Sachdev–Ye–Kitaev model as Liouville quantum mechanics

Dmitry Bagrets; Alexander Altland; Alex Kamenev

doi:10.1016/j.nuclphysb.2016.08.002

Sachdev–Ye–Kitaev model as Liouville quantum mechanics

Dmitry Bagrets, Alexander Altland, Alex Kamenev

Physics and Astronomy (Twin Cities)

Research output: Contribution to journal › Article › peer-review

187 Scopus citations

Abstract

We show that the proper inclusion of soft reparameterization modes in the Sachdev–Ye–Kitaev model of N randomly interacting Majorana fermions reduces its long-time behavior to that of Liouville quantum mechanics. As a result, all zero temperature correlation functions decay with the universal exponent ∝τ^−3/2 for times larger than the inverse single particle level spacing τ≫Nln⁡N. In the particular case of the single particle Green function this behavior is manifestation of the zero-bias anomaly, or scaling in energy as ϵ^1/2. We also present exact diagonalization study supporting our conclusions.

Original language	English (US)
Pages (from-to)	191-205
Number of pages	15
Journal	Nuclear Physics B
Volume	911
DOIs	https://doi.org/10.1016/j.nuclphysb.2016.08.002
State	Published - Oct 1 2016

Bibliographical note

Funding Information:
We thank L.I. Glazman for bringing the problem to our attention. A.K. was supported by DOE contract DEFG02-08ER46482 , and acknowledges support by QM2–Quantum Matter and Materials of Cologne University . Work supported by CRC 183 of the Deutsche Forschungsgemeinschaft .

Publisher Copyright:
© 2016 The Author(s)

Publisher link

10.1016/j.nuclphysb.2016.08.002

Find It

Find It at U of M Libraries

Cite this

@article{e4c947d87051419597b53d78910eae48,

title = "Sachdev–Ye–Kitaev model as Liouville quantum mechanics",

abstract = "We show that the proper inclusion of soft reparameterization modes in the Sachdev–Ye–Kitaev model of N randomly interacting Majorana fermions reduces its long-time behavior to that of Liouville quantum mechanics. As a result, all zero temperature correlation functions decay with the universal exponent ∝τ−3/2 for times larger than the inverse single particle level spacing τ≫Nln⁡N. In the particular case of the single particle Green function this behavior is manifestation of the zero-bias anomaly, or scaling in energy as ϵ1/2. We also present exact diagonalization study supporting our conclusions.",

author = "Dmitry Bagrets and Alexander Altland and Alex Kamenev",

note = "Funding Information: We thank L.I. Glazman for bringing the problem to our attention. A.K. was supported by DOE contract DEFG02-08ER46482 , and acknowledges support by QM2–Quantum Matter and Materials of Cologne University . Work supported by CRC 183 of the Deutsche Forschungsgemeinschaft . Publisher Copyright: {\textcopyright} 2016 The Author(s)",

year = "2016",

month = oct,

day = "1",

doi = "10.1016/j.nuclphysb.2016.08.002",

language = "English (US)",

volume = "911",

pages = "191--205",

journal = "Nuclear Physics B",

issn = "0550-3213",

publisher = "Elsevier",

}

TY - JOUR

T1 - Sachdev–Ye–Kitaev model as Liouville quantum mechanics

AU - Bagrets, Dmitry

AU - Altland, Alexander

AU - Kamenev, Alex

N1 - Funding Information: We thank L.I. Glazman for bringing the problem to our attention. A.K. was supported by DOE contract DEFG02-08ER46482 , and acknowledges support by QM2–Quantum Matter and Materials of Cologne University . Work supported by CRC 183 of the Deutsche Forschungsgemeinschaft . Publisher Copyright: © 2016 The Author(s)

PY - 2016/10/1

Y1 - 2016/10/1

N2 - We show that the proper inclusion of soft reparameterization modes in the Sachdev–Ye–Kitaev model of N randomly interacting Majorana fermions reduces its long-time behavior to that of Liouville quantum mechanics. As a result, all zero temperature correlation functions decay with the universal exponent ∝τ−3/2 for times larger than the inverse single particle level spacing τ≫Nln⁡N. In the particular case of the single particle Green function this behavior is manifestation of the zero-bias anomaly, or scaling in energy as ϵ1/2. We also present exact diagonalization study supporting our conclusions.

AB - We show that the proper inclusion of soft reparameterization modes in the Sachdev–Ye–Kitaev model of N randomly interacting Majorana fermions reduces its long-time behavior to that of Liouville quantum mechanics. As a result, all zero temperature correlation functions decay with the universal exponent ∝τ−3/2 for times larger than the inverse single particle level spacing τ≫Nln⁡N. In the particular case of the single particle Green function this behavior is manifestation of the zero-bias anomaly, or scaling in energy as ϵ1/2. We also present exact diagonalization study supporting our conclusions.

UR - http://www.scopus.com/inward/record.url?scp=84981332562&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84981332562&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2016.08.002

DO - 10.1016/j.nuclphysb.2016.08.002

M3 - Article

AN - SCOPUS:84981332562

SN - 0550-3213

VL - 911

SP - 191

EP - 205

JO - Nuclear Physics B

JF - Nuclear Physics B

ER -

Sachdev–Ye–Kitaev model as Liouville quantum mechanics

Abstract

Bibliographical note

Publisher link

Find It

Other files and links

Fingerprint

Cite this