Randomness and chaos in qubit models

Randomness and chaos in qubit models

We introduce randomness into a class of integrable models and study the spectral form factor as a diagnostic to distinguish between randomness and chaos. Spectral form factors exhibit a characteristic dip-ramp-plateau behavior in the N>2 SYK2 model at high temperatures that is absent in the N=2 S...

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Main Authors: Pak Hang Chris Lau, Chen-Te Ma, Jeff Murugan, Masaki Tezuka
Format: Article
Language:English
Published: Elsevier 2019-08-01
Series:Physics Letters B
Online Access:http://www.sciencedirect.com/science/article/pii/S0370269319304137
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spelling doaj-e0fae98653de467c85a4348f150ffed32020-11-25T00:47:58ZengElsevierPhysics Letters B0370-26932019-08-01795230235Randomness and chaos in qubit modelsPak Hang Chris Lau0Chen-Te Ma1Jeff Murugan2Masaki Tezuka3National Center for Theoretical Sciences, National Tsing-Hua University, Hsinchu 30013, Taiwan, ROC; Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA02139, USASchool of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China; The Laboratory for Quantum Gravity and Strings, Department of Mathematics and Applied Mathematics, University Of Cape Town, Private Bag, Rondebosch, 7701, South Africa; Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei 10617, Taiwan, ROC; Corresponding author at: School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China.The Laboratory for Quantum Gravity and Strings, Department of Mathematics and Applied Mathematics, University Of Cape Town, Private Bag, Rondebosch, 7701, South Africa; Kavli Institute for Theoretical Physics University of California, Santa Barbara, CA 93106, USADepartment of Physics, Kyoto University, Kyoto 606-8502, JapanWe introduce randomness into a class of integrable models and study the spectral form factor as a diagnostic to distinguish between randomness and chaos. Spectral form factors exhibit a characteristic dip-ramp-plateau behavior in the N>2 SYK2 model at high temperatures that is absent in the N=2 SYK2 model. Our results suggest that this dip-ramp-plateau behavior implies the existence of random eigenvectors in a quantum many-body system. To further support this observation, we examine the Gaussian random transverse Ising model and obtain consistent results without suffering from small N issues. Finally, we demonstrate numerically that expectation values of observables computed in a random quantum state at late times are equivalent to the expectation values computed in the thermal ensemble in a Gaussian random one-qubit model. Keywords: Randomness, Chaos, Spectral From Factor, Thermal Ensemblehttp://www.sciencedirect.com/science/article/pii/S0370269319304137
collection DOAJ
language English
format Article
sources DOAJ
author Pak Hang Chris Lau
Chen-Te Ma
Jeff Murugan
Masaki Tezuka
spellingShingle Pak Hang Chris Lau
Chen-Te Ma
Jeff Murugan
Masaki Tezuka
Randomness and chaos in qubit models
Physics Letters B
author_facet Pak Hang Chris Lau
Chen-Te Ma
Jeff Murugan
Masaki Tezuka
author_sort Pak Hang Chris Lau
title Randomness and chaos in qubit models
title_short Randomness and chaos in qubit models
title_full Randomness and chaos in qubit models
title_fullStr Randomness and chaos in qubit models
title_full_unstemmed Randomness and chaos in qubit models
title_sort randomness and chaos in qubit models
publisher Elsevier
series Physics Letters B
issn 0370-2693
publishDate 2019-08-01
description We introduce randomness into a class of integrable models and study the spectral form factor as a diagnostic to distinguish between randomness and chaos. Spectral form factors exhibit a characteristic dip-ramp-plateau behavior in the N>2 SYK2 model at high temperatures that is absent in the N=2 SYK2 model. Our results suggest that this dip-ramp-plateau behavior implies the existence of random eigenvectors in a quantum many-body system. To further support this observation, we examine the Gaussian random transverse Ising model and obtain consistent results without suffering from small N issues. Finally, we demonstrate numerically that expectation values of observables computed in a random quantum state at late times are equivalent to the expectation values computed in the thermal ensemble in a Gaussian random one-qubit model. Keywords: Randomness, Chaos, Spectral From Factor, Thermal Ensemble
url http://www.sciencedirect.com/science/article/pii/S0370269319304137
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AT chentema randomnessandchaosinqubitmodels
AT jeffmurugan randomnessandchaosinqubitmodels
AT masakitezuka randomnessandchaosinqubitmodels
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