4,156 research outputs found
Universal properties of many-body delocalization transitions
We study the dynamical melting of "hot" one-dimensional many-body localized
systems. As disorder is weakened below a critical value these non-thermal
quantum glasses melt via a continuous dynamical phase transition into classical
thermal liquids. By accounting for collective resonant tunneling processes, we
derive and numerically solve an effective model for such quantum-to-classical
transitions and compute their universal critical properties. Notably, the
classical thermal liquid exhibits a broad regime of anomalously slow
sub-diffusive equilibration dynamics and energy transport. The subdiffusive
regime is characterized by a continuously evolving dynamical critical exponent
that diverges with a universal power at the transition. Our approach elucidates
the universal long-distance, low-energy scaling structure of many-body
delocalization transitions in one dimension, in a way that is transparently
connected to the underlying microscopic physics.Comment: 12 pages, 6 figures; major changes from v1, including a modified
approach and new emphasis on conventional MBL systems rather than their
critical variant
Strong-Disorder Renormalization Group for Periodically Driven Systems
Quenched randomness can lead to robust non-equilibrium phases of matter in
periodically driven (Floquet) systems. Analyzing transitions between such
dynamical phases requires a method capable of treating the twin complexities of
disorder and discrete time-translation symmetry. We introduce a real-space
renormalization group approach, asymptotically exact in the strong-disorder
limit, and exemplify its use on the periodically driven interacting quantum
Ising model. We analyze the universal physics near the critical lines and
multicritical point of this model, and demonstrate the robustness of our
results to the inclusion of weak interactions.Comment: 11 pages, 6 figures; published versio
Supervisory observer for parameter and state estimation of nonlinear systems using the DIRECT algorithm
A supervisory observer is a multiple-model architecture, which estimates the
parameters and the states of nonlinear systems. It consists of a bank of state
observers, where each observer is designed for some nominal parameter values
sampled in a known parameter set. A selection criterion is used to select a
single observer at each time instant, which provides its state estimate and
parameter value. The sampling of the parameter set plays a crucial role in this
approach. Existing works require a sufficiently large number of parameter
samples, but no explicit lower bound on this number is provided. The aim of
this work is to overcome this limitation by sampling the parameter set
automatically using an iterative global optimisation method, called DIviding
RECTangles (DIRECT). Using this sampling policy, we start with 1 + 2np
parameter samples where np is the dimension of the parameter set. Then, the
algorithm iteratively adds samples to improve its estimation accuracy.
Convergence guarantees are provided under the same assumptions as in previous
works, which include a persistency of excitation condition. The efficacy of the
supervisory observer with the DIRECT sampling policy is illustrated on a model
of neural populations
Macrocyclic dizinc(II) alkyl and alkoxide complexes: Reversible CO2 uptake and polymerization catalysis testing
Quantum Brownian motion in a quasiperiodic potential
We consider a quantum particle subject to Ohmic dissipation, moving in a
bichromatic quasiperiodic potential. In a periodic potential the particle
undergoes a zero-temperature localization-delocalization transition as
dissipation strength is decreased. We show that the delocalized phase is absent
in the quasiperiodic case, even when the deviation from periodicity is
infinitesimal. Using the renormalization group, we determine how the effective
localization length depends on the dissipation. We show that {a similar problem
can emerge in} the strong-coupling limit of a mobile impurity moving in a
periodic lattice and immersed in a one-dimensional quantum gas.Comment: 5+6 pages, 1 figur
Localization-protected order in spin chains with non-Abelian discrete symmetries
We study the non-equilibrium phase structure of the three-state random
quantum Potts model in one dimension. This spin chain is characterized by a
non-Abelian symmetry recently argued to be incompatible with the
existence of a symmetry-preserving many-body localized (MBL) phase. Using exact
diagonalization and a finite-size scaling analysis, we find that the model
supports two distinct broken-symmetry MBL phases at strong disorder that either
break the clock symmetry or a chiral
symmetry. In a dual formulation, our results indicate the existence of a stable
finite-temperature topological phase with MBL-protected parafermionic end zero
modes. While we find a thermal symmetry-preserving regime for weak disorder,
scaling analysis at strong disorder points to an infinite-randomness critical
point between two distinct broken-symmetry MBL phases.Comment: 5 pages, 3 figures main text; 6 pages, 3 figures supplemental
material; Version 2 includes a corrected the form of the chiral order
parameter, and corresponding data, as well as larger system size numerics,
with no change to the phase structur
Particle-hole symmetry, many-body localization, and topological edge modes
We study the excited states of interacting fermions in one dimension with
particle-hole symmetric disorder (equivalently, random-bond XXZ chains) using a
combination of renormalization group methods and exact diagonalization. Absent
interactions, the entire many-body spectrum exhibits infinite-randomness
quantum critical behavior with highly degenerate excited states. We show that
though interactions are an irrelevant perturbation in the ground state, they
drastically affect the structure of excited states: even arbitrarily weak
interactions split the degeneracies in favor of thermalization (weak disorder)
or spontaneously broken particle-hole symmetry, driving the system into a
many-body localized spin glass phase (strong disorder). In both cases, the
quantum critical properties of the non-interacting model are destroyed, either
by thermal decoherence or spontaneous symmetry breaking. This system then has
the interesting and counterintuitive property that edges of the many-body
spectrum are less localized than the center of the spectrum. We argue that our
results rule out the existence of certain excited state symmetry-protected
topological orders.Comment: 9 pages. 7 figure
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