This document announces a seminar about dynamical many-body freezing in quantum systems. Dr. Analabha Roy from NITheP Stellenbosch node will present on how periodic driving can localize quantum magnets in Hilbert space through time-periodic quantum interference. Specifically, at certain drive amplitudes and frequencies, the evolution of local responses in systems like the transverse field Ising model can be completely arrested for any initial state via dynamical freezing. This is unlike classical models of hysteresis and has implications for disordered systems and experimental realizations.

1. NITheP cordially invites you to a seminar by:
Dr Analabha Roy
NITheP Stellenbosch node
Date: Wednesday 28 January 2015
Time: 14:00
Venue: NITheP Stellenbosch node, Seminar Room
TITLE: Dynamical Many-Body Freezing: Localizing quantum magnets in their Hilbert space by time-periodic
quantum interference
ABSTRACT: Dynamical freezing (DMF) is one of the most startling manifestations of quantum interference, where the evolution
of a simple system is frozen out under a suitably tuned periodic drive due to the coherent destruction of tunneling (CDT). In quantum
many body spin systems, such freezing can also occur via nonequilibrium dynamics analogous to CDT. At freezing, destructive
interference occurs between the time-evolving phases of all the degrees of freedom, causing the renormalized hopping term to
disappear under an external drive tuned to the freezing condition. We demonstrate the onset of this phenomenon by using the
rotated wave approximation (RWA) scheme in a paradigmatic example, the periodically driven Transverse Field Ising Model (TFIM).
At particular nontrivial values of drive amplitude and frequency, the time evolution of local responses can be arrested completely for
any arbitrary initial state via DMF. This is in stark contrast to classical models of hysteresis in Ising-like magnets, where "freezing"
occurs at infinite hysteresis and has a monotonic dependence on the external drive parameters. We try to generalize this
phenomenon by looking at more complex quantum systems, such as nonequilibrium BCS superfluids (using the Bogoliubov de-
Gennes approach out of equilibrium on the Keldysh Green's function), as well as the disordered TFIM (DTFIM). Freezing has
dramatic manifestation even in presence of extensive disorder, as we have seen in numerical simulations, as well as an analytical
understanding via RWA and asymptotic RG expansions of the Floquet Hamiltonian. In DTFIM without drive (quench dynamics), a
local response like the transverse magnetization relaxes exponentially with time with a decay time-scale tau due to random
longitudinal interactions between the spins. Under an external periodic drive at the freezing condition, this relaxation slows down (
tau shoots up) by several orders of magnitude. If drive frequency is increased maintaining the ratio with amplitude to a fixed
freezing value, then tau diverges exponentially with omega, and approaches ideal freezing as seen in the ordered TFIM. This
never happens when we place the drive outside the freezing condition, a counter-intuitive result.
The results can be easily extended for a larger family of disordered fermionic or bosonic systems. We discuss experimental
realizations, the relevance of this phenomenon in quantum error correction, as well as possible extensions to long-range interacting
systems.
Navrae/Enquiries: René Kotzé
Tel: 021 808 2653
Email: renekotze@sun.ac.za