Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session L55: One Dimensional Topological Systems |
Hide Abstracts |
Sponsoring Units: DCMP Chair: Thomas Bullard, UES, Inc. Room: Mile High Ballroom 2B |
Wednesday, March 4, 2020 8:00AM - 8:12AM |
L55.00001: Mesoscopic Conductance Fluctuations in Class D Superconducting Wires Daniil Antonenko, Pavel Ostrovsky, Mikhail Skvortsov We study disordered superconducting wires (length L) of class D via supersymmetric sigma-model approach in the critical regime between topological and trivial phases, where delocalization happens and average conductance scales as G ∼ L^{-1/2} [1]. In order to calculate the variance of conductance var G in the diffusive regime we introduce n=2 sigma-model and apply the method of transfer-matrix Hamiltonian, studying Laplace-Beltrami operator on the rank two symmetric superspace. We use Iwasawa decomposition to construct eigenbasis on this supermanifold, which appears to consist of three-parametric and one-parametric subsets, with the latter closely related to the eigenfunctions on the n=1 sigma-model manifold. Our approach allows to find var G at arbitrary lengths in the diffusive region with the crossover from the perturbative weak-localisation regime at L << ξ to the regime of a very broad conductance distribution at L >> ξ, where ξ is the correlation length of the wire. Also, we account to the possible back/forward channels imbalance, which is described by a Wess-Zumino-Witten term in the sigma-model action. |
Wednesday, March 4, 2020 8:12AM - 8:24AM |
L55.00002: Majorana bound states from textured chiral magnets Stefan Rex, Igor Gornyi, Alexander Mirlin Non-collinear magnetism combined with superconductivity can support the formation of localized Majorana bound states. |
Wednesday, March 4, 2020 8:24AM - 8:36AM |
L55.00003: Topological Phases in a One-dimensional Majorana-Bose-Hubbard Model Ananda Roy, Johannes Hauschild, Frank Pollmann Majorana zero modes (MZM-s) occurring at the edges of a 1D, p-wave, spinless superconductor, in absence of fluctuations of the phase of the superconducting order parameter, are quintessential examples of topologically-protected zero-energy modes occurring at the edges of 1D symmetry-protected topological phases. In this work, we numerically investigate the properties of the topological phase in the presence of phase-fluctuations using the density matrix renormalization group (DMRG) technique. To that end, we consider a one-dimensional array of MZM-s on superconducting islands at zero temperature. We show that the system can be in either a Mott-insulating phase, a Luttinger liquid (LL) phase of Cooper-pairs or another gapless phase. The latter phase can be viewed as a LL of charge-e bosons where nonlocal string correlation functions decay algebraically. These nonlocal correlation functions, together with correlation functions of the Cooper-pair creation operators, distinguish the different phases of the model. We map the system to an interacting model of spins coupled to rotors and use DMRG to characterize the different phases and the phase-transitions. |
Wednesday, March 4, 2020 8:36AM - 8:48AM |
L55.00004: Boundary-induced dynamics and quantum memory effect of 1D and 2D topological systems Chih-Chun Chien, Yan He The dynamics after a change of the boundary condition for selected 1D and 2D topological systems are analyzed. We consider the 1D Su-Schrieffer-Heeger (SSH) model and Kitaev model transforming from periodic to open boundary condition and the 2D Chern insulator (CI) and topological quadrupole insulator (TQI) transforming from a cylinder or Mobius strip to open boundary condition. In all the cases, we found the occupation of the topological edge states reaches a steady-state value after the transformation is completed in absence of any external dissipation mechanism. The steady-state value depends on the ramping rate of the boundary condition. The dependence of the steady-state occupation of the topological edge states on the ramping rate thus exemplifies one kind of quantum memory effect, which originates from the trapping of excitations due to the localized nature of the edge states. The mechanism suggests that this type of quantum memory effect may be universal in topological systems with localized edge states. |
Wednesday, March 4, 2020 8:48AM - 9:00AM |
