Kavli Affiliate: Debanjan Chowdhury
| First 5 Authors: Rohit Mukherjee, Haoyu Guo, Debanjan Chowdhury, ,
| Summary:
Periodically driven Floquet quantum many-body systems have revealed new
insights into the rich interplay of thermalization, and growth of entanglement.
The phenomenology of dynamical freezing, whereby a translationally invariant
many-body system exhibits emergent conservation laws and a slow growth of
entanglement entropy at certain fixed ratios of a drive amplitude and
frequency, presents a novel paradigm for retaining memory of an initial state
upto late times. Previous studies of dynamical freezing have largely been
restricted to a high-frequency Floquet-Magnus expansion, and numerical exact
diagonalization, which are unable to capture the slow approach to
thermalization (or lack thereof) in a systematic fashion. By employing Floquet
flow-renormalization, where the time-dependent part of the Hamiltonian is
gradually decoupled from the effective Hamiltonian using a sequence of unitary
transformations, we unveil the universal approach to dynamical freezing and
beyond, at asymptotically late times. We analyze the fixed-point behavior
associated with the flow-renormalization at and near freezing using both
exact-diagonalization and tensor-network based methods, and contrast the
results with conventional prethermal phenomenon. For a generic non-integrable
spin Hamiltonian with a periodic cosine wave drive, the flow approaches an
unstable fixed point with an approximate emergent symmetry. We observe that at
freezing the thermalization timescales are delayed compared to away from
freezing, and the flow trajectory undergoes a series of instanton events. Our
numerical results are supported by analytical solutions to the flow equations.
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