arXiv subjects

Cecile Monthus

Publications and source records attributed to Cecile Monthus.

At least 55 records · Page 3Linked to original sources

arXiv2019

Asymmetric scaling in large deviations for rare values bigger or smaller than the typical value

In various disordered systems or non-equilibrium dynamical models, the large deviations of some observables have been found to display different scalings for rare values bigger or smaller than the typical value. In the present paper, we revisit the simpler observables based on independent random variables, namely the empirical maximum, the empirical average, the empirical non-integer moments or other additive empirical observables, in order to describe the cases where asymmetric large deviations already occur. The unifying starting point to analyze the large deviations of these various empirical observables is given by the Sanov theorem for the large deviations of the empirical histogram : the rate function corresponds to the relative entropy with respect to the true probability distribution and it can be optimized in the presence of the appropriate constraints. Finally, the physical meaning of large deviations rate functions is discussed from the renormalization perspective.

cond-mat.stat-mech↗

arXiv2019

Revisiting classical and quantum disordered systems from the unifying perspective of large deviations

The theory of large deviations is already the natural language for the statistical physics of equilibrium and non-equilibrium. In the field of disordered systems, the analysis via large deviations is even more useful to describe within a unified perspective the typical events and the rare events that occur on various scales. In the present pedagogical introduction, we revisit various emblematic classical and quantum disordered systems in order to highlight the common underlying mechanisms from the point of view of large deviations.

cond-mat.dis-nn↗

arXiv2019

Microscopic Fluctuation Theory (mFT) for interacting Poisson processes

While the Macroscopic Fluctuation Theory (MFT) is a renormalized theory in the hydrodynamic limit based on a space-time local Lagrangian that is Gaussian with respect to the empirical current, C. Maes, K. Netocny and B. Wynants [Markov Proc. Rel. Fields. 14, 445 (2008)] have derived a microscopic Fluctuation Theory (mFT) for independent Markov jump processes based on a space-time local Lagrangian that is Poissonian with respect to the empirical flow, in direct relation with the general theory of large deviations at 'Level 2.5' for Markovian processes. Here we describe how this approach can be generalized to the presence of interactions, that can be either zero-range or involve neighbors, either for closed systems or for open systems with reservoirs.

cond-mat.stat-mech↗

arXiv2019

Large Deviations for the density and the current in Non-Equilibrium-Steady-States on disordered rings

The so-called 'Level 2.5' general result for the large deviations of the joint probability of the density and of the currents for Markov Jump processes is applied to the case of $N$ independent particles on a ring with random transition rates. We first focus on the Directed Trap model, where the contractions needed to obtain the large deviations properties of the density alone and of the current alone can be explicitly written in each disordered sample, and where the deformed Markov operator needed to evaluate the generating function of the current can be also explicitly analyzed via its highest eigenvalue and the corresponding left and right eigenvectors. We then turn to the non-directed model, where the tails for large currents $ j \to \pm \infty$ of the rate function for the current alone can still be studied explicitly, either via contraction or via the deformed Markov operator method. We mention the differences with the large deviations properties of the Fokker-Planck dynamics on disordered rings.

cond-mat.dis-nn↗

arXiv2018

Large Deviations for dynamical fluctuations of Open Markov processes, with application to random cascades on trees

The large deviations at 'Level 2.5 in time' for time-dependent ensemble-empirical-observables, introduced by C. Maes, K. Netocny and B. Wynants [Markov Proc. Rel. Fields. 14, 445 (2008)] for the case of $N$ independent Markov jump processes, are extended to the case of open Markov processes with reservoirs : explicit formulas are given for the joint probability of empirical occupation numbers and empirical flows, both for discrete-time dynamics and for continuous-time jump dynamics, with possibly time-dependent dynamical rules and/or time-dependent driving of the reservoirs. This general formalism is then applied to random cascades on trees, where particles are injected at the root via a 'source reservoir', while the particles are removed at the leaves of the last generation of the tree via 'sink reservoirs'.

cond-mat.stat-mech↗

arXiv2018

Topological phase transitions in random Kitaev $α$-chains

The topological phases of random Kitaev $α$-chains are labelled by the number of localized edge Majorana Zero Modes. The critical lines between these phases thus correspond to delocalization transitions for these localized edge Majorana Zero Modes. For the random Kitaev chain with next-nearest couplings, where there are three possible topological phases $n=0,1,2$, the two Lyapunov exponents of Majorana Zero Modes are computed for a specific solvable case of Cauchy disorder, in order to analyze how the phase diagram evolves as a function of the disorder strength. In particular, the direct phase transition between the phases $n=0$ and $n=2$ is possible only in the absence of disorder, while the presence of disorder always induces an intermediate phase $n=1$, as found previously via numerics for other distributions of disorder.

cond-mat.dis-nn↗

arXiv2018

On various levels of deterministic toy models for the Richardson cascade in turbulence