L55.00005: Interaction Driven Floquet Engineering of Topological Superconductivity in Rashba Nanowires Manisha Thakurathi, Pavel Aseev, Daniel Loss, Jelena Klinovaja We analyze, analytically and numerically, a periodically driven Rashba nanowire proximity coupled to an s-wave superconductor [1] using bosonization and renormalization group analysis in the regime of strong electron-electron interactions. Due to the repulsive interactions, the superconducting gap is suppressed, whereas the Floquet Zeeman gap is enhanced, resulting in a higher effective value of g-factor compared to the non-interacting case [2]. The flow equations for different coupling constants, velocities, and Luttinger-liquid parameters explicitly establish that even for small initial values of the Floquet Zeeman gap compared to the superconducting proximity gap, the interactions drive the system into the topological phase and the interband interaction term helps to achieve larger regions of the topological phase in parameter space. |
Wednesday, March 4, 2020 9:00AM - 9:12AM |
L55.00006: Almost strong 0, π edge modes in clean, interacting 1D Floquet systems Daniel Yates, Fabian H.L. Essler, Aditi Mitra Certain periodically driven quantum many-particle systems in one dimension are known to exhibit edge modes that are related to topological properties and lead to approximate degeneracies of the Floquet spectrum. A similar situation occurs in spin chains, where stable edge modes were shown to exist at all energies in certain integrable spin chains. Moreover, these edge modes were found to be remarkably stable to perturbations. Here we investigate the stability of edge modes in interacting, periodically driven, clean systems. We introduce a model that features edge modes that persist over times scales well in excess of the time needed for the bulk of the system to heat to infinite temperatures. |
Wednesday, March 4, 2020 9:12AM - 9:24AM |
L55.00007: Rigorous results on topological superconductivity with particle number conservation Matthew Lapa, Michael Levin Most theoretical studies of topological superconductors and their unpaired Majorana fermions rely on a mean-field (or Bogoliubov-de Gennes) approach to describe superconductivity, which violates particle number conservation (PNC). Recently, however, A.J. Leggett and others have argued that this violation of PNC may pose a serious conceptual problem for Majorana-based quantum computation. To resolve this issue, reliable results on number-conserving models of superconductivity are essential. As a first step in this direction, we use rigorous methods to study a number-conserving toy model of a topological superconducting wire. We prove that this model exhibits many of the desired properties of the mean-field models, including a finite energy gap in a sector of fixed total particle number, and the existence of long range “Majorana-like” correlations between the ends of the wire. These results show that many of the remarkable properties of mean-field models of topological superconductivity persist in more realistic models with number-conserving dynamics. |
Wednesday, March 4, 2020 9:24AM - 9:36AM |
L55.00008: Braiding Floquet Majorana Modes in One-Dimensional Topological Superconductors Bill Truong, Tami Pereg-Barnea, Kartiek Agarwal It is well-known that braiding Majorana zero modes in one-dimensional (1D) topological systems is a challenge since the modes hybridize when they are within proximity of each other. Recent developments have indicated that braiding in 1D can be accomplished through periodic driving. In our work, we study a 1D p-wave superconductor modelled as a Kitaev chain with the driving achieved by periodically modulating the parameters of the system. This Floquet system gives rise to Majorana edge modes of both zero and π quasienergy. We numerically implement the adiabatic protocol developed in Ref. [1] to braid the Floquet Majorana zero modes, using the Floquet Majorana π modes as an auxiliary degree of freedom. We consider the inclusion of interactions and disorder into the system and demonstrate the robustness of the protocol by examining quantities such as the exchange operator. |
Wednesday, March 4, 2020 9:36AM - 9:48AM |
