Sonika Johri

Singular behavior of eigenstates in Anderson's model of localization.

We observe an apparent singularity in the electronic properties of the Anderson model of localization with bounded diagonal disorder, which is clearly distinct from the well-established mobility edge (localization-delocalization transition) that occurs in dimensions d > 2. We present results of numerical calculations for Andersons original uniform (box) distribution of on-site disorder in dimensions d = 1, 2, and 3. To establish this hitherto unreported behavior, and to understand its evolution with disorder, we contrast the behavior of two different measures of the localization length of the electronic wave functions-the averaged inverse participation ratio and the Lyapunov exponent. Our data suggest that Andersons model exhibits richer behavior than has been established so far.

Comparison of the density-matrix renormalization group method applied to fractional quantum Hall systems in different geometries

Abstract We report a systematic study of the fractional quantum Hall effect (FQHE) using the density-matrix renormalization group (DMRG) method on two different geometries: the sphere and the cylinder. We provide convergence benchmarks based on model Hamiltonians known to possess exact zero-energy ground states, as well as an analysis of the number of sweeps and basis elements that need to be kept in order to achieve the desired accuracy. The ground state energies of the Coulomb Hamiltonian at ν = 1 / 3 and ν = 5 / 2 filling are extracted and compared with the results obtained by previous DMRG implementations in the literature. A remarkably rapid convergence in the cylinder geometry is noted and suggests that this boundary condition is particularly suited for the application of the DMRG method to the FQHE.

Entanglement spectroscopy on a quantum computer

We present a quantum algorithm to compute the entanglement spectrum of arbitrary quantum states. The interesting universal part of the entanglement spectrum is typically contained in the largest eigenvalues of the density matrix which can be obtained from the lower Renyi entropies through the Newton-Girard method. Obtaining the

Singular behavior of Anderson-localized wave functions for a two-site model

p

Large-disorder renormalization group study of the Anderson model of localization

largest eigenvalues (

RARE FLUCTUATION EFFECTS IN THE ANDERSON MODEL OF LOCALIZATION

\lambda_1>\lambda_2\ldots>\lambda_p

Many-Body Localization in Imperfectly Isolated Quantum Systems

) requires a parallel circuit depth of

Probing the geometry of the Laughlin state

\mathcal{O}(p(\lambda_1/\lambda_p)^p)

Numerical Study of a Many-Body Localized System Coupled to a Bath

and

Common path interference in Zener tunneling is a universal phenomenon

\mathcal{O}(p\log(N))