Exact dynamics in dual-unitary quantum circuits

By L. Piroli, B. Bertini, J. I. Cirac, Tomaz Prosen. Physical review B, 2019

176 citations recorded by the source corpus.

We consider the class of dual-unitary quantum circuits in 1 + 1 dimensions and introduce a notion of “solvable” matrix product states (MPSs), defined by a specific condition which allows us to tackle their time evolution analytically. We provide a classification of the latter, showing that they include certain MPSs of arbitrary bond dimension, and study analytically different aspects of their dynamics. For these initial states, we show that while any subsystem of size l reaches infinite temperature after a time t ∝ l, irrespective of the presence of conserved quantities, the light cone of two-point correlation functions displays qualitatively different features depending on the ergodicity of the quantum circuit, defined by the behavior of infinite-temperature dynamical correlation functions. Furthermore, we study the entanglement spreading from such solvable initial states, providing a closed formula for the time evolution of the entanglement entropy of a connected block. This generalizes recent results obtained in the context of the self-dual kicked Ising model. By comparison, we also consider a family of nonsolvable initial mixed states depending on one real parameter β, which, as β is varied from zero to infinity, interpolate between the infinite-temperature density matrix and arbitrary initial pure product states. We study analytically their dynamics for small values of β, and highlight the differences from the case of solvable MPSs.

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

View Paper: https://www.semanticscholar.org/paper/63036427269e86b2736b4ffcc4c6003f202d3bed

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Citations in the corpus

Entanglement Membrane in Chaotic Many-Body Systems (2019, methodology): “We also investigate a special case of the kicked Ising model that has maximal entanglement growth [35, 36] and the property of “dual unitarity” which, remarkably, allows a range of exact computations [36, 46–49].”