L55.00009: Universal delocalization transition in 1D chiral Floquet topological insulators Pratik Sathe, Albert Brown, Fenner Harper, Rahul Roy Periodically driven systems of non-interacting fermions, also known as Floquet topological insulators, exhibit novel topological characteristics distinct from those of static systems. In the case of 1D Floquet topological insulators with chiral symmetry (class AIII), the dynamical topological nature can be understood through studying the time evolution operator U(t) evaluated close to the midpoint of a driving period, i.e. U(T/2). We investigate the localization properties at this special point, for flat-band, two-step Floquet drives. Specifically, for topologically non-trivial disordered drives, we show that the localization length of eigenstates of U(T/2 - epsilon) diverges as epsilon approaches 0 as a power law with exponent nu = 2, and argue that this property is universal for this class of AIII models. |
Wednesday, March 4, 2020 9:48AM - 10:00AM |
L55.00010: Experimental study of 1D Su-Schrieffer-Heeger edge modes in a water-wave channel Adam Anglart, Pawel Obrepalski, Kei Kusumi, Agnes Maurel, Philippe Petitjeans, Vincent Pagneux The main objective of this work is to experimentally investigate the topologically protected edge-states and band gaps in a water waveguide with periodic geometry. One of the representations of the topological states, provided by the Su–Schrieffer–Heeger model (SSH) [1], is applied to describe the observed phenomena [2]. A waveguide with step periodic width as well as corresponding rectangular tank with constant width are examined using Confocal Displacement Sensors allowing the measurement of water surface displacements. 2D numerical simulations are carried out in order to verify the SSH model and experimental data. The obtained results show that this very simple setup exhibits all the properties of the SSH model with an excellent agreement to the water-wave systems. |
Wednesday, March 4, 2020 10:00AM - 10:12AM |
L55.00011: Path integral for spin-1 chain in the entangled basis Jung Hoon Han We develop path-integral formulation of spin-1 Haldane chain in the entangled, matrix product state (MPS) basis. Whereas the conventional path integral approach is founded on spin-based coherent states as the basis, we here adopt a new basis consisting of bond-based coherent states. The Affleck-Kennedy-Lieb-Tasaki (AKLT)-type ground state is obtained as the saddle point solution of the newly developed action. Small fluctuations around the saddle point are developed in terms of conventional gradient expansion. Ways to compute various correlation functions based on the effective action will be discussed. While certain crude approximations have to be made to proceed with the calculation, it appears that features of spin gap in the spin-1 chain seems nicely captured at the mean-field level by the path integral written in the entangled basis. This work was done in collaboration with Jin-Tae Kim, Rajarshi Pal, and Jin-Hong Park at SKKU. |
Wednesday, March 4, 2020 10:12AM - 10:24AM |
L55.00012: Detecting one-dimensional interacting topological phases by edge-state pinning Shun-Chiao Chang, Pavan Hosur In density matrix renormalization group (DMRG) simulations, edge states are often identified by computing edge-edge or bulk-edge two-point correlation functions. Since this approach involves computing the square of the local order parameter, very large systems at high precision are required to obtain reliable results when the order parameter is small, which is true, for instance, near a phase boundary. Moreover, the computational cost of this method increases drastically with the bulk entanglement. In this work, we propose and demonstrate an efficient method for detecting the topological edge states with DMRG. That is, we study edge states by pinning one edge with appropriate fields and observing the corresponding local order parameter of the other edge. The method is validated here for antiferromagnetic Heisenberg model, the simplest realization of the Haldane phase. It would be interesting to study other one-dimensional topological phases using this method. |
Wednesday, March 4, 2020 10:24AM - 10:36AM |
L55.00013: Generalized bulk-edge correspondence for non-hermitian topological phases Ken-Ichiro Imura, Yositake Takane takane@hiroshima-u.ac.jp In a recent paper [1] we have established that the idea of bulk-edge correspondence in the hermitian limit can be generalized to non-hermitian topological systems. But strictly speaking, the proof given there was limited to the regime of weak (perturbative) non-hermiticity. Here, we deepen the idea of the generalized bulk-edge correspondence proposed in Ref. [1] and give a more general proof valid also in the non-perturbative non-hermitian regime. |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700