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Register a new userFate of many-body localization under periodic driving
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Added by
Achilleas Lazarides
Publication date
2014
fields
Physics
and research's language is
English
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We study many-body localised quantum systems subject to periodic driving. We find that the presence of a mobility edge anywhere in the spectrum is enough to lead to delocalisation for any driving strength and frequency. By contrast, for a fully localised many-body system, a delocalisation transition occurs at a finite driving frequency. We present numerical studies on a system of interacting one-dimensional bosons and the quantum random energy model, as well as simple physical pictures accounting for those results.
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In this work we investigate the stability of an algebraically localized phase subject to periodic driving. First, we focus on a non-interacting model exhibiting algebraically localized single-particle modes. For this model we find numerically that the algebraically localized phase is stable under driving, meaning that the system remains localized at arbitrary frequencies. We support this result with analytical considerations using simple renormalization group arguments. Second, we inspect the case in which short-range interactions are added. By studying both, the eigenstates properties of the Floquet Hamiltonian and the out-of-equilibrium dynamics in the interacting model, we provide evidence that ergodicity is restored at any driving frequencies. In particular, we observe that for the accessible system sizes localization sets in at driving frequency that are comparable with the many-body bandwidth and thus it might be only transient, suggesting that the system might thermalize in the thermodynamic limit.
Sufficient disorder is believed to localize static and periodically-driven interacting chains. With quasiperiodic driving by $D$ incommensurate tones, the fate of this many-body localization (MBL) is unknown. We argue that randomly disordered MBL exists for $D=2$, but not for $D geq 3$. Specifically, a putative two-tone driven MBL chain is neither destabilized by thermal avalanches seeded by rare thermal regions, nor by the proliferation of long-range many-body resonances. For $D geq 3$, however, sufficiently large thermal regions have continuous local spectra and slowly thermalize the entire chain. En route, we generalize the eigenstate thermalization hypothesis to the quasiperiodically-driven setting, and verify its predictions numerically. Two-tone driving enables new topological orders with edge signatures; our results suggest that localization protects these orders indefinitely.
We examine the many-body localization (MBL) phase transition in one-dimensional quantum systems with quenched randomness and short-range interactions. Following recent works, we use a strong-randomness renormalization group (RG) approach where the phase transition is due to the so-called avalanche instability of the MBL phase. We show that the critical behavior can be determined analytically within this RG. On a rough $textit{qualitative}$ level the RG flow near the critical fixed point is similar to the Kosterlitz-Thouless (KT) flow as previously shown, but there are important differences in the critical behavior. Thus we show that this MBL transition is in a new universality class that is different from KT. The divergence of the correlation length corresponds to critical exponent $ u rightarrow infty$, but the divergence is weaker than for the KT transition.
Staring from the kicked rotator as a paradigm for a system exhibiting classical chaos, we discuss the role of quantum coherence resulting in dynamical localization in the kicked quantum rotator. In this context, the disorder-induced Anderson localization is also discussed. Localization in interacting, quantum many-body systems (many-body localization) may also occur in the absence of disorder, and a practical way to identify its occurrence is demonstrated for an interacting spin chain.
We study a quantum interacting spin system subject to an external drive and coupled to a thermal bath of spatially localized vibrational modes, serving as a model of Dynamic Nuclear Polarization. We show that even when the many-body eigenstates of the system are ergodic, a sufficiently strong coupling to the bath may effectively localize the spins due to many-body quantum Zeno effect, as manifested by the hole-burning shape of the electron paramagnetic resonance spectrum. Our results provide an explanation of the breakdown of the thermal mixing regime experimentally observed above 4 - 5 Kelvin.
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