A quantum Monte Carlo algorithm realizing an intrinsic relaxation

Tota Nakamura, Yoshiyuki Ito

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We propose a new quantum Monte Carlo algorithm that realizes a relaxation intrinsic to an original quantum system. The Monte Carlo dynamics satisfies the dynamic scaling relation τ ∼ ξz and is independent of the Trotter number. The finiteness of the Trotter number appears as the finite-size effect. An infinite Trotter number version of the algorithm, which enables us to observe a true relaxation of the original system, is also formulated. The strategy of the algorithm is a compromise between a conventional worldline local flip and a modern cluster loop flip. It is a local flip in the real-space direction and is a cluster flip in the Trotter direction. The new algorithm is tested using the transverse-field Ising model in two dimensions. An accurate phase diagram is obtained.

Original languageEnglish
Pages (from-to)2405-2408
Number of pages4
JournalJournal of the Physical Society of Japan
Volume72
Issue number10
DOIs
Publication statusPublished - 2003 Oct
Externally publishedYes

Fingerprint

Ising model
phase diagrams
scaling

Keywords

  • Nonequilibrium relaxation method
  • Quantum dynamics
  • Quantum Monte Carlo method
  • Transverse-field Ising model

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

A quantum Monte Carlo algorithm realizing an intrinsic relaxation. / Nakamura, Tota; Ito, Yoshiyuki.

In: Journal of the Physical Society of Japan, Vol. 72, No. 10, 10.2003, p. 2405-2408.

Research output: Contribution to journalArticle

@article{eccb5fe48cb345dfbef68d86abcd0597,
title = "A quantum Monte Carlo algorithm realizing an intrinsic relaxation",
abstract = "We propose a new quantum Monte Carlo algorithm that realizes a relaxation intrinsic to an original quantum system. The Monte Carlo dynamics satisfies the dynamic scaling relation τ ∼ ξz and is independent of the Trotter number. The finiteness of the Trotter number appears as the finite-size effect. An infinite Trotter number version of the algorithm, which enables us to observe a true relaxation of the original system, is also formulated. The strategy of the algorithm is a compromise between a conventional worldline local flip and a modern cluster loop flip. It is a local flip in the real-space direction and is a cluster flip in the Trotter direction. The new algorithm is tested using the transverse-field Ising model in two dimensions. An accurate phase diagram is obtained.",
keywords = "Nonequilibrium relaxation method, Quantum dynamics, Quantum Monte Carlo method, Transverse-field Ising model",
author = "Tota Nakamura and Yoshiyuki Ito",
year = "2003",
month = "10",
doi = "10.1143/JPSJ.72.2405",
language = "English",
volume = "72",
pages = "2405--2408",
journal = "Journal of the Physical Society of Japan",
issn = "0031-9015",
publisher = "Physical Society of Japan",
number = "10",

}

TY - JOUR

T1 - A quantum Monte Carlo algorithm realizing an intrinsic relaxation

AU - Nakamura, Tota

AU - Ito, Yoshiyuki

PY - 2003/10

Y1 - 2003/10

N2 - We propose a new quantum Monte Carlo algorithm that realizes a relaxation intrinsic to an original quantum system. The Monte Carlo dynamics satisfies the dynamic scaling relation τ ∼ ξz and is independent of the Trotter number. The finiteness of the Trotter number appears as the finite-size effect. An infinite Trotter number version of the algorithm, which enables us to observe a true relaxation of the original system, is also formulated. The strategy of the algorithm is a compromise between a conventional worldline local flip and a modern cluster loop flip. It is a local flip in the real-space direction and is a cluster flip in the Trotter direction. The new algorithm is tested using the transverse-field Ising model in two dimensions. An accurate phase diagram is obtained.

AB - We propose a new quantum Monte Carlo algorithm that realizes a relaxation intrinsic to an original quantum system. The Monte Carlo dynamics satisfies the dynamic scaling relation τ ∼ ξz and is independent of the Trotter number. The finiteness of the Trotter number appears as the finite-size effect. An infinite Trotter number version of the algorithm, which enables us to observe a true relaxation of the original system, is also formulated. The strategy of the algorithm is a compromise between a conventional worldline local flip and a modern cluster loop flip. It is a local flip in the real-space direction and is a cluster flip in the Trotter direction. The new algorithm is tested using the transverse-field Ising model in two dimensions. An accurate phase diagram is obtained.

KW - Nonequilibrium relaxation method

KW - Quantum dynamics

KW - Quantum Monte Carlo method

KW - Transverse-field Ising model

UR - http://www.scopus.com/inward/record.url?scp=0242541689&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0242541689&partnerID=8YFLogxK

U2 - 10.1143/JPSJ.72.2405

DO - 10.1143/JPSJ.72.2405

M3 - Article

VL - 72

SP - 2405

EP - 2408

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 10

ER -