Transport in the XX chain at zero temperature: Emergence of flat magnetization profiles

T. Antal, Z. Rácz, A. Rákos, G. M. Schütz

Research output: Contribution to journalArticle

102 Citations (Scopus)

Abstract

We study the connection between magnetization transport and magnetization profiles in zero-temperature XX chains. The time evolution of the transverse magnetization m(x,t) is calculated using an inhomogeneous initial state that is the ground state at fixed magnetization but with m reversed from -m0 for x0 for x>0. In the long-time limit, the magnetization evolves into a scaling form m(x,t)=Φ(x/t) and the profile develops a flat part (m=Φ=0) in the |x/t|≤c(m0) region. The flat region shrinks to zero if m0→1/2 while it expands with the maximum velocity c0=1 for m0→0. The states emerging in the scaling limit are compared to those of a homogeneous system where the same magnetization current is driven by a bulk field, and we find that the expectation values of various quantities (energy, occupation number in the fermionic representation) agree in the two systems.

Original languageEnglish
Pages (from-to)4912-4918
Number of pages7
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume59
Issue number5 B
Publication statusPublished - 1999

Fingerprint

Magnetization
magnetization
Zero
profiles
temperature
scaling
Scaling Limit
occupation
Expand
Ground State
Profile
emerging
Transverse
Scaling
ground state
Energy
energy

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics

Cite this

Transport in the XX chain at zero temperature : Emergence of flat magnetization profiles. / Antal, T.; Rácz, Z.; Rákos, A.; Schütz, G. M.

In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 59, No. 5 B, 1999, p. 4912-4918.

Research output: Contribution to journalArticle

@article{cef31d353eaa4503b5d5d5616be26109,
title = "Transport in the XX chain at zero temperature: Emergence of flat magnetization profiles",
abstract = "We study the connection between magnetization transport and magnetization profiles in zero-temperature XX chains. The time evolution of the transverse magnetization m(x,t) is calculated using an inhomogeneous initial state that is the ground state at fixed magnetization but with m reversed from -m0 for x0 for x>0. In the long-time limit, the magnetization evolves into a scaling form m(x,t)=Φ(x/t) and the profile develops a flat part (m=Φ=0) in the |x/t|≤c(m0) region. The flat region shrinks to zero if m0→1/2 while it expands with the maximum velocity c0=1 for m0→0. The states emerging in the scaling limit are compared to those of a homogeneous system where the same magnetization current is driven by a bulk field, and we find that the expectation values of various quantities (energy, occupation number in the fermionic representation) agree in the two systems.",
author = "T. Antal and Z. R{\'a}cz and A. R{\'a}kos and Sch{\"u}tz, {G. M.}",
year = "1999",
language = "English",
volume = "59",
pages = "4912--4918",
journal = "Physical review. E",
issn = "2470-0045",
publisher = "American Physical Society",
number = "5 B",

}

TY - JOUR

T1 - Transport in the XX chain at zero temperature

T2 - Emergence of flat magnetization profiles

AU - Antal, T.

AU - Rácz, Z.

AU - Rákos, A.

AU - Schütz, G. M.

PY - 1999

Y1 - 1999

N2 - We study the connection between magnetization transport and magnetization profiles in zero-temperature XX chains. The time evolution of the transverse magnetization m(x,t) is calculated using an inhomogeneous initial state that is the ground state at fixed magnetization but with m reversed from -m0 for x0 for x>0. In the long-time limit, the magnetization evolves into a scaling form m(x,t)=Φ(x/t) and the profile develops a flat part (m=Φ=0) in the |x/t|≤c(m0) region. The flat region shrinks to zero if m0→1/2 while it expands with the maximum velocity c0=1 for m0→0. The states emerging in the scaling limit are compared to those of a homogeneous system where the same magnetization current is driven by a bulk field, and we find that the expectation values of various quantities (energy, occupation number in the fermionic representation) agree in the two systems.

AB - We study the connection between magnetization transport and magnetization profiles in zero-temperature XX chains. The time evolution of the transverse magnetization m(x,t) is calculated using an inhomogeneous initial state that is the ground state at fixed magnetization but with m reversed from -m0 for x0 for x>0. In the long-time limit, the magnetization evolves into a scaling form m(x,t)=Φ(x/t) and the profile develops a flat part (m=Φ=0) in the |x/t|≤c(m0) region. The flat region shrinks to zero if m0→1/2 while it expands with the maximum velocity c0=1 for m0→0. The states emerging in the scaling limit are compared to those of a homogeneous system where the same magnetization current is driven by a bulk field, and we find that the expectation values of various quantities (energy, occupation number in the fermionic representation) agree in the two systems.

UR - http://www.scopus.com/inward/record.url?scp=4243241601&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4243241601&partnerID=8YFLogxK

M3 - Article

C2 - 11969443

AN - SCOPUS:4243241601

VL - 59

SP - 4912

EP - 4918

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 5 B

ER -