Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session Q36: Topological Quantum Information |
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Sponsoring Units: GQI Room: 703 |
Wednesday, March 5, 2014 2:30PM - 2:42PM |
Q36.00001: Matrix Product States for Chiral Topological Phases B. Andrei Bernevig, Benoit Estienne, Nicolas Regnault, Yangle Wu I show how, using interacting conformal field theory, an MPS representation can be obtained for both the ground-state and the quasihole excitations of chiral topological states of matter. I show that the advance allows for the accurate calculation of quantities such as topological entanglement entropy and non-abelian braiding. [Preview Abstract] |
Wednesday, March 5, 2014 2:42PM - 2:54PM |
Q36.00002: Entanglement spectrum of Levin-Wen model for topological phases in two dimensions Yuting Hu, Yong-Shi Wu We obtain explicitly the entanglement spectrum of ground states and excited states of the doubled Fibonacci Levin-Wen model. The entanglement spectrum has the topological degeneracy. We show that they exhibit the fractional exclusion statistics of chiral anyons. Moreover, we show that the entanglement spectrum can be mapped to a grand canonical ensemble of 1d system of the chiral Fibonacci anyons on the boundary, at a finite temperature determined by the quantum dimension of Fibonacci anyons. Finally, we show how that the topological quantum numbers of the bulk states can be detected by the entanglement spectrum [Preview Abstract] |
Wednesday, March 5, 2014 2:54PM - 3:06PM |
Q36.00003: Bulk Entanglement Spectrum Reveals Quantum Criticality within a Topological State Timothy Hsieh, Liang Fu A quantum phase transition is usually achieved by tuning physical parameters in a Hamiltonian at zero temperature. Here, we demonstrate that the ground state of a topological phase itself encodes critical properties of its transition to a trivial phase. To extract this information, we introduce a partition of the system into two subsystems both of which extend throughout the bulk in all directions. The resulting bulk entanglement spectrum has a low-lying part that resembles the excitation spectrum of a bulk Hamiltonian, which allows us to access a topological phase transition from a single wavefunction by tuning either the geometry of the partition or the entanglement temperature. As an example, this remarkable correspondence between topological phase transition and entanglement criticality is rigorously established for integer quantum Hall states. [Preview Abstract] |
Wednesday, March 5, 2014 3:06PM - 3:18PM |
Q36.00004: Exotic circuit elements from hybrid superconductor/quantum Hall systems David Clarke, Jason Alicea, Kirill Shtengel Heterostructures formed by quantum Hall systems and superconductors have recently been shown to support widely coveted Majorana fermion zero-modes and still more exotic `parafermionic' generalizations [1-3]. Here we establish that probing such zero-modes using quantum Hall edge states yields \emph{non-local} transport signatures that pave the way towards a variety of novel circuit elements. In particular, we demonstrate quite generally that at low energies the zero-modes convert chirally moving quasiparticles into oppositely charged quasiholes propagating in the same direction---that is, they swap the sign of the chiral edge currents [4]. One may then construct new and potentially useful circuit elements using this `perfect Andreev conversion' process, including superconducting current and voltage mirrors as well as transistors for fractional charge currents. Characterization of these circuit elements should provide striking evidence of the zero mode physics. \\ \\ 1. Clarke, Alicea, Shtengel, Nat. Commun. 4, 1348 (2013) \\ 2. Lindner, Berg, Refael, Stern, Phys. Rev. X 2, 041002 (2012) \\ 3. Cheng Phys. Rev. B 86, 195126 (2012) \\ 4. Barkeshli, Qi, arXiv:1302.2673 (2013) [Preview Abstract] |
Wednesday, March 5, 2014 3:18PM - 3:30PM |
Q36.00005: Exact zero modes and decoherence in systems of interacting Majorana fermions Guang Yang, Dmitri Feldman Majorana fermions often coexist with other low-energy fermionic degrees of freedom. In such situation, topological quantum computation requires the use of fermionic zero modes of a many-body system. We classify all such modes for interacting fermions and show how to select the mode that maximizes the decoherence time. We find that in a typical interacting system the maximal decoherence time is within one order of magnitude from the decoherence time of a qbit, based on the local part of the fermion parity operator. [Preview Abstract] |
Wednesday, March 5, 2014 3:30PM - 3:42PM |
