Related papers: Eigenstate Correlations in Dual-Unitary Quantum Ci…
We analyze in detail a sharp transition between the low-energy, low-dimensional eigenstates and the high-energy chaotic bulk of the spectrum for a simple supersymmetric quantum-mechanical model with Hamiltonian $\hat{H}_S =…
Spectral statistics such as the level spacing statistics and spectral form factor (SFF) are widely expected to accurately identify ``ergodicity'', including the presence of underlying macroscopic symmetries, in generic quantum systems…
The possible compatibility of density matrices for single-party subsystems is described by linear constraints on their respective spectra. Whenever some of those quantum marginal constraints are saturated, the total quantum state has a…
Random matrix theory (RMT) provides a successful model for quantum systems, whose classical counterpart has a chaotic dynamics. It is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Last decade witnessed…
The eigenstate entanglement entropy has been recently shown to be a powerful tool to distinguish integrable from generic quantum-chaotic models. In integrable models, a unique feature of the average eigenstate entanglement entropy (over all…
Spectral statistics and correlations are the usual way to study the presence or absence of quantum chaos in quantum systems. We present our investigation on the study of the fluctuation average and variance of certain correlation functions…
Multicomponent quantum Hall effect, under the interplay between intercomponent and intracomponent correlations, leads us to new emergent topological orders. Here, we report the theoretical discovery of fractional quantum hall effect of…
The spectral form factor (SFF) is a powerful diagnostic of random matrix behavior in quantum many-body systems. We introduce a family of random circuit ensembles whose SFFs can be computed \textit{exactly}. These ensembles describe the…
The set of covariance matrices of a continuous-variable quantum system with a finite number of degrees of freedom is a strict subset of the set of real positive-definite matrices due to Heisenberg's uncertainty principle. This has the…
Recent works have investigated the emergence of a new kind of random matrix behaviour in unitary dynamics following a quantum quench. Starting from a time-evolved state, an ensemble of pure states supported on a small subsystem can be…
The new phenomenon of semiquantum chaos is analyzed in a classically regular double-well oscillator model. Here it arises from a doubling of the number of effectively classical degrees of freedom, which are nonlinearly coupled in a Gaussian…
Correlations between the energies of a system's spectrum are one of the defining features of quantum chaos. They can be probed using the Spectral Form Factor (SFF). We investigate how each spectral distance contributes in building this…
The spectral correlation of a chaotic system with spin 1/2 is universally described by the GSE (Gaussian Symplectic Ensemble) of random matrices in the semiclassical limit. In semiclassical theory, the spectral form factor is expressed in…
It is predicted that for sufficiently strong electron-phonon coupling an anomalous quantum chaotic behavior develops in certain types of suspended electro-mechanical nanostructures, here comprised by a thin cylindrical quantum dot…
In quantum chaotic systems, the spectral form factor (SFF), defined as the Fourier transform of the two-level spectral correlation function, is known to follow random matrix theory (RMT), namely a 'ramp' followed by a 'plateau' in…
Quantum error correction was invented to allow for fault-tolerant quantum computation. Systems with topological order turned out to give a natural physical realization of quantum error correcting codes (QECC) in their groundspaces. More…
Following a recent work (briefly reviewed below) we consider temporal fluctuations in the reduced density matrix elements for a coupled system involving a pair of kicked rotors as also one made up of a pair of Harper Hamiltonians. These…
Recent work has shown that the entanglement of finite-temperature eigenstates in chaotic quantum many-body local Hamiltonians can be accurately described by an ensemble of random states with an internal $U(1)$ symmetry. We build upon this…
Signatures of dynamical quantum phase transitions and chaos can be found in the time evolution of generalized partition functions such as spectral form factors (SFF) and Loschmidt echoes. While a lot of work has focused on the nature of…
We show the emergence of random matrix theory (RMT) spectral correlations in the chaotic phase of generic periodically kicked interacting quantum many-body systems by analytically calculating spectral form factor (SFF), $K(t)$, up to two…