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Jun 27, 2018
06/18

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Cecile Monthus

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The Dyson hierarchical version of the quantum Ising chain with Long-Ranged power-law ferromagnetic couplings $J(r) \propto r^{-1-\sigma}$ and pure or random transverse fields is studied via real-space renormalization. For the pure case, the critical exponents are explicitly obtained as a function of the parameter $\sigma$, and are compared with previous results of other approaches. For the random case, the RG rules are numerically applied and the critical behaviors are compared with previous...

Topics: Condensed Matter, Disordered Systems and Neural Networks

Source: http://arxiv.org/abs/1503.03727

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Jun 30, 2018
06/18

by
Cecile Monthus

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The Lindblad dynamics with dephasing in the bulk and magnetization-driving at the two boundaries is studied for the quantum spin chain with random fields $h_j$ and couplings $J_j$ (that can be either uniform or random). In the regime of strong disorder in the random fields, or in the regime of strong bulk-dephasing, the effective dynamics can be mapped onto a classical Simple Symmetric Exclusion Process with quenched disorder in the diffusion coefficient associated to each bond. The properties...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1701.05090

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Jun 29, 2018
06/18

by
Cecile Monthus

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For the DNA denaturation transition in the presence of random contact energies, or equivalently the disordered wetting transition, we introduce a Strong Disorder Renewal Approach to construct the optimal contacts in each disordered sample of size $L$. The transition is found to be of infinite order, with a correlation length diverging with the essential singularity $\ln \xi(T) \propto |T-T_c |^{-1}$. In the critical region, we analyze the statistics over samples of the free-energy density $f_L$...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1611.00501

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Jun 29, 2018
06/18

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Cecile Monthus

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The finite temperature dynamics of the Dyson hierarchical classical spins models is studied via real-space renormalization rules concerning the couplings and the relaxation times. For the ferromagnetic model involving Long-Ranged coupling $J(r) \propto r^{-1-\sigma}$ in the region $1/2

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1601.05643

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Jun 30, 2018
06/18

by
Cecile Monthus

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For the quantum Ising chain, the self-dual block renormalization procedure of Fernandez-Pacheco [Phys. Rev. D 19, 3173 (1979)] is known to reproduce exactly the location of the zero-temperature critical point and the correlation length exponent $\nu=1$. Recently, Miyazaki and Nishimori [Phys. Rev. E 87, 032154 (2013)] have proposed to study the disordered quantum Ising model in dimensions $d>1$ by applying the Fernandez-Pacheco procedure successively in each direction. To avoid the...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1409.8459

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Jun 27, 2018
06/18

by
Cecile Monthus

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We consider $M \geq 2$ pure or random quantum Ising chains of $N$ spins when they are coupled via a single star junction at their origins or when they are coupled via two star junctions at the their two ends leading to the watermelon geometry. The energy gap is studied via a sequential self-dual real-space renormalization procedure that can be explicitly solved in terms of Kesten variables containing the initial couplings and and the initial transverse fields. In the pure case at criticality,...

Topics: Condensed Matter, Disordered Systems and Neural Networks

Source: http://arxiv.org/abs/1504.06414

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Jun 29, 2018
06/18

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Cecile Monthus

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For Anderson Localization models with multifractal eigenvectors on disordered samples containing $N$ sites, we analyze in a unified framework the consequences for the statistical properties of the Green function. We focus in particular on the imaginary part of the Green function at coinciding points $G^I_{xx}(E-i \eta)$ and study the scaling with the size $N$ of the moments of arbitrary indices $q$ when the broadening follows the scaling $\eta=\frac{c}{N^{\delta}}$. For the standard scaling...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1610.00417

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Jun 30, 2018
06/18

by
Cecile Monthus

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For Gaussian Spin Glasses in low dimensions, we introduce a simple Strong Disorder renormalization procedure at zero temperature. In each disordered sample, the difference between the ground states associated to Periodic and Anti-Periodic boundary conditions defines a system-size Domain Wall. The numerical study in dimensions $d=2$ (up to sizes $2048^2$) and $d=3$ (up to sizes $128^3$) yields fractal Domain Walls of dimensions $d_s(d=2) \simeq 1.27$ and $d_s(d=3) \simeq 2.55$ respectively.

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1411.5791

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Jun 29, 2018
06/18

by
Cecile Monthus

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For short-ranged disordered quantum models in one dimension, the Many-Body-Localization is analyzed via the adaptation to the Many-Body context [M. Serbyn, Z. Papic and D.A. Abanin, PRX 5, 041047 (2015)] of the Thouless point of view on the Anderson transition : the question is whether a local interaction between two long chains is able to reshuffle completely the eigenstates (Delocalized phase with a volume-law entanglement) or whether the hybridization between tensor states remains limited...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1603.04701

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Jun 28, 2018
06/18

by
Cecile Monthus

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The space of one-dimensional disordered interacting quantum models displaying a Many-Body-Localization Transition seems sufficiently rich to produce critical points with level statistics interpolating continuously between the Poisson statistics of the Localized phase and the Wigner-Dyson statistics of the Delocalized Phase. In this paper, we consider the strong disorder limit of the MBL transition, where the critical level statistics is close to the Poisson statistics. We analyse a...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1510.03711

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Jun 30, 2018
06/18

by
Cecile Monthus

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We consider the long-ranged Ising spin-glass with random couplings decaying as a power-law of the distance, in the region of parameters where the spin-glass phase exists with a positive droplet exponent. For the Metropolis single-spin-flip dynamics near zero temperature, we construct via real-space renormalization the full hierarchy of relaxation times of the master equation for any given realization of the random couplings. We then analyze the probability distribution of dynamical barriers as...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1405.2179

