Spatiotemporal evolution of topological order upon quantum quench across the critical point

Minchul Lee, Seungju Han, Mahn-Soo Choi

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We consider a topological superconducting wire and use the string order parameter to investigate the spatiotemporal evolution of the topological order upon a quantum quench across the critical point. We also analyze the propagation of the initially localized Majorana bound states after the quench, in order to examine the connection between the topological order and the unpaired Majorana states, which has been well established at equilibrium but remains illusive in dynamical situations. It is found that after the quench the string order parameters decay over a finite time and that the decaying behavior is universal, independent of the wire length and the final value of the chemical potential (the quenching parameter). It is also found that the topological order is revived repeatedly although the amplitude gradually decreases. Further, the topological order can propagate into the region which was initially in the nontopological state. It is observed that all these behaviors are in parallel and consistent with the propagation and dispersion of the Majorana wave functions. Finally, we propose local probing methods which can measure the nonlocal topological order.

Original languageEnglish
Article number063004
JournalNew Journal of Physics
Volume18
Issue number6
DOIs
Publication statusPublished - 2016 Jun 1

Fingerprint

critical point
strings
wire
propagation
quenching
wave functions
decay

Keywords

  • Majorana Fermion
  • quantum quenching
  • string order parameter
  • topological order
  • topological phase transition
  • topological superconductor

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Spatiotemporal evolution of topological order upon quantum quench across the critical point. / Lee, Minchul; Han, Seungju; Choi, Mahn-Soo.

In: New Journal of Physics, Vol. 18, No. 6, 063004, 01.06.2016.

Research output: Contribution to journalArticle

@article{b3475cb0cc654a778d3b5c16d1958f96,
title = "Spatiotemporal evolution of topological order upon quantum quench across the critical point",
abstract = "We consider a topological superconducting wire and use the string order parameter to investigate the spatiotemporal evolution of the topological order upon a quantum quench across the critical point. We also analyze the propagation of the initially localized Majorana bound states after the quench, in order to examine the connection between the topological order and the unpaired Majorana states, which has been well established at equilibrium but remains illusive in dynamical situations. It is found that after the quench the string order parameters decay over a finite time and that the decaying behavior is universal, independent of the wire length and the final value of the chemical potential (the quenching parameter). It is also found that the topological order is revived repeatedly although the amplitude gradually decreases. Further, the topological order can propagate into the region which was initially in the nontopological state. It is observed that all these behaviors are in parallel and consistent with the propagation and dispersion of the Majorana wave functions. Finally, we propose local probing methods which can measure the nonlocal topological order.",
keywords = "Majorana Fermion, quantum quenching, string order parameter, topological order, topological phase transition, topological superconductor",
author = "Minchul Lee and Seungju Han and Mahn-Soo Choi",
year = "2016",
month = "6",
day = "1",
doi = "10.1088/1367-2630/18/6/063004",
language = "English",
volume = "18",
journal = "New Journal of Physics",
issn = "1367-2630",
publisher = "IOP Publishing Ltd.",
number = "6",

}

TY - JOUR

T1 - Spatiotemporal evolution of topological order upon quantum quench across the critical point

AU - Lee, Minchul

AU - Han, Seungju

AU - Choi, Mahn-Soo

PY - 2016/6/1

Y1 - 2016/6/1

N2 - We consider a topological superconducting wire and use the string order parameter to investigate the spatiotemporal evolution of the topological order upon a quantum quench across the critical point. We also analyze the propagation of the initially localized Majorana bound states after the quench, in order to examine the connection between the topological order and the unpaired Majorana states, which has been well established at equilibrium but remains illusive in dynamical situations. It is found that after the quench the string order parameters decay over a finite time and that the decaying behavior is universal, independent of the wire length and the final value of the chemical potential (the quenching parameter). It is also found that the topological order is revived repeatedly although the amplitude gradually decreases. Further, the topological order can propagate into the region which was initially in the nontopological state. It is observed that all these behaviors are in parallel and consistent with the propagation and dispersion of the Majorana wave functions. Finally, we propose local probing methods which can measure the nonlocal topological order.

AB - We consider a topological superconducting wire and use the string order parameter to investigate the spatiotemporal evolution of the topological order upon a quantum quench across the critical point. We also analyze the propagation of the initially localized Majorana bound states after the quench, in order to examine the connection between the topological order and the unpaired Majorana states, which has been well established at equilibrium but remains illusive in dynamical situations. It is found that after the quench the string order parameters decay over a finite time and that the decaying behavior is universal, independent of the wire length and the final value of the chemical potential (the quenching parameter). It is also found that the topological order is revived repeatedly although the amplitude gradually decreases. Further, the topological order can propagate into the region which was initially in the nontopological state. It is observed that all these behaviors are in parallel and consistent with the propagation and dispersion of the Majorana wave functions. Finally, we propose local probing methods which can measure the nonlocal topological order.

KW - Majorana Fermion

KW - quantum quenching

KW - string order parameter

KW - topological order

KW - topological phase transition

KW - topological superconductor

UR - http://www.scopus.com/inward/record.url?scp=84976871184&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84976871184&partnerID=8YFLogxK

U2 - 10.1088/1367-2630/18/6/063004

DO - 10.1088/1367-2630/18/6/063004

M3 - Article

AN - SCOPUS:84976871184

VL - 18

JO - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

IS - 6

M1 - 063004

ER -