Aharonov-Bohm effect in lattice field theory

Yu. A. Sitenko, N.D. Vlasii

Enrico C. Domanti, P. Castorina, Dario Zappalà +1 more

Gauge theories arise in physical systems displaying space-time local symmetries. They provide a powerful description of important realms of physics ranging from fundamental interactions to statistical mechanics, condensed matter, and, more recently, quantum computation. As such, a remarkably deep understanding has been achieved in the field. With the advent of quantum technology, lower energy analogs, capable of capturing important features of the original quantum field theories through quantum simulation, have been intensively studied. Here, we propose a specific scheme implementing an quantum simulation of lattice gauge theories constrained to mesoscopic spatial scales. To this end, we study the dynamics of mesons residing in a ring-shaped lattice of mesoscopic size pierced by an effective magnetic field. In particular, we find a type of Aharonov-Bohm effect that goes beyond the particlelike effect, reflecting the features of the confining gauge potential. The coherence properties of the meson are quantified by the persistent current and by specific features of the correlation functions. When the magnetic field is quenched, Aharonov-Bohm oscillations and correlations start a specific matter-wave current dynamics. Published by the American Physical Society 2024

José A. R. Cembranos, David García-López, Zoe Garcia del Toro

A. Heil, Alfred Kersch, B. Reifenhäuser +1 more

The Aharonov-Bohm effect is studied to elucidate the existence of global effects in field theory, originating from the topology of the field configuration. The problem is formulated in the language of Maxwell's equations, cohomology and principal fibre bundle theory. The authors offer a motivation for the use of these concepts. In particular, the idealised and realistic descriptions of the Aharonov-Bohm effect are distinguished.

Luiz H. Santos, Juven Wang

It is known as a purely quantum effect that a magnetic flux affects the real physics of a particle, such as the energy spectrum, even if the flux does not interfere with the particle's path---the Aharonov-Bohm effect. Here we examine an Aharonov-Bohm effect on a many-body wave function. Specifically, we study this many-body effect on the gapless edge states of a bulk gapped phase protected by a global symmetry (such as ${\mathbb{Z}}_{N}$)---the symmetry-protected topological (SPT) states. The many-body analog of spectral shifts, the twisted wave function, and the twisted boundary realization are identified in this SPT state. An explicit lattice construction of SPT edge states is derived, and a challenge of gauging its non-onsite symmetry is overcome. Agreement is found in the twisted spectrum between a numerical lattice calculation and a conformal field theory prediction.

Simon N. M. Ruijsenaars