9 research outputs found
Long-range epidemic spreading in a random environment
Modeling long-range epidemic spreading in a random environment, we consider a
quenched disordered, -dimensional contact process with infection rates
decaying with the distance as . We study the dynamical behavior
of the model at and below the epidemic threshold by a variant of the
strong-disorder renormalization group method and by Monte Carlo simulations in
one and two spatial dimensions. Starting from a single infected site, the
average survival probability is found to decay as up to
multiplicative logarithmic corrections. Below the epidemic threshold, a
Griffiths phase emerges, where the dynamical exponent varies continuously
with the control parameter and tends to as the threshold is
approached. At the threshold, the spatial extension of the infected cluster (in
surviving trials) is found to grow as with a
multiplicative logarithmic correction, and the average number of infected sites
in surviving trials is found to increase as with
in one dimension.Comment: 12 pages, 6 figure
Density of critical clusters in strips of strongly disordered systems
We consider two models with disorder dominated critical points and study the
distribution of clusters which are confined in strips and touch one or both
boundaries. For the classical random bond Potts model in the large-q limit we
study optimal Fortuin-Kasteleyn clusters by combinatorial optimization
algorithm. For the random transverse-field Ising chain clusters are defined and
calculated through the strong disorder renormalization group method. The
numerically calculated density profiles close to the boundaries are shown to
follow scaling predictions. For the random bond Potts model we have obtained
accurate numerical estimates for the critical exponents and demonstrated that
the density profiles are well described by conformal formulae.Comment: 9 pages, 9 figure
Entanglement entropies in free fermion gases for arbitrary dimension
We study the entanglement entropy of connected bipartitions in free fermion
gases of N particles in arbitrary dimension d. We show that the von Neumann and
Renyi entanglement entropies grow asymptotically as N^(1-1/d) ln N, with a
prefactor that is analytically computed using the Widom conjecture both for
periodic and open boundary conditions. The logarithmic correction to the
power-law behavior is related to the area-law violation in lattice free
fermions. These asymptotic large-N behaviors are checked against exact
numerical calculations for N-particle systems.Comment: 6 pages, 9 fig
The cavity method for quantum disordered systems: from transverse random field ferromagnets to directed polymers in random media
Unusual area-law violation in random inhomogeneous systems
The discovery of novel entanglement patterns in quantum many-body systems is a prominent research direction in contemporary physics. Here we provide the example of a spin chain with random and inhomogeneous couplings that in the ground state exhibits a very unusual area-law violation. In the clean limit, i.e. without disorder, the model is the rainbow chain and has volume law entanglement. We show that, in the presence of disorder, the entanglement entropy exhibits a power-law growth with the subsystem size, with an exponent 1/2. By employing the strong disorder renormalization group (SDRG) framework, we show that this exponent is related to the survival probability of certain random walks. The ground state of the model exhibits extended regions of short-range singlets (that we term 'bubble' regions) as well as rare long range singlet ('rainbow' regions). Crucially, while the probability of extended rainbow regions decays exponentially with their size, that of the bubble regions is power law. We provide strong numerical evidence for the correctness of SDRG results by exploiting the free-fermion solution of the model. Finally, we investigate the role of interactions by considering the random inhomogeneous XXZ spin chain. Within the SDRG framework and in the strong inhomogeneous limit, we show that the above area-law violation takes place only at the free-fermion point of phase diagram. This point divides two extended regions, which exhibit volume-law and area-law entanglement, respectively
Strong disorder RG approach â a short review of recent developments
The strong disorder RG approach for random systems has been extended in many new directions since our previous review of 2005 [F. Igloi, C. Monthus, Phys. Rep. 412, 277 (2005)]. The aim of the present colloquium paper is thus to give an overview of these various recent developments. In the field of quantum disordered models, recent progress concern infinite disorder fixed points for short-ranged models in higher dimensions d > 1, strong disorder fixed points for long-ranged models, scaling of the entanglement entropy in critical ground-states and after quantum quenches, the RSRG-X procedure to construct the whole set excited stated and the RSRG-t procedure for the unitary dynamics in many-body-localized phases, the Floquet dynamics of periodically driven chains, the dissipative effects induced by the coupling to external baths, and Anderson Localization models. In the field of classical disordered models, new applications include the contact process for epidemic spreading, the strong disorder renormalization procedure for general master equations, the localization properties of random elastic networks, and the synchronization of interacting non-linear dissipative oscillators. Application of the method for aperiodic (or deterministic) disorder is also mentioned