubbed topological entanglement negativity. As a demonstration, we study the toric code model in d spatial dimension for d=2,3,4, and find that a topological ordered state at finite temperature has non-zero topological entanglement negativity, whose value is equal to topological entanglement entropy at zero temperature. To calculate entanglement negativity, we develop a general tool for any commuting projector Hamiltonians to derive the spectrum of a thermal state under partial transpose, allowing us to map the calculation of negativity to a classical statistical mechanics problem. Relatedly, using the idea of minimally entangled typical thermal states, we derive necessary conditions for the existence of finite temperature topological order in any CSS code Hamiltonians. |
Monday, March 2, 2020 5:18PM - 5:30PM |
D54.00015: Aharonov-Bohm Effect without Using Vector Potential XIANG LI, Hans Hansson, Wei Ku Aharonov-Bohm effect is a pure quantum effect that describes a phase shift of a quantum particle due to magnetic flux present in space inaccessible to the particle. Such a non-local effect appears to be impossible classically given the locality of coupling between a particle and magnetic field. Typically, this effect is accounted for via the use of a gauge-dependent vector potential, which extends to the entire space beyond the region with finite magnetic field and thus recovers the locality of the theory. This leads to a perspective of electromagnetic potential being more “fundamental” than the electromagnetic field in quantum mechanics, despite the gauge dependent nature of the vector potential. Here, we demonstrate that this effect can be completely accounted for by consideration of the gauge invariant magnetic field only, if the entire system is included in the analysis. This gauge invariant picture provides an alternative intuitive physical understanding that explicitly encapsulates the non-locality of quantum mechanics in the presence of magnetic field. |
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