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Title: Lifetime of Almost Strong Edge-Mode Operators in One-Dimensional, Interacting, Symmetry Protected Topological Phases

Abstract

Almost strong edge-mode operators arising at the boundaries of certain interacting one-dimensional symmetry protected topological phases with Z2 symmetry have infinite temperature lifetimes that are nonperturbatively long in the integrability breaking terms, making them promising as bits for quantum information processing. We extract the lifetime of these edge-mode operators for small system sizes as well as in the thermodynamic limit. For the latter, a Lanczos scheme is employed to map the operator dynamics to a one-dimensional tight-binding model of a single particle in Krylov space. We suggest this model to be that of a spatially inhomogeneous Su-Schrieffer-Heeger model with a hopping amplitude that increases away from the boundary, and a dimerization that decreases away from the boundary. We associate this dimerized or staggered structure with the existence of the almost strong mode. Thus, the short time dynamics of the almost strong mode is that of the edge mode of the Su-Schrieffer-Heeger model, while the long time dynamics involves decay due to tunneling out of that mode, followed by chaotic operator spreading. Furthermore, we show that competing scattering processes can lead to interference effects that can significantly enhance the lifetime.

Authors:
 [1];  [2];  [1]
  1. New York University (NYU), NY (United States)
  2. Stony Brook University, NY (United States); Simons Center for Geometry and Physics, Stony Brook, NY (United States)
Publication Date:
Research Org.:
New York Univ. (NYU), NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1630429
Alternate Identifier(s):
OSTI ID: 1656779
Grant/Contract Number:  
SC0010821
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 124; Journal Issue: 20; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Symmetry protected topological states; Topological materials; Approximation methods for many-body systems; Topological states of matter

Citation Formats

Yates, Daniel, Abanov, Alexander, and Mitra, Aditi. Lifetime of Almost Strong Edge-Mode Operators in One-Dimensional, Interacting, Symmetry Protected Topological Phases. United States: N. p., 2020. Web. doi:10.1103/PhysRevLett.124.206803.
Yates, Daniel, Abanov, Alexander, & Mitra, Aditi. Lifetime of Almost Strong Edge-Mode Operators in One-Dimensional, Interacting, Symmetry Protected Topological Phases. United States. doi:https://doi.org/10.1103/PhysRevLett.124.206803
Yates, Daniel, Abanov, Alexander, and Mitra, Aditi. Fri . "Lifetime of Almost Strong Edge-Mode Operators in One-Dimensional, Interacting, Symmetry Protected Topological Phases". United States. doi:https://doi.org/10.1103/PhysRevLett.124.206803.
@article{osti_1630429,
title = {Lifetime of Almost Strong Edge-Mode Operators in One-Dimensional, Interacting, Symmetry Protected Topological Phases},
author = {Yates, Daniel and Abanov, Alexander and Mitra, Aditi},
abstractNote = {Almost strong edge-mode operators arising at the boundaries of certain interacting one-dimensional symmetry protected topological phases with Z2 symmetry have infinite temperature lifetimes that are nonperturbatively long in the integrability breaking terms, making them promising as bits for quantum information processing. We extract the lifetime of these edge-mode operators for small system sizes as well as in the thermodynamic limit. For the latter, a Lanczos scheme is employed to map the operator dynamics to a one-dimensional tight-binding model of a single particle in Krylov space. We suggest this model to be that of a spatially inhomogeneous Su-Schrieffer-Heeger model with a hopping amplitude that increases away from the boundary, and a dimerization that decreases away from the boundary. We associate this dimerized or staggered structure with the existence of the almost strong mode. Thus, the short time dynamics of the almost strong mode is that of the edge mode of the Su-Schrieffer-Heeger model, while the long time dynamics involves decay due to tunneling out of that mode, followed by chaotic operator spreading. Furthermore, we show that competing scattering processes can lead to interference effects that can significantly enhance the lifetime.},
doi = {10.1103/PhysRevLett.124.206803},
journal = {Physical Review Letters},
number = 20,
volume = 124,
place = {United States},
year = {2020},
month = {5}
}

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Works referenced in this record:

Parafermionic edge zero modes in Z n -invariant spin chains
journal, November 2012


Topological insulators and superconductors
journal, October 2011


Statistical localization: From strong fragmentation to strong edge modes
journal, March 2020


Anyons in an exactly solved model and beyond
journal, January 2006


Infinite coherence time of edge spins in finite-length chains
journal, February 2018


Soliton excitations in polyacetylene
journal, August 1980


Strong zero modes in a class of generalized Ising spin ladders with plaquette interactions
journal, July 2019


Asymptotics of Toeplitz determinants and the emptiness formation probability for the XY spin chain
journal, May 2005

  • Franchini, Fabio; Abanov, Alexander G.
  • Journal of Physics A: Mathematical and General, Vol. 38, Issue 23
  • DOI: 10.1088/0305-4470/38/23/002

A Universal Operator Growth Hypothesis
journal, October 2019


Quantized Hall Conductance in a Two-Dimensional Periodic Potential
journal, August 1982


Solitons in Polyacetylene
journal, June 1979


The noncommutative geometry of the quantum Hall effect
journal, October 1994

  • Bellissard, J.; van Elst, A.; Schulz‐ Baldes, H.
  • Journal of Mathematical Physics, Vol. 35, Issue 10
  • DOI: 10.1063/1.530758

Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures
journal, January 1997


On the evolution of operator complexity beyond scrambling
journal, October 2019

  • Barbón, J. L. F.; Rabinovici, E.; Shir, R.
  • Journal of High Energy Physics, Vol. 2019, Issue 10
  • DOI: 10.1007/JHEP10(2019)264

Strong zero modes and eigenstate phase transitions in the XYZ/interacting Majorana chain
journal, June 2016


Search for Majorana Fermions in Superconductors
journal, April 2013


New directions in the pursuit of Majorana fermions in solid state systems
journal, June 2012


A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems
journal, June 2017

  • Abanin, Dmitry; De Roeck, Wojciech; Ho, Wen Wei
  • Communications in Mathematical Physics, Vol. 354, Issue 3
  • DOI: 10.1007/s00220-017-2930-x

Almost strong ( 0 , π ) edge modes in clean interacting one-dimensional Floquet systems
journal, May 2019


Unpaired Majorana fermions in quantum wires
journal, October 2001


Prethermal Strong Zero Modes and Topological Qubits
journal, December 2017


Long coherence times for edge spins
journal, June 2017

  • Kemp, Jack; Yao, Norman Y.; Laumann, Christopher R.
  • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2017, Issue 6
  • DOI: 10.1088/1742-5468/aa73f0

Non-Abelian anyons and topological quantum computation
journal, September 2008


Enhancing correlation times for edge spins through dissipation
journal, September 2018


Parafermionic clock models and quantum resonance
journal, June 2017


Stability of zero modes in parafermion chains
journal, October 2014


Boundary conformal field theory and tunneling of edge quasiparticles in non-Abelian topological states
journal, July 2009


Topological phases of fermions in one dimension
journal, February 2011


Topological insulators and superconductors: tenfold way and dimensional hierarchy
journal, June 2010