Locality, Quantum Fluctuations, and Scrambling

Thermalization of chaotic quantum many-body systems under unitary time evolution is related to the growth in complexity of initially simple Heisenberg operators. Operator growth is a manifestation of information scrambling and can be diagnosed by out-of-time-order correlators (OTOCs). However, the b...

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Autores principales:	Shenglong Xu, Brian Swingle
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2019
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/91fa47a6f01e43769479444a90c74ee2
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spelling	oai:doaj.org-article:91fa47a6f01e43769479444a90c74ee22021-12-02T11:09:43ZLocality, Quantum Fluctuations, and Scrambling10.1103/PhysRevX.9.0310482160-3308https://doaj.org/article/91fa47a6f01e43769479444a90c74ee22019-09-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.9.031048http://doi.org/10.1103/PhysRevX.9.031048https://doaj.org/toc/2160-3308Thermalization of chaotic quantum many-body systems under unitary time evolution is related to the growth in complexity of initially simple Heisenberg operators. Operator growth is a manifestation of information scrambling and can be diagnosed by out-of-time-order correlators (OTOCs). However, the behavior of OTOCs of local operators in generic chaotic local Hamiltonians remains poorly understood, with some semiclassical and large-N models exhibiting exponential growth of OTOCs and a sharp chaos wave front and other random circuit models showing a diffusively broadened wave front. In this paper, we propose a unified physical picture for scrambling in chaotic local Hamiltonians. We construct a random time-dependent Hamiltonian model featuring a large-N limit where the OTOC obeys a Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) type equation and exhibits exponential growth and a sharp wave front. We show that quantum fluctuations manifest as noise (distinct from the randomness of the couplings in the underlying Hamiltonian) in the FKPP equation and that the noise-averaged OTOC exhibits a crossover to a diffusively broadened wave front. At small N, we demonstrate that operator growth dynamics, averaged over the random couplings, can be efficiently simulated for all time using matrix product state techniques. To show that time-dependent randomness is not essential to our conclusions, we push our previous matrix product operator methods to very large size and show that data for a time-independent Hamiltonian model are also consistent with a diffusively broadened wave front.Shenglong XuBrian SwingleAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 9, Iss 3, p 031048 (2019)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Shenglong Xu Brian Swingle Locality, Quantum Fluctuations, and Scrambling
description	Thermalization of chaotic quantum many-body systems under unitary time evolution is related to the growth in complexity of initially simple Heisenberg operators. Operator growth is a manifestation of information scrambling and can be diagnosed by out-of-time-order correlators (OTOCs). However, the behavior of OTOCs of local operators in generic chaotic local Hamiltonians remains poorly understood, with some semiclassical and large-N models exhibiting exponential growth of OTOCs and a sharp chaos wave front and other random circuit models showing a diffusively broadened wave front. In this paper, we propose a unified physical picture for scrambling in chaotic local Hamiltonians. We construct a random time-dependent Hamiltonian model featuring a large-N limit where the OTOC obeys a Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) type equation and exhibits exponential growth and a sharp wave front. We show that quantum fluctuations manifest as noise (distinct from the randomness of the couplings in the underlying Hamiltonian) in the FKPP equation and that the noise-averaged OTOC exhibits a crossover to a diffusively broadened wave front. At small N, we demonstrate that operator growth dynamics, averaged over the random couplings, can be efficiently simulated for all time using matrix product state techniques. To show that time-dependent randomness is not essential to our conclusions, we push our previous matrix product operator methods to very large size and show that data for a time-independent Hamiltonian model are also consistent with a diffusively broadened wave front.
format	article
author	Shenglong Xu Brian Swingle
author_facet	Shenglong Xu Brian Swingle
author_sort	Shenglong Xu
title	Locality, Quantum Fluctuations, and Scrambling
title_short	Locality, Quantum Fluctuations, and Scrambling
title_full	Locality, Quantum Fluctuations, and Scrambling
title_fullStr	Locality, Quantum Fluctuations, and Scrambling
title_full_unstemmed	Locality, Quantum Fluctuations, and Scrambling
title_sort	locality, quantum fluctuations, and scrambling
publisher	American Physical Society
publishDate	2019
url	https://doaj.org/article/91fa47a6f01e43769479444a90c74ee2
work_keys_str_mv	AT shenglongxu localityquantumfluctuationsandscrambling AT brianswingle localityquantumfluctuationsandscrambling
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Locality, Quantum Fluctuations, and Scrambling

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