Asymmetric butterfly velocities in Hamiltonian and circuit models

Abstract

The butterfly velocity $v_B$ has been proposed as a characteristic velocity for information propagation in local systems. It can be measured by the ballistic spreading of local operators in time (or, equivalently, by out-of-time-ordered commutators). In general, this velocity can depend on the direction of spreading and, indeed, the asymmetry between different directions can be made arbitrarily large using arbitrarily deep quantum circuits. Nevertheless, in almost all examples of local time-independent Hamiltonians that have been examined thus far, this velocity is independent of the direction of information propagation. In this work, we present two models with asymmetric $v_B$. The first is a time-independent Hamiltonian in one dimension with local, 3-site interactions. The second is a class of local unitary circuits, which we call $n$-staircases, where $n$ serves as a tunable parameter interpolating from $n=1$ with symmetric spreading to $n=\infty$ with completely chiral information propagation.

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Cited by in corpus (6)

• The entanglement membrane in chaotic many-body systems
• Quantum Information Scrambling in Quantum Many-body Scarred Systems
• Real-time correlators in chaotic quantum many-body systems
• Operator Spreading in the Memory Matrix Formalism
• Anomalous Quantum Information Scrambling for ${\mathbb{Z}}_3$ Parafermion Chains
• Directional scrambling of quantum information in helical multiferroics