Related papers: Delocalization in Tight-Binding Hamiltonians: A Mo…
We prove the existence of extensive many-body Hamiltonians with few-body interactions and a many-body mobility edge: all eigenstates below a nonzero energy density are localized in an exponentially small fraction of "energetically allowed…
We investigate quantum phase transitions in which a change in the type of entanglement from bound entanglement to either free entanglement or separability may occur. In particular, we present a theoretical method to construct a class of…
We investigate the dynamics of a quantum system subjected to a time-dependent and conditional resetting protocol. Namely, we ask: what happens when the unitary evolution of the system is repeatedly interrupted at random time instants with…
We present a numerical method based on real-space renormalization that outputs the exact ground space of "frustration-free" Hamiltonians. The complexity of our method is polynomial in the degeneracy of the ground spaces of the Hamiltonians…
We have numerically investigated localization properties in the one-dimensional tight-binding model with chaotic binary on-site energy sequences generated by a modified Bernoulli map with the stationary-nonstationary chaotic transition…
The discretization approximation method commonly used to simulate the dynamics of quantum system coupled to the environment in continuum often suffers from the periodically partial recovery of initial state because of the effect of finite…
The location of the mobility edge is a long standing problem in Anderson localization. In this paper, we show that the effective confining potential introduced in the localization landscape (LL) theory predicts the onset of delocalization…
Many-body localization (MBL) addresses the absence of thermalization in interacting quantum systems, with non-ergodic high-energy eigenstates behaving as ground states, only area-law entangled. However, computing highly excited many-body…
The localization in a disordered system of $N$ interacting spins coupled by the long-range anisotropic interaction $1/R^{\alpha}$ is investigated using a finite size scaling in a $d=1$ -dimensional system for $N=8, 10, 12, 14$. The results…
We consider d dimensional systems which are localized in the absence of interactions, but whose single particle (SP) localization length diverges near a discrete set of (single-particle) energies, with critical exponent \nu. This class…
The ground-state properties of a few spin-1/2 fermions with different masses and interacting via short-range contact forces are studied within an exact diagonalization approach. It is shown that, depending on the shape of the external…
Transitions between the quantum Hall state and the Anderson insulator are studied in a two dimensional tight binding model with a uniform magnetic field and a random potential. By the string (anyon) gauge, the weak magnetic field regime is…
Analytic and numerical results for quasiperiodic tight-binding models are reviewed, with emphasis on two and three-dimensional models which so far are beyond a mathematically rigorous treatment. In particular, we consider energy spectra of…
A general decentralized computational framework for set-valued state estimation and prediction for the class of systems that accept a hybrid state machine representation is considered in this article. The decentralized scheme consists of a…
One dimensional pinning models have been widely studied in the physical and mathematical literature, also in presence of disorder. Roughly speaking, they undergo a transition between a delocalized phase and a localized one. In mathematical…
We study the properties of the ground states of the one- and two-dimensional Hubbard models at half filling and moderate doping using entanglement-based measures, which we calculate numerically using the momentum-space density matrix…
Reconstructing a quantum system's Hamiltonian from limited yet experimentally observable information is interesting both as a practical task and from a fundamental standpoint. We pose and investigate the inverse problem of reconstructing a…
We investigate the entanglement in Hubbard models of hardcore bosons in $1D$, with an additional hardcore interaction on nearest neighbouring sites. We derive analytical formulas for the bipartite entanglement entropy for any number of…
The presence of a topologically non-trivial discrete invariants implies the existence of gapless modes in finite samples, but it does not necessarily imply their localization. The disappearance of the indirect energy gap in the bulk…
Characterizing the entanglement structure of ground states of local Hamiltonians is a fundamental problem in quantum information. In this work we study the computational complexity of this problem, given the Hamiltonian as input. Our main…