We construct a complete set of quasi-local integrals motion for the many-body localized phase interacting fermions in disordered potential. The can be chosen to have binary spectrum $\{0,1\}$, thus constituting exact quasiparticle occupation number operators Fermi insulator. map problem onto non-Hermitian hopping on lattice operator space. show how built, under certain approximations, as convergent series interaction strength. An estimate its radius convergence is given, which also provides...

We study the breaking of ergodicity measured in terms return probability evolution a quantum state spin chain. In non-ergodic phase evolves much smaller fraction Hilbert space than would be allowed by conservation extensive observables. By anomalous scaling participation ratios with system size we are led to consider distribution wave function coefficients, standard observable modern studies Anderson localization. finally present criterion for identification ergodicity-breaking (many-body...

We study high temperature spin transport in a disordered Heisenberg chain the ergodic regime. By employing density matrix renormalization group technique for of stationary states boundary-driven Lindblad equation we are able to extremely large systems (400 spins). find both diffusive and subdiffusive phase depending on strength disorder anisotropy parameter chain. Studying finite-size effects show numerically theoretically that very crossover length exists controls passage clean-system...

Statistical analysis of the eigenfunctions Anderson tight-binding model with on-site disorder on regular random graphs strongly suggests that extended states are multifractal at any finite disorder. The spectrum fractal dimensions $f(\ensuremath{\alpha})$ defined in Eq. (3) remains positive for $\ensuremath{\alpha}$ noticeably far from 1 even when is several times weaker than one which leads to localization; i.e., ergodicity can be reached only absence one-particle multifractality Bethe...

We review the current (as of Fall 2016) status studies on emergent integrability in many-body localized models. start by explaining how phenomenology fully systems can be recovered if one assumes existence a complete set (quasi)local operators which commute with Hamiltonian (local integrals motion, or LIOMs). describe evolution this idea from initial conjecture, to perturbative constructions, mathematical proof given for disordered spin chain. discuss proposed numerical algorithms...

We present a detailed analysis of the length- and timescales needed to approach critical region MBL from delocalised phase, studying both eigenstates time evolution an initial state. For we show that in there is single length, which function disorder strength, controlling finite-size flow. Small systems look localised, only for larger do resonances develop restore ergodicity form eigenstate thermalisation hypothesis. transport properties, study necessary spin across domain wall, showing how...

We show how lattice gauge theories can display many-body localization dynamics in the absence of disorder. Our starting point is observation that, for some generic translationally invariant states, Gauss law effectively induces a which be described as disorder average over superselection sectors. carry out extensive exact simulations on real-time Schwinger model, describing coupling between U(1) fields and staggered fermions. results memory effects slow, double-logarithmic entanglement...

We find the exact Casimir force between a plate and cylinder, geometry intermediate parallel plates, where is known exactly, sphere, it at large separations. The has an unexpectedly weak decay approximately L/[H3 ln(H/R)] plate-cylinder separations H (L R are cylinder length radius), due to transverse magnetic modes. Path integral quantization with partial wave expansion additionally gives qualitative difference for density of states electric modes, corrections finite temperatures.

In two remarkable recent papers the planar perturbative expansion was proposed for universal function of coupling appearing in dimensions high-spin operators $\mathcal{N}=4$ super Yang-Mills theory. We study numerically integral equation derived by Beisert, Eden, and Staudacher, which resums series. a confirmation anti--de Sitter-space/conformal-field-theory (AdS/CFT) correspondence, we find smooth whose leading terms at strong match results obtained semiclassical folded string spinning...

The quantum random energy model provides a mean-field description of the equilibrium spin glass transition. We show that it further exhibits many-body localization - delocalization (MBLD) transition when viewed as closed system. structure allows an analytically tractable MBLD using forward-scattering approximation and replica techniques. predictions are in good agreement with numerics. lies at density significantly above transition, indicating system dynamics freezes well outside traditional...

We study the return probability for Anderson model on random regular graph and give evidence of existence two distinct phases: a fully ergodic nonergodic one. In phase, decays polynomially with time oscillations, being attribute Wigner-Dyson-like behavior, while in phase decay follows stretched exponential decay. phenomenological interpretation terms classical walker. Furthermore, comparing typical mean values probability, we show how to differentiate an from benchmark this method first...

