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Register a new userMany-Body Localization with Quasiperiodic Driving
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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.
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We study the many body localization (MBL) transition for interacting fermions subject to quasiperiodic potentials by constructing the local integrals of motion (LIOMs) in the MBL phase as time-averaged local operators. We study numerically how these time-averaged operators evolve across the MBL transition. We find that the norm of such time-averaged operators drops discontinuously to zero across the transition; as we discuss, this implies that LIOMs abruptly become unstable at some critical localization length of order unity. We analyze the LIOMs using hydrodynamic projections and isolating the part of the operator that is associated with interactions. Equipped with this data we perform a finite-size scaling analysis of the quasiperiodic MBL transition. Our results suggest that the quasiperiodic MBL transition occurs at considerably stronger quasiperiodic modulations, and has a larger correlation-length critical exponent, than previous studies had found.
We propose a method for detecting many-body localization (MBL) in disordered spin systems. The method involves pulsed, coherent spin manipulations that probe the dephasing of a given spin due to its entanglement with a set of distant spins. It allows one to distinguish the MBL phase from a non-interacting localized phase and a delocalized phase. In particular, we show that for a properly chosen pulse sequence the MBL phase exhibits a characteristic power-law decay reflecting its slow growth of entanglement. We find that this power-law decay is robust with respect to thermal and disorder averaging, provide numerical simulations supporting our results, and discuss possible experimental realizations in solid-state and cold atom systems.
We investigate the phase transition between an ergodic and a many-body localized phase in infinite anisotropic spin-$1/2$ Heisenberg chains with binary disorder. Starting from the Neel state, we analyze the decay of antiferromagnetic order $m_s(t)$ and the growth of entanglement entropy $S_{textrm{ent}}(t)$ during unitary time evolution. Near the phase transition we find that $m_s(t)$ decays exponentially to its asymptotic value $m_s(infty) eq 0$ in the localized phase while the data are consistent with a power-law decay at long times in the ergodic phase. In the localized phase, $m_s(infty)$ shows an exponential sensitivity on disorder with a critical exponent $ usim 0.9$. The entanglement entropy in the ergodic phase grows subballistically, $S_{textrm{ent}}(t)sim t^alpha$, $alphaleq 1$, with $alpha$ varying continuously as a function of disorder. Exact diagonalizations for small systems, on the other hand, do not show a clear scaling with system size and attempts to determine the phase boundary from these data seem to overestimate the extent of the ergodic phase.
Isolated quantum systems with quenched randomness exhibit many-body localization (MBL), wherein they do not reach local thermal equilibrium even when highly excited above their ground states. It is widely believed that individual eigenstates capture this breakdown of thermalization at finite size. We show that this belief is false in general and that a MBL system can exhibit the eigenstate properties of a thermalizing system. We propose that localized approximately conserved operators (l$^*$-bits) underlie localization in such systems. In dimensions $d>1$, we further argue that the existing MBL phenomenology is unstable to boundary effects and gives way to l$^*$-bits. Physical consequences of l$^*$-bits include the possibility of an eigenstate phase transition within the MBL phase unrelated to the dynamical transition in $d=1$ and thermal eigenstates at all parameters in $d>1$. Near-term experiments in ultra-cold atomic systems and numerics can probe the dynamics generated by boundary layers and emergence of l$^*$-bits.
We propose a scaling theory for the many-body localization (MBL) phase transition in one dimension, building on the idea that it proceeds via a quantum avalanche. We argue that the critical properties can be captured at a coarse-grained level by a Kosterlitz-Thouless (KT) renormalization group (RG) flow. On phenomenological grounds, we identify the scaling variables as the density of thermal regions and the lengthscale that controls the decay of typical matrix elements. Within this KT picture, the MBL phase is a line of fixed points that terminates at the delocalization transition. We discuss two possible scenarios distinguished by the distribution of rare, fractal thermal inclusions within the MBL phase. In the first scenario, these regions have a stretched exponential distribution in the MBL phase. In the second scenario, the near-critical MBL phase hosts rare thermal regions that are power-law distributed in size. This points to the existence of a second transition within the MBL phase, at which these power-laws change to the stretched exponential form expected at strong disorder. We numerically simulate two different phenomenological RGs previously proposed to describe the MBL transition. Both RGs display a universal power-law length distribution of thermal regions at the transition with a critical exponent $alpha_c=2$, and continuously varying exponents in the MBL phase consistent with the KT picture.
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