The Desnyanski-Novikov shell model is a deterministic dynamical model for scalar velocities $v_t(n)$ defined on the one-dimensional-lattice $n=0,1,2,..$ labelling the length-scales $l_n=l_0 2^{-n}$, in order to describe the cascade of energy from the biggest scale where it is injected by some external forcing towards the smaller scales where it is dissipated by viscosity. We describe the generalization of this model in two directions : (i) the one-dimensional-lattice $n=0,1,2,..$ labelling the length-scales $l_n=l_0 2^{-n}$ is replaced by a scale-spatial tree structure of nested cells in order to allow spatial heterogeneities between different coherent structures that are localized in different regions of the whole volume ; (ii) the scalar velocities $v_t(n)$ are replaced by 3D-vector velocities in order to take into account the vorticity in the dynamical equations and to include vortex-stretching effects.

cond-mat.stat-mech↗

arXiv2018

Even and odd normalized zero modes in random interacting Majorana models respecting the Parity $P$ and the Time-Reversal-Symmetry $T$

For random interacting Majorana models where the only symmetries are the Parity $P$ and the Time-Reversal-Symmetry $T$, various approaches are compared to construct exact even and odd normalized zero modes $Γ$ in finite size, i.e. hermitian operators that commute with the Hamiltonian, that square to the Identity, and that commute (even) or anticommute (odd) with the Parity $P$. Even Normalized Zero-Modes $Γ^{even}$ are well known under the name of 'pseudo-spins' $τ^z_n$ in the field of Many-Body-Localization or more precisely 'Local Integrals of Motion' (LIOMs) in the Many-Body-Localized-Phase where the pseudo-spins happens to be spatially localized. Odd Normalized Zero-Modes $Γ^{odd}$ are popular under the name of 'Majorana Zero Modes' or 'Strong Zero Modes'. Explicit examples for small systems are described in detail. Applications to real-space renormalization procedures based on blocks containing an odd number of Majorana fermions are also discussed.

cond-mat.dis-nn↗

arXiv2018

Many-Body-Localization : Strong Disorder perturbative approach for the Local Integrals of Motion

For random quantum spin models, the strong disorder perturbative expansion of the Local Integrals of Motion (LIOMs) around the real-spin operators is revisited. The emphasis is on the links with other properties of the Many-Body-Localized phase, in particular the memory in the dynamics of the local magnetizations and the statistics of matrix elements of local operators in the eigenstate basis. Finally, this approach is applied to analyze the Many-Body-Localization transition in a toy model studied previously from the point of view of the entanglement entropy.

cond-mat.dis-nn↗

arXiv2018

Strong Disorder Renormalization for the dynamics of Many-Body-Localized systems : iterative elimination of the fastest degree of freedom via the Floquet expansion

The Vosk-Altman Strong Disorder Renormalization for the unitary dynamics of various random quantum spin chains is reformulated as follows : the local degree of freedom characterized by the highest eigenfrequency $Ω$ can be considered as a high-frequency-Floquet-periodic-driving for the neighboring slower degrees of freedom. Then the two first orders of the high-frequency expansion for the effective Floquet Hamiltonian can be used to generate the emergent Local Integrals of Motion (LIOMs) and to derive the renormalization rules for the effective dynamics of the remaining degrees of freedom. The flow for this effective Floquet Hamiltonian is equivalent to the RSRG-X procedure to construct the whole set of eigenstates that generalizes the Fisher RSRG procedure constructing the ground state. This general framework is applied to the random-transverse-field XXZ spin chain in its Many-Body-Localized phase, in order to derive the renormalization rules associated to the elimination of the biggest transverse field and to the elimination of the biggest coupling respectively.

cond-mat.dis-nn↗

arXiv2018

Strong Disorder Real-Space Renormalization for the Many-Body-Localized phase of random Majorana models

For the Many-Body-Localized phase of random Majorana models, a general Strong Disorder Real-Space Renormalization procedure known as RSRG-X [D. Pekker, G. Refael, E. Altman, E. Demler and V. Oganesyan, Phys. Rev. X 4, 011052 (2014)] is described to produce the whole set of excited states, via the iterative construction of the Local Integrals of Motion (LIOMs). The RG rules are then explicitly derived for arbitrary quadratic Hamiltonians (free-fermions models) and for the Kitaev chain with local interactions involving even numbers of consecutive Majorana fermions. The emphasis is put on the advantages of the Majorana language over the usual quantum spin language to formulate unified RSRG-X rules.

cond-mat.dis-nn↗

arXiv2018

On the simplest scale invariant Tree-Tensor-States preserving the quantum symmetries of the antiferromagnetic XXZ chain

For the line of critical antiferromagnetic XXZ chains with coupling $J>0$ and anisotropy $0<Δ\leq 1$, we describe how the block-spin renormalization procedure preserving the $SU_q(2)$ symmetry introduced by Martin-Delgado and Sierra [Phys. Rev. Lett. 76, 1146 (1996)] can be reformulated as the translation-invariant scale-invariant Tree-Tensor-State of the smallest dimension that is compatible with the quantum symmetries of the model. The properties of this Tree-Tensor-State are studied in detail via the ground-state energy, the magnetizations and the staggered magnetizations, as well as the Shannon-Renyi entropies characterizing the multifractality of the components of the wave function.

