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Scaling theory of topological phase transitions

Topologically ordered systems are characterized by topological invariants that are often calculated from the momentum space integration of a certain function that represents the curvature of the many-body state. The curvature function may be Berry curvature, Berry connection, or other quantities dep... Full description

Journal Title: Journal of Physics: Condensed Matter 2016, Vol.28(5), p.055601 (7pp)
Main Author: Chen, Wei
Format: Electronic Article Electronic Article
Language: English
Subjects:
ID: ISSN: 0953-8984 ; E-ISSN: 1361-648X ; DOI: 10.1088/0953-8984/28/5/055601
Link: http://dx.doi.org/10.1088/0953-8984/28/5/055601
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recordid: iop10.1088/0953-8984/28/5/055601
title: Scaling theory of topological phase transitions
format: Article
creator:
  • Chen, Wei
subjects:
  • Condensed Matter - Mesoscale And Nanoscale Physics
  • Condensed Matter - Statistical Mechanics
ispartof: Journal of Physics: Condensed Matter, 2016, Vol.28(5), p.055601 (7pp)
description: Topologically ordered systems are characterized by topological invariants that are often calculated from the momentum space integration of a certain function that represents the curvature of the many-body state. The curvature function may be Berry curvature, Berry connection, or other quantities depending on the system. Akin to stretching a messy string to reveal the number of knots it contains, a scaling procedure is proposed for the curvature function in inversion symmetric systems, from which the topological phase transition can be identified from the flow of the driving energy parameters that control the topology (hopping, chemical potential, etc) under scaling. At an infinitesimal operation, one obtains the renormalization group (RG) equations for the driving energy parameters. A length scale defined from the curvature function near the gap-closing momentum is suggested to characterize the scale invariance at critical points and fixed points, and displays a universal critical behavior in a variety of systems examined.
language: eng
source:
identifier: ISSN: 0953-8984 ; E-ISSN: 1361-648X ; DOI: 10.1088/0953-8984/28/5/055601
fulltext: no_fulltext
issn:
  • 0953-8984
  • 1361-648X
  • 09538984
  • 1361648X
url: Link


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descriptionTopologically ordered systems are characterized by topological invariants that are often calculated from the momentum space integration of a certain function that represents the curvature of the many-body state. The curvature function may be Berry curvature, Berry connection, or other quantities depending on the system. Akin to stretching a messy string to reveal the number of knots it contains, a scaling procedure is proposed for the curvature function in inversion symmetric systems, from which the topological phase transition can be identified from the flow of the driving energy parameters that control the topology (hopping, chemical potential, etc) under scaling. At an infinitesimal operation, one obtains the renormalization group (RG) equations for the driving energy parameters. A length scale defined from the curvature function near the gap-closing momentum is suggested to characterize the scale invariance at critical points and fixed points, and displays a universal critical behavior in a variety of systems examined.
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abstractTopologically ordered systems are characterized by topological invariants that are often calculated from the momentum space integration of a certain function that represents the curvature of the many-body state. The curvature function may be Berry curvature, Berry connection, or other quantities depending on the system. Akin to stretching a messy string to reveal the number of knots it contains, a scaling procedure is proposed for the curvature function in inversion symmetric systems, from which the topological phase transition can be identified from the flow of the driving energy parameters that control the topology (hopping, chemical potential, etc) under scaling. At an infinitesimal operation, one obtains the renormalization group (RG) equations for the driving energy parameters. A length scale defined from the curvature function near the gap-closing momentum is suggested to characterize the scale invariance at critical points and fixed points, and displays a universal critical behavior in a variety of systems examined.
doi10.1088/0953-8984/28/5/055601
date2016-02-10