Accessing scrambling using matrix product operators

By Shenglong Xu, Brian Swingle. Nature Physics, 2018

160 citations recorded by the source corpus.

Scrambling, a process in which quantum information spreads over a complex quantum system, becoming inaccessible to simple probes, occurs in generic chaotic quantum many-body systems, ranging from spin chains to metals and even to black holes. Scrambling can be measured using out-of-time-ordered correlators (OTOCs), which are closely tied to the growth of Heisenberg operators. We present a general method to calculate OTOCs of local operators in one-dimensional systems based on approximating Heisenberg operators as matrix product operators (MPOs). Contrary to the common belief that such tensor network methods work only at early times, we show that the entire early growth region of the OTOC can be captured using an MPO approximation with modest bond dimension. We analytically establish the goodness of the approximation by showing that, if an appropriate OTOC is close to its initial value, then the associated Heisenberg operator has low entanglement across a given cut. We use the method to study scrambling in a chaotic spin chain with $$201$$ 201 sites. On the basis of these data and previous results, we conjecture a universal form for the dynamics of the OTOC near the wavefront. We show that this form collapses the chaotic spin chain data over more than 15 orders of magnitude. A general method is proposed to calculate the out-of-time-ordered correlators (OTOCs) in one-dimensional systems. Motivated by the results obtained from its application to various systems, a universal form for the dynamics of OTOCs is conjectured.

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

View Paper: https://www.semanticscholar.org/paper/5588cb4820e5500a71ed38c8d03508d3a0204d15

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

A Universal Operator Growth Hypothesis (2018, unknown): “[17] Shenglong Xu and Brian Swingle, “Accessing scrambling using matrix product operators,” arXiv:1802.”
Quantum epidemiology: operator growth, thermal effects, and SYK (2018, background): “1 Systems with both spatial locality and a large number of internal degrees of freedom–such as (chaotic) field theories in the large-N limit – display both linear spatial growth and exponential internal size growth [12–16].”
Scrambling Dynamics and Out-of-Time-Ordered Correlators in Quantum Many-Body Systems (2022, methodology): “ing spin chains [66, 67] and circuit models [68–71].”
Velocity-dependent Lyapunov exponents in many-body quantum, semiclassical, and classical chaos (2018, background): “manuscript, a study [86] conjecturing the form of the OTOC in Eq.”