Q36.00006: Braiding Majorana states in helical magnetic atom chains Ching-Kai Chiu, Mohammad Vazifeh, Marcel Franz A helical magnetic atom chain deposited on the top of a superconductor can be realized as a 1D topological superconductor. We propose an innovative braiding protocol for Majorana zero modes at the ends of the magnetic chains for topological quantum computing. Braiding of exchanging particles can be implemented by moving only a \emph{single} Majorana mode from one end to the other end. During the movement, the other Majorana mode teleports to the beginning position of the moving Majorana mode due to the finite size coupling of Majorana modes. Furthermore, the operation of changing the signs of the two Majorana modes can be achieved by rotating the direction of the magnetic moments by pi without moving Majorana modes at the ends. [Preview Abstract] |
Wednesday, March 5, 2014 3:42PM - 3:54PM |
Q36.00007: Robustness of zero-modes in parafermion chains Adam Jermyn, Roger Mong, Jason Alicea Several models for 1D topological phases are known to host zero-modes that enable high-fidelity quantum information storage and manipulation. The Majorana fermion chain provides a classic example. Here the system supports Majorana zero-modes that guarantee two-fold degeneracy in the ground state and excited states to within exponential accuracy. Chains of ``parafermions''--which represent generalized Majorana fermions--also support zero-modes, but, curiously, only under much more restricted circumstances as shown recently by Fendley. We shed light on this interesting finding by exploring the properties of ground-states and excited states in parafermion chains using analytic methods as well as DMRG and exact diagonalization of a truncated Hilbert space model. We show that the absence of exact zero-modes admits a simple physical picture in terms of domain-wall dynamics. [Preview Abstract] |
Wednesday, March 5, 2014 3:54PM - 4:06PM |
Q36.00008: Topological Insulating Phases of Non-Abelian Anyonic Chains Wade DeGottardi I will present work on the topological insulating phases of non-abelian anyonic chains, focusing on antiferromagnetically coupled spin-1/2 su(2)$_k$ chains at any level $k$. The topological phases of these systems are characterized by anyonic end modes. A detailed discussion of the two most prominent cases is given: Majorana fermions (at $k = 2$) and Fibonacci anyons ($k = 3$). A renormalization group approach which allows for a straightforward determination of the topological phases of these systems will be discussed. This work reveals a deep connection between topological order and spontaneous symmetry breaking in these systems. It will be argued that the emergent anyons may be more easily manipulated than the physical quasiparticles and could be used to perform quantum computation. [Preview Abstract] |
Wednesday, March 5, 2014 4:06PM - 4:18PM |
Q36.00009: Entanglement Inequalities for Majorana Fermions in Semiconductor Nanowires David Drummond, Alexey Kovalev, Chang-Yu Hou, Leonid P. Pryadko, Kirill Shtengel Recent work has provided evidence that unpaired Majorana fermions may exist at the ends of a semiconductor nanowire in the presence of s-wave superconductivity, a magnetic field, and strong spin-orbit coupling. While Majorana fermions are interesting in their own right as self-conjugate quasiparticles, they are also sought after because they could serve as the stable building blocks of topological quantum computing. We propose an experiment that would establish the entanglement of these Majorana fermions by testing an analog of the Bell and CHSH inequalities in nanowire systems. Our proposal is viable with realistic system parameters, simple ``keyboard'' gating, and projective measurement. Simulation results indicate entanglement can be demonstrated with a relatively small amount of accuracy in the gate operations. Our proposal for testing entanglement inequalities can also be adapted to other systems where Majorana fermions may be present, such as topological insulators. In addition to providing further evidence for the existence of the unpaired Majorana fermions, our proposal could be used as an experimental stepping stone to more complicated braiding experiments. [Preview Abstract] |
Wednesday, March 5, 2014 4:18PM - 4:30PM |
Q36.00010: Detection of zero-modes induced by defect in the Kitaev quantum wire model Sheng-Wen Li, Zeng-Zhao Li, Chang-Pu Sun The Kitaev quantum wire model has two Majorana edge states for open boundary condition. The existence of a defect on a homogenous quantum wire would effectively cut off the wire at this position and generate new boundaries. In this case, another pair of low-energy modes would emerge, localized on both sides of this site, whose energies also approach zero for strong defect. We build up an exactly solvable quantum Langevin equation to describe the electrical current of the quantum wire contacted with two normal leads. If the lead is put besides different sites of the quantum wire, we obtain different transportation profile. When the lead is contacted with the site beside the defect, we would observe a splitting in the differential conductance spectrum, which is determined by the defect strength. [Preview Abstract] |
