We generalize the recently introduced Density‐Matrix Renormalization Group (DMRG‐X) [Khemani et al, PRL 2016] algorithm to obtain Floquet eigenstates of one‐dimensional, periodically driven many‐body localized systems. This generalization is made possible by the fact that the time‐evolution operator for a period can be efficiently represented using a matrix‐product operator. We first benchmark the method by comparing to exact diagonalization for small systems. We then obtain Floquet eigenstates for larger systems and show unambiguously that the characteristic area‐law scaling remains robust.
Matrix product operator approach to nonequilibrium Floquet steady states
We present a numerical method to simulate nonequilibrium Floquet steady states of one-dimensional periodically driven many-body systems coupled to a dissipative bath, based on a matrix product operator ansatz for the Floquet density matrix in frequency space. This method enables access to large systems beyond the reach of exact simulations, while retaining the periodic micromotion information. An excited-state extension of this technique allows computation of the dynamical approach to the steady state. We benchmark our method with a driven-dissipative Ising model and apply it to study the possibility of stabilizing prethermal discrete time-crystalline order by coupling to a cold bath.
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- Award ID(s):
- 1653007
- PAR ID:
- 10492968
- Publisher / Repository:
- Physical Review B
- Date Published:
- Journal Name:
- Physical Review B
- Volume:
- 106
- Issue:
- 22
- ISSN:
- 2469-9950
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1103/PhysRevB.106.L220307
