Related papers: Localization Bounds for Multiparticle Systems
The presence of flat bands is a source of localization in lattice systems. While flat bands are often unstable with respect to interactions between the particles, they can persist in certain cases. We consider a diamond ladder with…
On physical grounds, one expects locally interacting quantum many-body systems to feature a finite group velocity. This intuition is rigorously underpinned by Lieb-Robinson bounds that state that locally interacting Hamiltonians with…
Systems with quasiperiodic disorder are known to exhibit localization transition in low dimension. After a critical strength of disorder all the states of the system become localized, thereby ceasing the particle motion in the system.…
We consider a system realized with one spinless quantum particle and an array of $N$ spins 1/2 in dimension one and three. We characterize all the Hamiltonians obtained as point perturbations of an assigned free dynamics in terms of some…
Discrete lattice models are a cornerstone of quantum many-body physics. They arise as effective descriptions of condensed matter systems and lattice-regularized quantum field theories. Lieb-Robinson bounds imply that if the degrees of…
We show that a one-dimensional Hubbard model with all-to-all coupling may exhibit many-body localization in the presence of local disorder. We numerically identify the parameter space where many-body localization occurs using exact…
First theoretical and numerical results on the global structure of the energy shell, the Green function spectra and the eigenfunctions, both localized and ergodic, in a generic conservative quantum system are presented. In case of quantum…
A large class of quantum phase transitions for quantum lattice systems are characterized by local order parameters. It is shown that local order parameters may be systematically constructed from tensor network representations of quantum…
Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a…
Using the density matrix renormalization group algorithm, we investigate the lattice model for spinless fermions in one dimension in the presence of a strong interaction and disorder. The phase sensitivity of the ground state energy is…
We consider spinless fermions on a finite one-dimensional lattice, interacting via nearest-neighbor repulsion and subject to a strong electric field. In the non-interacting case, due to Wannier-Stark localization, the single-particle wave…
Using variational density matrix optimization with two- and three-index conditions we study the one-dimensional Hubbard model with periodic boundary conditions at various filling factors. Special attention is directed to the full…
We study the spectral statistics of interacting spinless fermions in a two-dimensional disordered lattice. Within a full quantum treatment for small few-particle-systems, we compute the low-energy many-body states numerically. While at weak…
The energy level spacing distribution of a tight-binding hamiltonian is monitored across the mobility edge for a fixed disorder strength. Any mixing of extended and localized levels is avoided in the configurational averages, thus…
We prove Lieb-Robinson bounds for the dynamics of systems with an infinite dimensional Hilbert space and generated by unbounded Hamiltonians. In particular, we consider quantum harmonic and certain anharmonic lattice systems.
Localization marks the breakdown of thermalization in subregions of quantum many-body systems in the presence of sufficiently large disorder. In this paper, we use numerical techniques to study thermalization and localization in a many-body…
These lecture notes focus on the application of ideas of locality, in particular Lieb-Robinson bounds, to quantum many-body systems. We consider applications including correlation decay, topological order, a higher dimensional…
We study finite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which…
Many-body localization transition in a periodically driven quantum system is investigated using a solution of a matching Bethe lattice problem for Floquet states of a quantum random energy model with a generalization to more realistic…
We consider two particles with a local interaction $U$ in a random potential at a scale $L_1$ (the one particle localization length). A simplified description is provided by a Gaussian matrix ensemble with a preferential basis. We define…