Abstract
We introduce a novel class of quantum circuits that are unitary along three distinct "arrows of time". These dynamics share some of the analytical tractability of "dual-unitary" circuits, while exhibiting distinctive and richer phenomenology. We find that two-point correlations in these dynamics are strictly confined to three directions in $(1+1)$-dimensional spacetime -- the two light cone edges, $\delta x=\pm v\delta t$, and the static worldline $\delta x=0$. Along these directions, correlation functions are obtained exactly in terms of quantum channels built from the individual gates that make up the circuit. We prove that, for a class of initial states, entanglement grows at the maximum allowed speed up to an entropy density of at least one half of the thermal value, at which point it becomes model-dependent. Finally, we extend our circuit construction to $2+1$ dimensions, where two-point correlation functions are confined to the one-dimensional edges of a tetrahedral light cone -- a subdimensional propagation of information reminiscent of "fractonic" physics.
Highlights
The dynamics of quantum many-body systems play a central role in many areas of physics, from nonequilibrium statistical mechanics to applied quantum information science
We have introduced a large family of quantum many-body evolutions, dubbed triunitary circuits, in which crucial properties including correlations and entanglement are analytically tractable
This tractability stems from their peculiar causal structure, which features three distinct “arrows of time” under which the dynamics are unitary
Summary
The dynamics of quantum many-body systems play a central role in many areas of physics, from nonequilibrium statistical mechanics to applied quantum information science. These models allow us to extend and generalize results obtained on “dual-unitary” models.
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