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View article: Quantum chaos challenges many-body localization
Quantum chaos challenges many-body localization Open
Characterizing states of matter through the lens of their ergodic properties is a fascinating new direction of research. In the quantum realm, the many-body localization (MBL) was proposed to be the paradigmatic ergodicity breaking phenome…
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Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model Open
We study spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model, a variant of the k-body embedded random ensembles studied for several decades in the context of nuclear physics and quantum chaos. We show analytically that the…
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Chaos, complexity, and random matrices Open
Chaos and complexity entail an entropic and computational obstruction to describing a system, and thus are intrinsically difficult to characterize. In this paper, we consider time evolution by Gaussian Unitary Ensemble (GUE) Hamiltonians a…
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Spectral statistics across the many-body localization transition Open
The many-body localization transition (MBLT) between ergodic and many-body\nlocalized phase in disordered interacting systems is a subject of much recent\ninterest. Statistics of eigenenergies is known to be a powerful probe of\ncrossovers…
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Sharp nonasymptotic bounds on the norm of random matrices with independent entries Open
We obtain nonasymptotic bounds on the spectral norm of random matrices with independent entries that improve significantly on earlier results. If $X$ is the $n\\times n$ symmetric matrix with $X_{ij}\\sim N(0,b_{ij}^{2})$, we show that\n¶\…
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Ergodicity breaking transition in finite disordered spin chains Open
We study disorder-induced ergodicity breaking transition in high-energy eigenstates of interacting spin-1/2 chains. Using exact diagonalization we introduce a cost function approach to quantitatively compare different scenarios for the eig…
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Quantum phase estimation of multiple eigenvalues for small-scale (noisy) experiments Open
Quantum phase estimation (QPE) is the workhorse behind any quantum algorithm and a promising method for determining ground state energies of strongly correlated quantum systems. Low-cost QPE techniques make use of circuits which only use a…
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Entrywise eigenvector analysis of random matrices with low expected rank Open
Recovering low-rank structures via eigenvector perturbation analysis is a common problem in statistical machine learning, such as in factor analysis, community detection, ranking, matrix completion, among others. While a large variety of b…
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AdS3 gravity and random CFT Open
A bstract We compute the path integral of three-dimensional gravity with negative cosmological constant on spaces which are topologically a torus times an interval. These are Euclidean wormholes, which smoothly interpolate between two asym…
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Thouless energy and multifractality across the many-body localization transition Open
Thermal and many-body localized phases are separated by a dynamical phase\ntransition of a new kind. We analyze the distribution of off-diagonal matrix\nelements of local operators across the many-body localization transition (MBLT)\nin a …
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Eigenstate thermalization hypothesis and out of time order correlators Open
The eigenstate thermalization hypothesis (ETH) implies a form for the matrix elements of local operators between eigenstates of the Hamiltonian, expected to be valid for chaotic systems. Another signal of chaos is a positive Lyapunov expon…
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Spectral Statistics and Many-Body Quantum Chaos with Conserved Charge Open
We investigate spectral statistics in spatially extended, chaotic many-body quantum systems with a conserved charge. We compute the spectral form factor K(t) analytically for a minimal Floquet circuit model that has a U(1) symmetry encoded…
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Decay properties of spectral projectors with applications to electronic structure Open
Motivated by applications in quantum chemistry and solid state physics, we\napply general results from approximation theory and matrix analysis to the\nstudy of the decay properties of spectral projectors associated with large and\nsparse …
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Many-body localization and thermalization: Insights from the entanglement spectrum Open
We study the entanglement spectrum in the many body localizing and\nthermalizing phases of one and two dimensional Hamiltonian systems, and\nperiodically driven `Floquet' systems. We focus on the level statistics of the\nentanglement spect…
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Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems Open
We study the transition between integrable and chaotic behavior in dissipative open quantum systems, exemplified by a boundary driven quantum spin chain. The repulsion between the complex eigenvalues of the corresponding Liouville operator…