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Jun 29, 2018
06/18

by
Cecile Monthus

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To understand the finite-size-scaling properties of phases transitions in classical and quantum models in the presence of quenched disorder, it has proven to be fruitful to introduce the notion of a finite-size-pseudo-critical point in each disordered sample and to analyze its sample-to-sample fluctuations as a function of the size. For the Many-Body-Localization transition, where very strong eigenstate-to-eigenstate fluctuations have been numerically reported even within a given disordered...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1606.07590

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Jun 30, 2018
06/18

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Cecile Monthus

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The Lindblad dynamics of the XX quantum chain with large random fields $h_j$ (the couplings $J_j$ can be either uniform or random) is considered for boundary-magnetization-drivings acting on the two end-spins. Since each boundary-reservoir tends to impose its own magnetization, we first study the relaxation spectrum in the presence of a single reservoir as a function of the system size via some boundary-strong-disorder renormalization approach. The non-equilibrium-steady-state in the presence...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1701.02102

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Jun 29, 2018
06/18

by
Cecile Monthus

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For disordered interacting quantum systems, the sensitivity of the spectrum to twisted boundary conditions depending on an infinitesimal angle $\phi$ can be used to analyze the Many-Body-Localization Transition. The sensitivity of the energy levels $E_n(\phi)$ is measured by the level curvature $K_n=E_n"(0)$, or more precisely by the Thouless dimensionless curvature $k_n=K_n/\Delta_n$, where $\Delta_n$ is the level spacing that decays exponentially with the size $L$ of the system. For...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1607.00750

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Jun 28, 2018
06/18

by
Cecile Monthus

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The generalization of the Dyson Brownian Motion approach of random matrices to Anderson Localization (AL) models [Chalker, Lerner and Smith PRL 77, 554 (1996)] and to Many-Body Localization (MBL) Hamiltonians [Serbyn and Moore arxiv:1508.07293] is revisited to extract the level repulsion exponent $\beta$, where $\beta=1$ in the delocalized phase governed by the Wigner-Dyson statistics, $\beta=0$ in the localized phase governed by the Poisson statistics, and $0 |^2 | |^2 $ for consecutive...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1510.08322

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Jun 30, 2018
06/18

by
Cecile Monthus

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For the one-dimensional long-ranged Ising spin-glass with random couplings decaying with the distance $r$ as $J(r) \sim r^{-\sigma}$ and distributed with the L\'evy symmetric stable distribution of index $1 1/\mu$ where the energy is extensive. We study two real space renormalization procedures at zero temperature, namely a simple box decimation that leads to explicit calculations, and a strong disorder decimation that can be studied numerically on large sizes. The droplet exponent governing...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1403.1098

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Jun 29, 2018
06/18

by
Cecile Monthus

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For random L\'evy matrices of size $N \times N$, where matrix elements are drawn with some heavy-tailed distribution $P(H_{ij}) \propto N^{-1} |H_{ij} |^{-1-\mu}$ with $0

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1606.03241

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Jun 28, 2018
06/18

by
Cecile Monthus

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A Fully Many-Body Localized (FMBL) quantum disordered system is characterized by the emergence of an extensive number of local conserved operators that prevents the relaxation towards thermal equilibrium. These local conserved operators can be seen as the building blocks of the whole set of eigenstates. In this paper, we propose to construct them explicitly via some block real-space renormalization. The principle is that each RG step diagonalizes the smallest remaining blocks and produces a...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1509.06258

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Jun 28, 2018
06/18

by
Cecile Monthus

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We consider the Dyson hierarchical version of the quantum Spin-Glass with random Gaussian couplings characterized by the power-law decaying variance $\overline{J^2(r)} \propto r^{-2\sigma}$ and a uniform transverse field $h$. The ground state is studied via real-space renormalization to characterize the spinglass-paramagnetic zero temperature quantum phase transition as a function of the control parameter $h$. In the spinglass phase $h

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1506.06012

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Jun 26, 2018
06/18

by
Cecile Monthus

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The Shannon and the Renyi entropies of the ground state wavefunction in the pure and in the random quantum Ising chain are studied via the self-dual Fernandez-Pacheco real-space renormalization procedure. In particular, we analyze the critical behavior of the leading extensive term at the quantum phase transition : the derivative with respect to the control parameter is found to be logarithmically divergent in the pure case, and to display a cusp singularity in the random case. This cusp...

Topics: Statistical Mechanics, Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1501.05416

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Jun 29, 2018
06/18

by
Cecile Monthus

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The iterative methods to diagonalize matrices and many-body Hamiltonians can be reformulated as flows of Hamiltonians towards diagonalization driven by unitary transformations that preserve the spectrum. After a comparative overview of the various types of discrete flows (Jacobi, QR-algorithm) and differential flows (Toda, Wegner, White) that have been introduced in the past, we focus on the random XXZ chain with random fields in order to determine the best closed flow within a given subspace...

Topics: Disordered Systems and Neural Networks, Mathematical Physics, Condensed Matter, Mathematics

Source: http://arxiv.org/abs/1602.03064

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Jun 30, 2018
06/18

by
Cecile Monthus; Thomas Garel

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For the Ising model with Gaussian random coupling of average $J_0$ and unit variance, the zero-temperature spinglass-ferromagnetic transition as a function of the control parameter $J_0$ can be studied via the size-$L$ dependent renormalized coupling defined as the domain-wall energy $J^R(L) \equiv E_{GS}^{(AF)}(L)-E_{GS}^{(F)}(L)$ (i.e. the difference between the ground state energies corresponding to AntiFerromagnetic and and Ferromagnetic boundary conditions in one direction). We study...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1401.6342