Effective gauge theory of strongly correlated systems

Naoto Nagaosa

Olav F. Syljuåsen

C. S. Chisholm, Anika Frölian, E. Neri +3 more

Topological gauge theories provide powerful effective descriptions of certain strongly correlated systems, a prime example being the Chern-Simons gauge theory of fractional quantum Hall states.Engineering topological gauge theories in controlled quantum systems is of both conceptual and practical importance, as it would provide access to systems with exotic excitations such as anyons without the need for strong correlations.Here, we discuss a scheme to engineer the chiral BF theory, a minimal model of a topological gauge theory corresponding to a one-dimensional reduction of the Chern-Simons theory, with ultracold atoms.Using the local conservation laws of the theory, we encode its quantum Hamiltonian into an ultracold quantum gas with chiral interactions.Building on a seminal proposal by Edmonds et al. [Phys. Rev. Lett. 110, 085301 (2013)], we show how to implement it in a Raman-coupled Bose-Einstein condensate with imbalanced scattering lengths, as we have recently realized experimentally [Frölian et al., Nature (London) 608, 293 (2022)]. We discuss the properties of the chiral condensate from a gauge theory perspective and assess the validity of the effective quantum description for accessible experimental parameters via numerical simulations.Our approach lays the foundation for realizing topological gauge theories in higher dimensions with Bose-Einstein condensates.

Masuo Suzuki

Ikuo Ichinose, Tetsuo Matsui

In a recent Letter, Nayak argued that slave partices are always confined in gauge theories of strongly-correlated electron systems like the t-J model. The argument mostly relies on Elitzur's theorem and the fact that the effective gauge theory under discussion is at infinite coupling. On the other hand, in the previous papers we studied dynamics of the gauge theory of the t-J model showing that the slave particles are in the Coulomb phase below certain critical temperature T{CSS} that depends on hole doping. We comment on the discrepancy between the results in two papers.

Naoto Nagaosa