Exact solution of one class of Maryland model

TL;DR

This paper provides an exact solution for a class of Maryland models, including special cases like the original Maryland model and its relation to Bloch oscillations, advancing understanding of these quantum systems.

Contribution

It offers an exact analytical solution for the one-body Maryland model with Toeplitz interaction matrices, clarifying its relation to Bloch oscillations and extending to many-body cases.

Findings

Exact solutions for Maryland models with doubly infinite Hilbert space

Connection established between Maryland model and Bloch oscillations

Extension to many-body Luttinger model case

Abstract

The Hamiltonian H of one-body Maryland model is defined as the sum of a linear unperturbed Hamiltonian H_0 and the interaction V, which is a Toeplitz matrix. Maryland model with a doubly infinite Hilbert space are exactly solved. Special cases of one-body Maryland model include the original Maryland model (Phys. Rev. Lett. 49, 833 (1982) and Physica 10D, 369 (1984)), which describes a quantum kickied linear rotator and single band Bloch oscillations. Maryland model and single band Bloch oscillations are the same Hamiltonian in two different representations. A special case of many-body Maryland model is Luttinger model.