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Krylov complexity from integrability to chaos Open
A bstract We apply a notion of quantum complexity, called “Krylov complexity”, to study the evolution of systems from integrability to chaos. For this purpose we investigate the integrable XXZ spin chain, enriched with an integrability bre…
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Adiabatic Eigenstate Deformations as a Sensitive Probe for Quantum Chaos Open
In the past decades, it was recognized that quantum chaos, which is essential for the emergence of statistical mechanics and thermodynamics, manifests itself in the effective description of the eigenstates of chaotic Hamiltonians through r…
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Universal Spectra of Random Lindblad Operators Open
To understand the typical dynamics of an open quantum system in continuous time, we introduce an ensemble of random Lindblad operators, which generate completely positive Markovian evolution in the space of the density matrices. The spectr…
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Entanglement negativity in random spin chains Open
We investigate the logarithmic negativity in strongly-disordered spin chains\nin the random-singlet phase. We focus on the spin-1/2 random Heisenberg chain\nand the random XX chain. We find that for two arbitrary intervals the\ndisorder-av…
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Semidefinite programs on sparse random graphs and their application to community detection Open
Denote by A the adjacency matrix of an Erdos-Renyi graph with bounded average degree. We consider the problem of maximizing over the set of positive semidefinite matrices X with diagonal entries X_ii=1. We prove that for large (bounded) av…
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Quantum chaos transition in a two-site Sachdev-Ye-Kitaev model dual to an eternal traversable wormhole Open
It has been recently proposed by Maldacena and Qi that an eternal traversable\nwormhole in a two dimensional Anti de Sitter space (${\\rm AdS}_2$) is the\ngravity dual of the low temperature limit of two Sachdev-Ye-Kitaev (SYK) models\ncou…
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Eigenstate thermalization and quantum chaos in the Holstein polaron model Open
The eigenstate thermalization hypothesis (ETH) is a successful theory that provides sufficient criteria for ergodicity in quantum many-body systems. Most studies were carried out for Hamiltonians relevant for ultracold quantum gases and si…
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Orthogonal Random Features Open
We present an intriguing discovery related to Random Fourier Features: in Gaussian kernel approximation, replacing the random Gaussian matrix by a properly scaled random orthogonal matrix significantly decreases kernel approximation error.…
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Spectral form factors and late time quantum chaos Open
This is a collection of notes about spectral form factors of standard ensembles in random matrix theory, written for the practical usage of the current study of late time quantum chaos. More precisely, we consider the Gaussian unitary ense…
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Noninteracting fermions at finite temperature in a-dimensional trap: Universal correlations Open
We study a system of $N$ non-interacting spin-less fermions trapped in a confining potential, in arbitrary dimensions $d$ and arbitrary temperature $T$. The presence of the trap introduces an edge where the average density of fermions vani…
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Generic dynamical features of quenched interacting quantum systems: Survival probability, density imbalance, and out-of-time-ordered correlator Open
We study numerically and analytically the quench dynamics of isolated many-body quantum systems. Using full random matrices from the Gaussian orthogonal ensemble, we obtain analytical expressions for the evolution of the survival probabili…
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Return probability for the Anderson model on the random regular graph Open
We study the return probability for the Anderson model on the random regular graph and give evidence of the existence of two distinct phases: a fully ergodic and nonergodic one. In the ergodic phase, the return probability decays polynomia…
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Introduction to Random Matrices - Theory and Practice Open
This is a book for absolute beginners. If you have heard about random matrix theory, commonly denoted RMT, but you do not know what that is, then welcome!, this is the place for you. Our aim is to provide a truly accessible introductory ac…
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From non-ergodic eigenvectors to local resolvent statistics and back: A random matrix perspective Open
We study the statistics of the local resolvent and non-ergodic properties of eigenvectors for a generalised Rosenzweig-Porter N × N random matrix model, undergoing two transitions separated by a delocalised non-ergodic phase. Interpreting …
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Random projections through multiple optical scattering: Approximating Kernels at the speed of light Open
Random projections have proven extremely useful in many signal processing and machine learning applications. However, they often require either to store a very large random matrix, or to use a different, structured matrix to reduce the com…