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Abstract |
In the past decade a great deal of progress has been made in the study of many-body systems out of
equilibrium, where certain integrable models have played a significant role in our understanding of specific
but prototypical problems. Even in these cases, however, the full relaxation dynamics has proven to be
hard to tackle in the presence of interactions, both analytically and numerically. In this talk, I will discuss
how analytically tractable systems may be obtained by considering 1D “quantum circuit’’ toy models for
the many-body dynamics, allowing for analytic solutions even in the absence of conservation laws (i.e.
integrability). I will focus on a class of chaotic “dual-unitary” quantum circuits, and certain integrable
quantum cellular automata, showing that in both cases the dynamics of correlation functions and
entanglement can be described exactly. Our approach is based on a representation of the effect of the
global evolution on finite subsystems in terms of tensor networks, which is applicable even beyond the
exactly solvable cases presented. I will conclude by discussing how related ideas may lead to the
construction of more general solvable dynamics beyond integrability. |
