Renormalization group study of random quantum magnets

Istvn A. Kovcs, F. Iglói

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

We have developed a very efficient numerical algorithm of the strong disorder renormalization group method to study the critical behaviour of the random transverse field Ising model, which is a prototype of random quantum magnets. With this algorithm we can renormalize an N-site cluster within a time NlogN, independently of the topology of the graph, and we went up to N ∼ 4 × 106. We have studied regular lattices with dimension D ≤ 4 as well as Erds-Rényi random graphs, which are infinite dimensional objects. In all cases the quantum critical behaviour is found to be controlled by an infinite disorder fixed point, in which disorder plays a dominant role over quantum fluctuations. As a consequence the renormalization procedure as well as the obtained critical properties are asymptotically exact for large systems. We have also studied Griffiths singularities in the paramagnetic and ferromagnetic phases and generalized the numerical algorithm for other random quantum systems.

Original languageEnglish
Article number404204
JournalJournal of Physics Condensed Matter
Volume23
Issue number40
DOIs
Publication statusPublished - Oct 12 2011

Fingerprint

Magnets
magnets
disorders
Ising model
renormalization group methods
topology
prototypes
Topology

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Materials Science(all)

Cite this

Renormalization group study of random quantum magnets. / Kovcs, Istvn A.; Iglói, F.

In: Journal of Physics Condensed Matter, Vol. 23, No. 40, 404204, 12.10.2011.

Research output: Contribution to journalArticle

@article{74947052c8444927ad5e2d722e4a1ad2,
title = "Renormalization group study of random quantum magnets",
abstract = "We have developed a very efficient numerical algorithm of the strong disorder renormalization group method to study the critical behaviour of the random transverse field Ising model, which is a prototype of random quantum magnets. With this algorithm we can renormalize an N-site cluster within a time NlogN, independently of the topology of the graph, and we went up to N ∼ 4 × 106. We have studied regular lattices with dimension D ≤ 4 as well as Erds-R{\'e}nyi random graphs, which are infinite dimensional objects. In all cases the quantum critical behaviour is found to be controlled by an infinite disorder fixed point, in which disorder plays a dominant role over quantum fluctuations. As a consequence the renormalization procedure as well as the obtained critical properties are asymptotically exact for large systems. We have also studied Griffiths singularities in the paramagnetic and ferromagnetic phases and generalized the numerical algorithm for other random quantum systems.",
author = "Kovcs, {Istvn A.} and F. Igl{\'o}i",
year = "2011",
month = "10",
day = "12",
doi = "10.1088/0953-8984/23/40/404204",
language = "English",
volume = "23",
journal = "Journal of Physics Condensed Matter",
issn = "0953-8984",
publisher = "IOP Publishing Ltd.",
number = "40",

}

TY - JOUR

T1 - Renormalization group study of random quantum magnets

AU - Kovcs, Istvn A.

AU - Iglói, F.

PY - 2011/10/12

Y1 - 2011/10/12

N2 - We have developed a very efficient numerical algorithm of the strong disorder renormalization group method to study the critical behaviour of the random transverse field Ising model, which is a prototype of random quantum magnets. With this algorithm we can renormalize an N-site cluster within a time NlogN, independently of the topology of the graph, and we went up to N ∼ 4 × 106. We have studied regular lattices with dimension D ≤ 4 as well as Erds-Rényi random graphs, which are infinite dimensional objects. In all cases the quantum critical behaviour is found to be controlled by an infinite disorder fixed point, in which disorder plays a dominant role over quantum fluctuations. As a consequence the renormalization procedure as well as the obtained critical properties are asymptotically exact for large systems. We have also studied Griffiths singularities in the paramagnetic and ferromagnetic phases and generalized the numerical algorithm for other random quantum systems.

AB - We have developed a very efficient numerical algorithm of the strong disorder renormalization group method to study the critical behaviour of the random transverse field Ising model, which is a prototype of random quantum magnets. With this algorithm we can renormalize an N-site cluster within a time NlogN, independently of the topology of the graph, and we went up to N ∼ 4 × 106. We have studied regular lattices with dimension D ≤ 4 as well as Erds-Rényi random graphs, which are infinite dimensional objects. In all cases the quantum critical behaviour is found to be controlled by an infinite disorder fixed point, in which disorder plays a dominant role over quantum fluctuations. As a consequence the renormalization procedure as well as the obtained critical properties are asymptotically exact for large systems. We have also studied Griffiths singularities in the paramagnetic and ferromagnetic phases and generalized the numerical algorithm for other random quantum systems.

UR - http://www.scopus.com/inward/record.url?scp=80053311808&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053311808&partnerID=8YFLogxK

U2 - 10.1088/0953-8984/23/40/404204

DO - 10.1088/0953-8984/23/40/404204

M3 - Article

C2 - 21931186

AN - SCOPUS:80053311808

VL - 23

JO - Journal of Physics Condensed Matter

JF - Journal of Physics Condensed Matter

SN - 0953-8984

IS - 40

M1 - 404204

ER -