Designer stealthy disordered spin chains and their quantum behavior

Abstract

The goal of this thesis is to study disordered stealthy hyperuniform spin chains on a one-dimensional integer lattice with classical and quantum interactions. Hyperuniform systems possess anomalously suppressed long-wavelength density fluctuations. Stealthy hyperuniform systems are transparent to radiation with wavelength greater than 2π/K, where K is an exclusion radius in k-space [1]. Disordered hyperuniformity characterizes an interesting variety of physical systems, including large-scale structure in the Universe [2], the arrangement of avian photoreceptors [3], and disordered 2D photonic materials with complete photonic band gaps [4]. We enumerate all periodic stealthy hyperuniform one-dimensional spin systems up to a finite unit cell size. To study the enumerated stealthy configurations, we make use of a recently developed inverse statistical mechanics method for classical spin systems [5, 6] as well as quantum Monte Carlo simulation. The inverse method finds classical spin-spin interaction potentials that stabilize the stealthy configurations as classical ground states. By adding a transverse field to the designer Hamiltonian, we observe how the classically disordered spin states behave with additional quantum fluctuations and discover fascinating ordering behavior for an exemplary stealthy system.