Effects of Peierls phases in open linear chains

The introduction of Peierls phases in open tight-binding chains without closed paths in either real or synthetic dimensions is understood to be physically inconsequential, as one assumes they can always be gauged away. Here, we show that this assumption does not necessarily hold for all systems in open chains, as closed paths may appear in the Fock space where these phases can lead to the creation of magnetic flux analogs with physical effects. This idea is first illustrated in the quadratic Kitaev model, where different patterns for the Peierls phases are studied and their independent manipulation is seen to be able to drive the appearance of topological states and Majorana flat bands. We then consider a system with quartic interactions, namely an extended Bose-Hubbard (EBH) open chain with a finite Peierls phase associated with the hopping terms. Focusing on the strong interactions limit of the two-body sector, we show the decisive influence of these phases on the two-band spectrum of the higher energy subspace, which behaves as an effective sawtooth chain with magnetic flux at each plaquette. In particular, both the width of the energy gap between the two bands and the position of the in-gap edge states can be controlled by the Peierls phase. Finally, by translating this two-particle one-dimensional (1D) system into a single-particle two-dimensional (2D) one, and subsequently mapping it onto an equivalent electrical LC circuit, we identify a parameter set for which in-gap states are only present for certain finite phase values. Tuning the circuit to these parameters generates the corresponding boundary voltage states, providing an experimentally detectable signature of the effects induced by manipulating Peierls phases in a model built on an open linear chain.