cond-mat.str-el↗

arXiv2017

Random Transverse Field Spin-Glass Model on the Cayley tree : phase transition between the two Many-Body-Localized Phases

The quantum Ising model with random couplings and random transverse fields on the Cayley tree is studied by Real-Space-Renormalization in order to construct the whole set of eigenstates. The renormalization rules are analyzed via large deviations. The phase transition between the paramagnetic and the spin-glass Many-Body-Localized phases involves the activated exponent $ψ=1$ and the correlation length exponent $ν=1$. The spin-glass-ordered cluster containing $N_{SG}$ spins is found to be extremely sparse with respect to the total number $N$ of spins : its size grows only logarithmically at the critical point $N_{SG}^{criti} \propto \ln N$, and it is sub-extensive $N_{SG} \propto N^θ$ in the finite region of the spin-glass phase where the continuously varying exponent $θ$ remains in the interval $0<θ<1$.

cond-mat.dis-nn↗

arXiv2017

Multifractality in the generalized Aubry-Andre quasiperiodic localization model with power-law hoppings or power-law Fourier coefficients

The nearest-neighbor Aubry-André quasiperiodic localization model is generalized to include power-law translation-invariant hoppings $T_l\propto t/l^a$ or power-law Fourier coefficients $W_m \propto w/m^b$ in the quasi-periodic potential. The Aubry-André duality between $T_l$ and $W_m$ is manifest when the Hamiltonian is written in the real-space basis and in the Fourier basis on a finite ring. The perturbative analysis in the amplitude $t$ of the hoppings yields that the eigenstates remain power-law localized in real space for $a>1$ and are critical for $a_c=1$ where they follow the Strong Multifractality linear spectrum, as in the equivalent model with random disorder. The perturbative analysis in the amplitude $w$ of the quasi-periodic potential yields that the eigenstates remain delocalized in real space (power-law localized in Fourier space) for $b>1$ and are critical for $b_c=1$ where they follow the Weak Multifractality gaussian spectrum in real space (or Strong Multifractality linear spectrum in the Fourier basis). This critical case $b_c=1$ for the Fourier coefficients $W_m$ corresponds to a periodic function with discontinuities, instead of the cosinus of the standard self-dual Aubry-André model.

cond-mat.dis-nn↗

arXiv2017

Periodically driven random quantum spin chains : Real-Space Renormalization for Floquet localized phases

When random quantum spin chains are submitted to some periodic Floquet driving, the eigenstates of the time-evolution operator over one period can be localized in real space. For the case of periodic quenches between two Hamiltonians (or periodic kicks), where the time-evolution operator over one period reduces to the product of two simple transfer matrices, we propose a Block-self-dual renormalization procedure to construct the localized eigenstates of the Floquet dynamics. We also discuss the corresponding Strong Disorder Renormalization procedure, that generalizes the RSRG-X procedure to construct the localized eigenstates of time-independent Hamiltonians.

cond-mat.dis-nn↗

arXiv2017

Boundary-driven Lindblad dynamics of random quantum spin chains : strong disorder approach for the relaxation, the steady state and the current

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 of two reservoirs can be then analyzed from the effective renormalized Linbladians associated to the two reservoirs. The magnetization is found to follow a step profile, as found previously in other localized chains. The strong disorder approach allows to compute explicitly the location of the step of the magnetization profile and the corresponding magnetization-current for each disordered sample in terms of the random fields and couplings.

cond-mat.dis-nn↗

arXiv2017

Dissipative random quantum spin chain with boundary-driving and bulk-dephasing: magnetization and current statistics in the Non-Equilibrium-Steady-State

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 of the corresponding Non-Equilibrium-Steady-State in each disordered sample between the two reservoirs are studied in detail by extending the methods that have been previously developed for the Symmetric Exclusion Process without disorder. Explicit results are given for the magnetization profile, for the two-point correlations, for the mean current and for the current fluctuations, in terms of the random fields and couplings defining the disordered sample.

cond-mat.dis-nn↗

arXiv2017

Statistical properties of the Green function in finite size for Anderson Localization models with multifractal eigenvectors

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 $G^I_{xx}(E-i η)$ and study the scaling with the size $N$ of the moments of arbitrary indices $q$ when the broadening follows the scaling $η=\frac{c}{N^δ}$. For the standard scaling regime $δ=1$, we find in the two limits $c \ll 1$ and $c \gg 1$ that the moments are governed by the anomalous exponents $Δ(q)$ of individual eigenfunctions, without the assumption of strong correlations between the weights of consecutive eigenstates at the same point. For the non-standard scaling regimes $0<δ<1$, we obtain that the imaginary Green function follows some Fréchet distribution in the typical region, while rare events are important to obtain the scaling of the moments. We describe the application to the case of Gaussian multifractality and to the case of linear multifractality.

cond-mat.dis-nn↗