Nonlinear Lifshitz Photon Theory in Condensed Matter Systems

TL;DR

This paper introduces a nonlinear Lifshitz photon theory describing a gauge boson with quadratic dispersion in condensed matter, analyzing its symmetries, decay, and implications for systems like quantum spin ice.

Contribution

It develops a novel interacting gauge theory with unique symmetries and decay properties, extending the understanding of Lifshitz photons in condensed matter systems.

Findings

Decay rate of the Lifshitz photon estimated.

Wilson loop deviates from perimeter law with a logarithmic correction.

Connections to quantum spin ice and ferromagnets explored.

Abstract

We present an interacting theory of a $U(1)$ gauge boson with a quadratic dispersion relation, which we call the "nonlinear Lifshitz photon theory.'' The Lifshitz photon is a three-dimensional generalization of the Tkachenko mode in rotating superfluids. Starting from the Wigner crystal of charged particles coupled to a dynamical $U(1)$ gauge field, after integrating out gapped degrees of freedom, we arrive at the Lagrangian for the nonlinear Lifshitz photon. The symmetries of the theory include a global $U(1)$ 1-form symmetry and nonlinearly realized "magnetic" translation and rotation symmetries. The interaction terms in the theory lead to the decay of the Lifshitz photon, the rate of which we estimate. We show that the Wilson loop, which plays the role of the order parameter of the spontaneous breaking of the 1-form global symmetry, deviates from the perimeter law by an additional logarithmic factor. We explore potential connections to other condensed matter systems, with a particular focus on quantum spin ice and ferromagnets. Finally, we generalize our theory to higher dimensions.