Locality, Quantum Fluctuations, and Scrambling

By Shenglong Xu, Brian Swingle. Physical Review X, 2018

137 citations recorded by the source corpus.

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 wavefront and other random circuit models showing a diffusively broadened wavefront. 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 wavefront. 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 cross-over to a diffusively broadened wavefront. 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 wavefront.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a22db731afd7501bb2985bf953c3d777bff6fa98

How researchers see this paper

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In Artificial Intelligence

1. A. Nahum
2. Matthew Fisher
3. V. Khemani
4. S. Vijay
5. E. Altman
6. D. Parker
7. Xiangyu Cao
8. Thomas Scaffidi

In Atomic and Molecular Physics, and Optics

1. A. Nahum
2. Matthew Fisher
3. V. Khemani
4. S. Vijay
5. E. Altman
6. D. Parker
7. Thomas Scaffidi
8. Xiangyu Cao

In Statistical and Nonlinear Physics

1. A. Nahum
2. V. Khemani
3. Matthew Fisher
4. S. Vijay
5. E. Altman
6. Xiangyu Cao
7. D. Huse

Citations in the corpus

• A Universal Operator Growth Hypothesis (2018, background): “[18] Shenglong Xu and Brian Swingle, “Locality, quantum fluctuations, and scrambling,” arXiv:1805.”
• Random Quantum Circuits (2022, background): “An example is the “Brownian circuit” (90, 91, 133, 236, 237): this is a Hamiltonian spin chain where the couplings fluctuate like white noise.”