Berry Phase and Topology in Ultrastrongly Coupled Quantum Light-Matter Systems

TL;DR

This paper develops a theoretical framework to analyze quantum geometry and topology in ultrastrong light-matter systems, revealing new topological phase transitions and mapping to well-known models.

Contribution

It introduces an efficient method to evaluate Berry phase and Chern number in ultrastrong coupling regimes, and uncovers novel reentrant topological transitions.

Findings

Reentrant transition to trivial phase in deep strong coupling

Mapping to Haldane honeycomb model

Accurate evaluation of topological invariants in ultrastrong coupling

Abstract

Strong coupling between matter and quantized electromagnetic fields in a cavity has emerged as a possible route toward controlling the phase of matter in the absence of an external drive. We develop a faithful and efficient theoretical framework to analyze quantum geometry and topology in materials ultrastrongly coupled to cavity electromagnetic fields in two dimensions. The formalism allows us to accurately evaluate geometrical and topological quantities, such as Berry phase and Chern number, in ultrastrong and deep strong coupling regimes. We apply our general framework to analyze a concrete model of massive Dirac fermions coupled to a circularly polarized cavity mode. Surprisingly, in addition to an ordinary transition to the topological phase, our analysis reveals a qualitatively new feature in deep strong coupling regimes, namely, the emergence of reentrant transition to the topologically trivial phase. We also present its intuitive understanding by showing the unitary mapping between the low-energy effective theory of strongly coupled light-matter systems and the Haldane honeycomb model.