It is a notoriously hard problem to access the long-time dynamics of a many-body system after a global quench with tensor network methods, due to the linear growth of entanglement with time.
In this talk, I will revisit a clever approach that attempts to overcome this limitation by approximating correlation functions on infinite systems with matrix product states (MPSs) in the temporal direction.
I will provide non-trivial examples of strictly discrete dynamics where this MPS approximation becomes efficient (and even exact in some cases!), allowing one to compute expectation values of local observables for arbitrarily long times.
Finally, I will discuss how the infinite-time steady state of this discrete dynamics connects to the time-continuum limit, and establish the emergence of sharp transitions as the Trotter step is varied.
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