相关论文: Statistics of matrix elements of local operators i…
We demonstrate the connection between an operator's matrix element distribution and entangling power via numerical simulations of random, pseudo-random, and quantum chaotic operators. Creating operators with a random distribution of matrix…
We numerically analyze the statistical properties of complex system with conditions subjecting the matrix elements to a set of specific constraints besides symmetry, resulting in various structures in their matrix representation. Our…
Local observables and their translationally invariant counterparts are generally thought as providing the same predictions for experimental measurements. This is used in the context of their expectation values, which are indeed the same in…
Recent experimental and theoretical developments in many-body quantum systems motivate the study of their out-of-equilibrium properties through multi-time correlation functions. We consider the dynamics of higher-order out-of-time-order…
Out-of-time-order correlators (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalisation in interacting quantum many-body systems. It was recently argued that the expected exponential growth of…
We study the universality of spectral statistics of large random matrices. We consider $N\times N$ symmetric, hermitian or quaternion self-dual random matrices with independent, identically distributed entries (Wigner matrices) where the…
We introduce a family of random matrices where correlations between matrix elements are induced via interaction-derived Boltzmann factors. Varying these yields access to different ensembles. We find a universal scaling behavior of the…
We investigate a spatial subsystem entropy extracted from the one-particle density matrix (OPDM) in one-dimensional disordered interacting fermions that host a many-body localized (MBL) phase. Deep in the putative MBL regime, this OPDM…
We study the statistics of local energy minima in the configuration space and the energy relaxation due to activated hopping in a system of interacting electrons in a random environment. The distribution of the local minima is exponential,…
The relationship between physical observables defined in lattice models and the associated (quasi-)primary scaling operators of the underlying field-theory is revisited. In the context of local scale-invariance, we argue that this…
The Eigenstate Thermalization Hypothesis (ETH) was developed as a framework for understanding how the principles of statistical mechanics emerge in the long-time limit of isolated quantum many-body systems. Since then, ETH has shifted the…
We investigate the physical consequences of having a spectrum that satisfies random matrix theory (RMT) for generic Lindbladians, and compare its implications for spatially local and completely random Lindblad dynamics in one spatial…
We numerically study the random-hopping fermions (the Cruetz ladder) with repulsion and investigate how the interactions deform localized eigenstates by means of the one particle-density matrix (OPDM). The ground state exhibits resurgence…
We study the matrix elements of local and nonlocal operators in the single-particle eigenstates of two paradigmatic quantum-chaotic quadratic Hamiltonians; the quadratic Sachdev-Ye-Kitaev (SYK2) model and the three-dimensional Anderson…
This work describes the statistics for the occupation numbers of quantum levels in a large isolated quantum system, where all possible superpositions of eigenstates are allowed, provided all these superpositions have the same fixed energy.…
We show that the diagonal matrix elements $< Or^{p} >,$ where $O$ $={1,\beta,i\mathbf{\alpha n}\beta}$ are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb…
Understanding the asymptotic behavior of physical quantities in the thermodynamic limit is a fundamental problem in statistical mechanics. In this paper, we study how fast the eigenstate expectation values of a local operator converge to a…
In classical systems, our recent theoretical study provides new insight into how spatial constraint on the system connects with macroscopic properties, which lead to universal representation of equilibrium macroscopic physical property and…
Consider the $n!$ different unitary matrices that permute $n$ $d$-dimensional quantum systems. If $d\geq n$ then they are linearly independent. This paper discusses a sense in which they are approximately orthogonal (with respect to the…
We investigate the statistical properties of the eigenvalues and eigenvectors in a random matrix ensemble with $H_{ij}\sim |i-j|^{-\mu}$. It is known that this model shows a localization-delocalization transition (LDT) as a function of the…