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: [email protected]

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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: [email protected]