Wednesday, March 5, 2014 4:30PM - 4:42PM |
Q36.00011: Teleportation-induced entanglement of two nanomechanical oscillators coupled to a topological superconductor Stefan Walter, Jan Carl Budich A one-dimensional topological superconductor features a single fermionic zero mode that is delocalized over two Majorana bound states located at the ends of the system. We study a pair of spatially separated nanomechanical oscillators tunnel-coupled to these Majorana modes. Most interestingly, we demonstrate that the combination of electron-phonon coupling and a finite charging energy on the mesoscopic topological superconductor can lead to an effective superexchange between the oscillators via the non-local fermionic zero mode. We further show that this teleportation mechanism leads to entanglement of the two oscillators over distances that can significantly exceed the coherence length of the superconductor. [Preview Abstract] |
Wednesday, March 5, 2014 4:42PM - 4:54PM |
Q36.00012: ABSTRACT WITHDRAWN |
Wednesday, March 5, 2014 4:54PM - 5:06PM |
Q36.00013: Entanglement spectra between coupled Tomonaga-Luttinger liquids: Applications to ladder systems and topological phases Rex Lundgren, Yohei Fuji, Shunsuke Fukuwara, Masaki Oshikawa We study the entanglement spectrum (ES) and entropy between two coupled Tomonaga-Luttinger liquids (TLLs) on parallel periodic chains. This problem gives access to the entanglement properties of various interesting systems, such as spin ladders as well as two-dimensional topological phases. By expanding interchain interactions to quadratic order in bosonic fields, we are able to calculate the ES for both gapped and gapless systems using only methods for free theories. In certain gapless phases of coupled non-chiral TLLs, we interestingly find an ES with a dispersion relation proportional to the square root of the subsystem momentum, which we relate to a long-range interaction in the entanglement Hamiltonian. We numerically demonstrate this unusual dispersion in a model of hard-core bosons on a ladder. In gapped phases of coupled non-chiral TLLs, which are relevant to spin ladders and topological insulators, we show that the ES consists of linearly dispersing modes, which resembles the spectrum of a single-chain TLL but is characterized by a modified TLL parameter. Based on a calculation for coupled chiral TLLs, we are also able to provide a very simple proof for the correspondence between the ES and the edge-state spectrum in quantum Hall systems. Based of arXiv:1310:0829 [Preview Abstract] |
Wednesday, March 5, 2014 5:06PM - 5:18PM |
Q36.00014: On the spreading rate of entanglement in a many-body localized quantum spin chain Arun Nanduri, Hyungwon Kim, David Huse Although the many-body localized phase does not allow the transport of local observables, the unbounded logarithmic growth of bipartite entanglement entropy, $S$, has recently been observed (Bardarson et al., Phys. Rev. Lett. {\bf 109}, 017202 (2012)). We aim to elucidate the origin of this logarithmic growth through exact diagonalization methods, analyzing an XXZ spin model with random longitudinal fields. Based on a proposed phenomenology of entanglement spreading (Huse and Oganesyan, arXiv:1305.4915v1), we connect the rate of entanglement spreading with the localization length ($\xi$) of the system and the saturated entanglement entropy per spin ($s_{\infty}$). We find that the time dependence of the entanglement spreading takes the form $S\sim \xi s_{\infty} \log t$. [Preview Abstract] |
Wednesday, March 5, 2014 5:18PM - 5:30PM |
Q36.00015: Exotic topological order from quantum fractal code Beni Yoshida We present a large class of three-dimensional spin models that possess topological order with stability against local perturbations, but are beyond description of topological quantum field theory. Conventional topological spin liquids, on a formal level, may be viewed as condensation of string-like extended objects with discrete gauge symmetries, being at fixed points with continuous scale symmetries. In contrast, ground states of fractal spin liquids are condensation of highly-fluctuating fractal objects with certain algebraic symmetries, corresponding to limit cycles under real-space renormalization group transformations which naturally arise from discrete scale symmetries of underlying fractal geometries. A particular class of three-dimensional models proposed in this paper may potentially saturate quantum information storage capacity for local spin systems. [Preview Abstract] |
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