4,307 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
Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
We address the hydrodynamics of operator spreading in interacting integrable
lattice models. In these models, operators spread through the ballistic
propagation of quasiparticles, with an operator front whose velocity is locally
set by the fastest quasiparticle velocity. In interacting integrable systems,
this velocity depends on the density of the other quasiparticles, so
equilibrium density fluctuations cause the front to follow a biased random
walk, and therefore to broaden diffusively. Ballistic front propagation and
diffusive front broadening are also generically present in non-integrable
systems in one dimension; thus, although the mechanisms for operator spreading
are distinct in the two cases, these coarse grained measures of the operator
front do not distinguish between the two cases. We present an expression for
the front-broadening rate; we explicitly derive this for a particular
integrable model (the "Floquet-Fredrickson-Andersen" model), and argue on
kinetic grounds that it should apply generally. Our results elucidate the
microscopic mechanism for diffusive corrections to ballistic transport in
interacting integrable models.Comment: Published versio
The periodic sl(2|1) alternating spin chain and its continuum limit as a bulk Logarithmic Conformal Field Theory at c=0
The periodic sl(2|1) alternating spin chain encodes (some of) the properties
of hulls of percolation clusters, and is described in the continuum limit by a
logarithmic conformal field theory (LCFT) at central charge c=0. This theory
corresponds to the strong coupling regime of a sigma model on the complex
projective superspace , and the spectrum of critical exponents can be
obtained exactly. In this paper we push the analysis further, and determine the
main representation theoretic (logarithmic) features of this continuum limit by
extending to the periodic case the approach of [N. Read and H. Saleur, Nucl.
Phys. B 777 316 (2007)]. We first focus on determining the representation
theory of the finite size spin chain with respect to the algebra of local
energy densities provided by a representation of the affine Temperley-Lieb
algebra at fugacity one. We then analyze how these algebraic properties carry
over to the continuum limit to deduce the structure of the space of states as a
representation over the product of left and right Virasoro algebras. Our main
result is the full structure of the vacuum module of the theory, which exhibits
Jordan cells of arbitrary rank for the Hamiltonian.Comment: 69pp, 8 fig
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
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
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