Electric Circuit Realizations of Fracton Physics

TL;DR

This paper proposes classical electric circuits that mimic fracton quasiparticle behavior by enforcing dipole moment conservation, providing a platform for experimental testing and potential quantum extensions.

Contribution

It introduces a novel circuit design using transformers to realize fracton physics and demonstrates their properties through simulations.

Findings

Circuits can preserve initial dipole moments indefinitely in ideal conditions.

Flux leakage causes eventual violation of fracton constraints in realistic systems.

Proposed circuits can serve as experimental platforms and DC filters.

Abstract

We design a set of classical macroscopic electric circuits in which charge exhibits the mobility restrictions of fracton quasiparticles. The crucial ingredient in these circuits is a transformer, which induces currents between pairs of adjacent wires. For an appropriately designed geometry, this induction serves to enforce conservation of dipole moment. We show that a network of capacitors connected via ideal transformers will forever remember the dipole moment of its initial charge configuration. Relaxation of the dipole moment in realistic systems can only occur via flux leakage in the transformers, which will lead to violations of fracton physics at the longest times. We propose a concrete diagnostic for these "fractolectric" circuits in the form of their characteristic equilibrium charge configurations, which we verify using simple circuit simulation software. These circuits not only provide an experimental testing ground for fracton physics, but also serve as DC filters. We outline extensions of these ideas to circuits featuring other types of higher moment conservation laws, as well as to higher-dimensional circuits which act as fracton "current-ice." While our focus is on classical circuits, we discuss how these ideas can be straightforwardly extended to realize quantized fractons in superconducting circuits.