One-dimensional discrete gauge theories coupled to matter– towards exotic quantum dynamics of fractionalized phases

Being the backbone of our understanding of the microscopic laws of Nature, gauge theories enable us to investigate early moments after the Big Bang and the physics in the vicinity of black holes.

Moreover, gauge theories are also our best means to capture fractionalization of low-energy excitations in strongly correlated many-body problems and elucidate subtle features of quantum matter such as topological order, anyons, and entanglement.I intend to investigate theoretically the quantum interplay of the one-dimensional discrete Z2 gauge theory with single-component complex fermions.

I will start with developing the analytical understanding of quantum dynamics in the strong-coupling limit, where the theory becomes integrable and the powerful methods of the Bethe ansatz and generalized hydrodynamics are applicable.

These findings will be complemented with many-body numerical studies that rely on efficient state-of-the-art matrix product state tools.

Moreover, with the help of the coupled-wire construction, I will apply the acquired knowledge about this model to the more challenging two-dimensional problem.This work will reveal the dynamical properties of unconventional spin chains and will help to interpret the results of ongoing quantum simulations of discrete gauge theories in cold atom experiments.

It will also shed new light on the hydrodynamic description of integrable models with hard-core constraints and elucidate how lattice confinement leads to slow quantum dynamics.