Influence Matrix Approach to Many-Body Floquet Dynamics

The description of time evolution in many-body systems is generally challenging due to the dynamical generation of quantum entanglement. The folding algorithm based on matrix-product state (MPS) can reduce entanglement by using space direction evolution instead of time evolution. At the mathematical level, the Influence Matrix (IM) approach, inspired by the Feynman-Vernon influence functional, bears a similarity to Folding algorithm. For certain special values of the model parameters, Influence Matrix can be obtained exactly which represents a perfect dephaser (PD). Physically, a PD corresponds to a many-body system that acts as a perfectly Markovian bath on itself.

In this talk, I will introduce Folding algorithm to Influence Matrix approach. I will obtain Influence Matrix exactly by MPS language at perfect dephaser points, and show Influence Matrix acts as a perfectly Markovian bath at this point.

[1] M. C. Bañuls, M. B. Hastings, F. Verstraete, and J. I. Cirac, Matrix Product States for Dynamical Simulation of Infinite Chains, Phys. Rev. Lett. 102, 240603 (2009).

[2] Lerose A, Sonner M, Abanin D A. Influence matrix approach to many-body Floquet dynamics[J]. Physical Review X, 2021, 11(2): 021040.