Related papers: Probing quantum chaos through singular-value corre…
It is often expected (and assumed) for a quantum chaotic system that the presence of correlated eigenvalues implies that all the other properties as dictated by random matrix theory are satisfied. We demonstrate using the spin-$1/2$ kicked…
Noise on quantum devices is much more complex than it is commonly given credit. Far from usual models of decoherence, nearly all quantum devices are plagued both by a continuum of environments and temporal instabilities. These induce noisy…
We explore the eigenvalue statistics of a non-Hermitian version of the Su-Schrieffer-Heeger model, with imaginary on-site potentials and randomly distributed hopping terms. We find that owing to the structure of the Hamiltonian, eigenvalues…
Recent studies have revealed intriguing similarities between the contribution of wormholes to the gravitational path integral and the phenomenon of replica symmetry breaking observed in spin glasses and other disordered systems.…
We study the asymptotic behavior of the eigenvalues of Gaussian perturbations of large Hermitian random matrices for which the limiting eigenvalue density vanishes at a singular interior point or vanishes faster than a square root at a…
In this work, we present a method to exponentiate non-sparse indefinite low-rank matrices on a quantum computer. Given an operation for accessing the elements of the matrix, our method allows singular values and associated singular vectors…
We propose a measure of quantum state complexity defined by minimizing the spread of the wave-function over all choices of basis. Our measure is controlled by the "survival amplitude" for a state to remain unchanged, and can be efficiently…
We study how Sachdev-Ye-Kitaev (SYK) interactions can arise from localized single-particle states on a system that is effectively one dimensional. If a local interaction is projected onto coarse localized orbitals, the resulting couplings…
Under unitary evolution, chaotic quantum systems initialized in simple states rapidly develop high complexity, precluding any efficient classical description. Quantum chaos is traditionally characterized by spectral properties of the…
Ensembles of quantum chaotic systems are expected to exhibit energy eigenvalues with random-matrix-like level repulsion between pairs of energies separated by less than the inverse Thouless time. Recent research has shown that exact and…
Chaotic systems that decompose into two cells connected only by a narrow channel exhibit characteristic deviations of their quantum spectral statistics from the canonical random-matrix ensembles. The equilibration between the cells…
We consider Random Matrix Theories with non-Gaussian potentials that have a rich phase structure in the large $N$ limit. We calculate the Spectral Form Factor (SFF) in such models and present them as interesting examples of dynamical models…
Inspired by recent developments in the study of the model of double scaled SYK (DSSYK), as elucidated in a recent paper, we embark on a re-evaluation of the Sachdev-Ye-Kitaev (SYK) model. Our motivation stems from the insights gained from…
We present a detailed quantitative analysis of spectral correlations in the Sachdev-Ye-Kitaev (SYK) model. We find that the deviations from universal Random Matrix Theory (RMT) behavior are due to a small number of long-wavelength…
Finding the ground state of strongly-interacting fermionic systems is often the prerequisite for fully understanding both quantum chemistry and condensed matter systems. The Sachdev--Ye--Kitaev (SYK) model is a representative example of…
We discuss higher dimensional generalizations of the 0+1-dimensional Sachdev-Ye-Kitaev (SYK) model that has recently become the focus of intensive interdisciplinary studies by, both, the condensed matter and field-theoretical communities.…
Strongly correlated metals comprise an enduring puzzle at the heart of condensed matter physics. Commonly a highly renormalized heavy Fermi liquid occurs below a small coherence scale, while at higher temperatures a broad incoherent regime…
Pseudo-hermitian matrices are matrices hermitian with respect to an indefinite metric. They can be thought of as the truncation of pseudo-hermitian operators, defined over some Krein space, together with the associated metric, to a finite…
The random matrix theory (RMT) can be used to classify both topological phases of matter and quantum chaos. We develop a systematic and transformative RMT to classify the quantum chaos in the colored Sachdev-Ye-Kitaev (SYK) model first…
Several condensed-matter platforms have been proposed recently to realize the Sachdev-Ye-Kitaev (SYK) model in their low-energy limit. In these proposed realizations, the characteristic SYK behavior is expected to occur under certain…