arXiv subjects

Nathan L. Harshman

Publications and source records attributed to Nathan L. Harshman.

3 recordsLinked to original sources

arXiv2026

Symmetry and integrability in the anyon-Hubbard model

Recent cold atom experiments have realized one-dimensional anyons and enabled the tuning of 1D~statistics between bosons and fermions. Here, we analyze the symmetries, integrability, and resulting degeneracies of the underlying anyon-Hubbard model of finite length. Our results reveal a switching between symmetry classes AI, BDI, and CI in dependence on system size, particle number, and boundary conditions, and show that two anyons with periodic boundaries are integrable, while two anyons with open boundary conditions are not. We include a comprehensive analysis of all model limits, especially of interacting bosons and pseudofermions and resolve spectral signatures. We additionally reveal an exactly solvable doublon state that hides in the continuum of scattering states and the exact solution of the nullspace of two noninteracting anyons. The uncovered symmetries shape the fundamental properties of the one-dimensional anyons at hand, and the predicted states are accessible in state-of-the-art experiments.

cond-mat.quant-gas↗

arXiv2026

Partial solvability induced by dark states in a box trap with decentered two-body interaction

We consider a generalization of the two-body contact interaction for nonrelativistic particles confined to a one-dimensional box, in which the interaction is decentered, i.e., the particles interact only when they are separated by a distance c. In contrast to the harmonically trapped system, this model is nonintegrable. Despite this, we demonstrate that the system exhibits partial solvability due to the presence of dark states, i.e., bosonic or fermionic states unaffected by the interaction. These states form exactly solvable subspaces embedded within an interacting spectrum. We characterize the stationary properties of the system, identify the conditions for the appearance of dark states, and show how they structure the spectrum and delineate interacting and noninteracting sectors.

quant-ph↗

arXiv2020

A Solvable Model for Decoupling of Interacting Clusters

We consider M clusters of interacting particles, whose in-group interactions are arbitrary, and inter-group interactions are approximated by oscillator potentials. We show that there are masses and frequencies that decouple the in-group and inter-group degrees of freedom, which reduces the initial problem to M independent problems that describe each of the relative in-group systems. The dynamics of the M center-of-mass coordinates is described by the analytically solvable problem of M coupled harmonic oscillators. This paper derives and discusses these decoupling conditions. Furthermore, to illustrate our findings, we consider a charged impurity interacting with a ring of ions. We argue that the impurity can be used to probe the center-of-mass dynamics of the ions.

quant-ph↗