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:
-
- New York University (NYU), NY (United States)
- 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. 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. https://doi.org/10.1103/PhysRevLett.124.206803. https://www.osti.gov/servlets/purl/1630429.
@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 = {Fri May 22 00:00:00 EDT 2020},
month = {Fri May 22 00:00:00 EDT 2020}
}
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Works referenced in this record:
Parafermionic edge zero modes in Z n -invariant spin chains
journal, November 2012
- Fendley, Paul
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2012, Issue 11
Topological insulators and superconductors
journal, October 2011
- Qi, Xiao-Liang; Zhang, Shou-Cheng
- Reviews of Modern Physics, Vol. 83, Issue 4
Statistical localization: From strong fragmentation to strong edge modes
journal, March 2020
- Rakovszky, Tibor; Sala, Pablo; Verresen, Ruben
- Physical Review B, Vol. 101, Issue 12
Anyons in an exactly solved model and beyond
journal, January 2006
- Kitaev, Alexei
- Annals of Physics, Vol. 321, Issue 1
Infinite coherence time of edge spins in finite-length chains
journal, February 2018
- Maceira, Ivo A.; Mila, Frédéric
- Physical Review B, Vol. 97, Issue 6
Soliton excitations in polyacetylene
journal, August 1980
- Su, W. P.; Schrieffer, J. R.; Heeger, A. J.
- Physical Review B, Vol. 22, Issue 4
Strong zero modes in a class of generalized Ising spin ladders with plaquette interactions
journal, July 2019
- Vasiloiu, Loredana M.; Carollo, Federico; Marcuzzi, Matteo
- Physical Review B, Vol. 100, Issue 2
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
A Universal Operator Growth Hypothesis
journal, October 2019
- Parker, Daniel E.; Cao, Xiangyu; Avdoshkin, Alexander
- Physical Review X, Vol. 9, Issue 4
Quantized Hall Conductance in a Two-Dimensional Periodic Potential
journal, August 1982
- Thouless, D. J.; Kohmoto, M.; Nightingale, M. P.
- Physical Review Letters, Vol. 49, Issue 6
Solitons in Polyacetylene
journal, June 1979
- Su, W. P.; Schrieffer, J. R.; Heeger, A. J.
- Physical Review Letters, Vol. 42, Issue 25
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
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
Strong zero modes and eigenstate phase transitions in the XYZ/interacting Majorana chain
journal, June 2016
- Fendley, Paul
- Journal of Physics A: Mathematical and Theoretical, Vol. 49, Issue 30
Search for Majorana Fermions in Superconductors
journal, April 2013
- Beenakker, C. W. J.
- Annual Review of Condensed Matter Physics, Vol. 4, Issue 1
New directions in the pursuit of Majorana fermions in solid state systems
journal, June 2012
- Alicea, Jason
- Reports on Progress in Physics, Vol. 75, Issue 7
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
Almost strong ( ) edge modes in clean interacting one-dimensional Floquet systems
journal, May 2019
- Yates, Daniel J.; Essler, Fabian H. L.; Mitra, Aditi
- Physical Review B, Vol. 99, Issue 20
Unpaired Majorana fermions in quantum wires
journal, October 2001
- Kitaev, A. Yu
- Physics-Uspekhi, Vol. 44, Issue 10S
Prethermal Strong Zero Modes and Topological Qubits
journal, December 2017
- Else, Dominic V.; Fendley, Paul; Kemp, Jack
- Physical Review X, Vol. 7, Issue 4
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
Non-Abelian anyons and topological quantum computation
journal, September 2008
- Nayak, Chetan; Simon, Steven H.; Stern, Ady
- Reviews of Modern Physics, Vol. 80, Issue 3
Enhancing correlation times for edge spins through dissipation
journal, September 2018
- Vasiloiu, Loredana M.; Carollo, Federico; Garrahan, Juan P.
- Physical Review B, Vol. 98, Issue 9
Parafermionic clock models and quantum resonance
journal, June 2017
- Moran, N.; Pellegrino, D.; Slingerland, J. K.
- Physical Review B, Vol. 95, Issue 23
Stability of zero modes in parafermion chains
journal, October 2014
- Jermyn, Adam S.; Mong, Roger S. K.; Alicea, Jason
- Physical Review B, Vol. 90, Issue 16
Boundary conformal field theory and tunneling of edge quasiparticles in non-Abelian topological states
journal, July 2009
- Fendley, Paul; Fisher, Matthew P. A.; Nayak, Chetan
- Annals of Physics, Vol. 324, Issue 7
Topological phases of fermions in one dimension
journal, February 2011
- Fidkowski, Lukasz; Kitaev, Alexei
- Physical Review B, Vol. 83, Issue 7
Topological insulators and superconductors: tenfold way and dimensional hierarchy
journal, June 2010
- Ryu, Shinsei; Schnyder, Andreas P.; Furusaki, Akira
- New Journal of Physics, Vol. 12, Issue 6
Topologically Protected Long Edge Coherence Times in Symmetry-Broken Phases
journal, June 2019
- Parker, Daniel E.; Vasseur, Romain; Scaffidi, Thomas
- Physical Review Letters, Vol. 122, Issue 24