We study many-body localization (MBL) transition in disordered Floquet systems using a polynomially filtered exact diagonalization (POLFED) algorithm. focus on kicked Ising model and quantitatively demonstrate that finite-size effects at the MBL are less severe than random field XXZ spin chains widely studied context of MBL. Our conclusions extend also to other models, indicating smaller those observed usually considered autonomous chains. observe consistent signatures phase for several...

We perform a thorough and complete analysis of the Anderson localization transition on several models random graphs with regular connectivity. The unprecedented precision abundance our exact diagonalization data (both spectra eigenstates), together new finite size scaling statistical graph ensembles, unveils universal behavior which is described by two simple, integer, exponents. A by-product such reconciliation tension between results perturbation theory coming from strong disorder earlier...

We present a renormalization group (RG) analysis of the problem Anderson localization on random regular graph (RRG) which generalizes RG Abrahams, Anderson, Licciardello, and Ramakrishnan to infinite-dimensional graphs. The equations necessarily involve two parameters (one being changing connectivity subtrees), but we show that one-parameter scaling hypothesis is recovered for sufficiently large system sizes both eigenstates spectrum observables. also explain nonmonotonic behavior dynamical...

We study the Casimir force acting on a conducting piston with arbitrary cross section. find exact solution for rectangular section and first three terms in asymptotic expansion small height to width ratio when is arbitrary. Though weakened by presence of walls, turns out be always attractive. Claims repulsive forces related configurations, like cube, are invalidated cutoff dependence.

We propose a new approach to the Casimir effect based on classical ray optics. define and compute contribution of optical paths force between rigid bodies. reproduce standard result for parallel plates agree over wide range parameters with recent numerical treatment sphere plate Dirichlet boundary conditions. Our improves upon proximity approximation. It can be generalized easily other geometries, conditions, computation energy densities, many situations.

It is well known that one can map certain properties of random matrices, fermionic gases, and zeros the Riemann zeta function to a unique point process on real line . Here we analytically provide exact generalizations such in d-dimensional Euclidean space for any d, which are special cases determinantal processes. In particular, obtain n-particle correlation functions n, completely specify processes We also demonstrate spin-polarized systems have these same each dimension. The d shown be...

In this paper we analyze the predictions of forward approximation in some models which exhibit an Anderson (single-) or many-body localized phase. This approximation, consists summing over amplitudes only shortest paths locator expansion, is known to over-estimate critical value disorder determines onset Nevertheless, results provided by become more and accurate as local coordination (dimensionality) graph, defined hopping matrix, made larger. sense, can be regarded a mean field theory for...

We study the finite-time dynamics of an initially localized wave packet in Anderson model on random regular graph (RRG) and show presence a subdiffusion phase coexisting both with ergodic putative nonergodic phases. The full probability distribution $\mathrm{\ensuremath{\Pi}}(x,t)$ particle to be at some distance $x$ from initial state time $t$ is shown spread subdiffusively over range disorder strengths. comparison this result ${\mathbb{Z}}^{d}$ lattices, $d>2$, which subdiffusive only...

Isolated quantum systems with quenched randomness exhibit many-body localization (MBL), wherein they do not reach local thermal equilibrium even when highly excited above their ground states. It is widely believed that individual eigenstates capture this breakdown of thermalization at finite size. We show belief false in general and a MBL system can the eigenstate properties thermalizing system. propose localized approximately conserved operators (l$^*$-bits) underlie such systems. In...

The intriguing phenomenon of many-body localization (MBL) has attracted significant interest recently, but a complete characterization is still lacking. In this work, we introduce the total correlations, concept from quantum information theory capturing multi-partite to study phenomenon. We demonstrate that correlations diagonal ensemble provides meaningful diagnostic tool pin-down, probe, and better understand MBL transition ergodicity breaking in systems. particular, show sub-linear...

We study Casimir forces on the partition in a closed box (piston) with perfect metallic boundary conditions. Related geometries have generated interest as candidates for repulsive force. By using an optical path expansion we solve exactly case of piston rectangular cross section, and find that force always attracts to nearest base. For arbitrary sections, can use density states compute limit small height width ratios. The corrections between parallel plates are found interesting dependence...

We analyze the statistical properties of entanglement a large bipartite quantum system. By framing problem in terms random matrices and fictitious temperature, we unveil existence two phase transitions, characterized by different spectra reduced density matrices.