Operator and Entanglement Dynamics in Asymmetric Quantum Systems

Abstract

Thermalization is an important aspect in quantum physics from condensed matter to black holes. It allows initially local information to be spread and hidden throughout a system. This spreading happens at a finite speed, and can be quantified using the butterfly velocity vB or the entanglement velocity vE. These speeds are well-studied, and are independent of each other up to the constraint vB > vE. Although it is possible to have a direction-dependent vB, little work has been done to study systems like this. In this thesis we study two systems on spin chains with asymmetric butterfly velocities, which we call vB±. In the first, a system with a time-independent Hamiltonian, we study vB through operator spreading. We show that the system is slightly asymmetric, with vB+ > vB−. The second system is a quantum circuit with random unitary dynamics. Using entanglement dynamics to measure the butterfly velocity, we show that these systems can have vB+/vB− arbitrarily large.