Spectral statistics of disordered systems encode Thouless and Heisenberg timescales, whose ratio determines whether the system is chaotic or localized. We show that scaling time with size disorder strength very similar in one-body Anderson models quantum many-body systems. argue two parameter breaks down vicinity transition to localized phase, signaling a slowing-down dynamics.

We study time dynamics of 1D disordered Heisenberg spin-1/2 chain focusing on a regime large system sizes and long evolution. This is relevant for observation many-body localization (MBL), phenomenon that expected to freeze the prevent it from reaching thermal equilibrium. Performing extensive numerical simulations imbalance, quantity often employed in experimental studies MBL, we show slow power-law decay imbalance persists disorder strengths exceeding by at least factor 2 current estimates...

Quantum systems evolving unitarily and subject to quantum measurements exhibit various types of non-equilibrium phase transitions, arising from the competition between unitary evolution measurements. Dissipative transitions in steady states time-independent Liouvillians measurement induced at level trajectories are two primary examples such transitions. Investigating a many-body spin system periodic resetting measurements, we argue that dissipative Floquet dynamics provides natural framework...

We investigate the structure of many-body wave functions 1D quantum circuits with local measurements employing participation entropies. The leading term in system size dependence entropy indicates a model-dependent multifractal scaling at any nonzero measurement rate. subleading contains universal information about measurement-induced phase transitions and plays role an order parameter, being constant error-correcting vanishing Zeno phase. provide robust numerical evidence investigating...

Many-body unitary dynamics interspersed with repeated measurements display a rich phenomenology hallmarked by measurement-induced phase transitions. Employing feedback-control operations that steer the toward an absorbing state, we study entanglement entropy behavior at state transition. For short-range control operations, observe transition between phases distinct sub-extensive scalings of entropy. In contrast, system undergoes volume-law and area-law for long-range feedback operations. The...

Polynomially filtered exact diagonalization method (POLFED) for large sparse matrices is introduced. The algorithm finds an optimal basis of a subspace spanned by eigenvectors with eigenvalues close to specified energy target spectral transformation using high order polynomial the matrix. memory requirements scale better system size than in state-of-the-art shift-invert approach. potential POLFED demonstrated examining many-body localization transition 1D interacting quantum spin-1/2 chains....

Contrary to claims that a fundamental limit of precision in quantum metrology can be broken certain circumstances, new analysis shows this is not the case once one takes into account time needed perform operations.

The possibility of observing many-body localization ultracold atoms in a one-dimensional optical lattice is discussed for random interactions. In the noninteracting limit, such system reduces to single-particle physics absence disorder, i.e., extended states. effect, observed inherently due interactions and thus genuine effect. studied, manifests itself lack thermalization visible temporal propagation specially prepared initial state, transport properties, logarithmic growth entanglement...

We compare the accuracy of two prime time evolution algorithms involving matrix product states---tDMRG (time-dependent density renormalization group) and TDVP variational principle). The latter is supposed to be superior within a limited fixed auxiliary space dimension. Surprisingly, we find that performance depends on model considered. In particular, many-body localized systems as well crossover regions between delocalized phases are better described by tDMRG, contrary regime where indeed...

Level statistics of systems that undergo many--body localization transition are studied. An analysis the gap ratio from perspective inter- and intra-sample randomness allows us to pin point differences between transitions in random quasi-random disorder, showing effects due Griffiths rare events for former case. It is argued case disorder exhibits universal features identified by constructing an appropriate model intermediate spectral which a generalization family short-range plasma models....

The interplay between unitary dynamics and local quantum measurements results in unconventional nonunitary dynamical phases transitions. In this paper we investigate the of $(d+1)$-dimensional hybrid stabilizer circuits, for $d=1,2,3$. We characterize measurement-induced their transitions using large-scale numerical simulations focusing on entanglement measures, purification dynamics, wave-function structure. Our findings demonstrate transition $(d+1)$ spatiotemporal dimensions is conformal...

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...

Universal quantum computing requires nonstabilizer (magic) states. Quantifying the nonstabilizerness and relating it to other resources is vital for characterizing complexity of many-body systems. In this work, we prove that a state stabilizer if only all states belonging its Clifford orbit have flat probability distribution on computational basis. This implies, in particular, multifractal are nonstabilizers. We introduce flatness, measure based participation entropy quantifies wave-function...

Many-body localization for a system of bosons trapped in one-dimensional lattice is discussed. Two models that may be realized cold atoms optical lattices are considered. The model with random on-site potential compared previously introduced interactions model. While the origin and character disorder both systems different they show interesting similar properties. In particular, many-body appears sufficiently large as verified by time evolution initial density wave states well using...

We numerically study level statistics of disordered interacting quantum many-body systems. A two-parameter plasma model which controls the repulsion exponent $\ensuremath{\beta}$ and range $h$ interactions between eigenvalues is shown to reproduce accurately features across transition from ergodic localized phase. Analysis higher-order spacing ratios indicates that considered $\ensuremath{\beta}\ensuremath{-}h$ accounts even for long-range spectral correlations allows us obtain a clear...

We study the XXZ model with a random magnetic field in contact weakly disordered spin chain, acting as finite thermal bath. revise Fermi's golden rule description of interaction between bath and contrasting it nonperturbative quantum avalanche scenario for thermalization system. employ two-point correlation functions to define extent $\xi_d$ thermalized region next Unbounded growth proportional logarithm time or faster is signature an avalanche. Such behavior signifies system, we confirm...

Understanding how errors deteriorate the information encoded in a many-body quantum system is fundamental problem with practical implications for technologies. Here, we investigate class of encoding-decoding random circuits subject to local coherent and incoherent errors. We analytically demonstrate existence phase transition from an error-protecting error-vulnerable occurring when error strength increased. This accompanied by R\'enyi entropy transitions onset multifractal features system....

The quantum sun model is an interacting that exhibits sharp signatures of ergodicity breaking phase transition. Here, we show the a many-body mobility edge. We provide analytical arguments for its existence, complemented by state-of-the-art numerical simulations analyzing gap ratios, Thouless times as well entanglement entropy eigenstates. also introduce with particle number conservation and argue it shares many similarities unrestricted predecessor.

Thermalization of random-field Heisenberg spin chain is probed by time evolution density correlation functions. Studying the impacts average energies initial product states on dynamics system, we provide arguments in favor existence a mobility edge large system-size limit.

We analyze the finite-size scaling of average gap ratio and entanglement entropy across many-body localization (MBL) transition in one dimensional Heisenberg spin chain with quasiperiodic (QP) potential. By using recently introduced cost-function approach, we compare different scenarios for exact diagonalization systems up to 22 lattice sites. Our findings suggest that MBL QP belongs class Berezinskii-Kosterlitz-Thouless transition, same as case uniformly disordered advocated recent studies....

The unitary dynamics of a quantum system initialized in selected basis state yield, generically, that is superposition all the states. This process, associated with information scrambling and intimately tied to resource theory coherence, may be viewed as gradual delocalization system's Hilbert space. work analyzes space under random circuits, which serve minimal model chaotic many-body systems. We employ analytical methods based on replica trick Weingarten calculus investigate time evolution...

Abstract Magic is the resource that quantifies amount of beyond-Clifford operations necessary for universal quantum computing. It bounds cost classically simulating systems via stabilizer circuits central to error correction and computation. In this paper, we investigate how fast generic many-body dynamics generate magic resources under constraints locality unitarity, focusing on spreading in brick-wall random unitary circuits. We explore scalable measures intimately connected algebraic...