Deconfinement and glassy behavior of U(1) quantum spin liquids

We revisit the mapping of U(1) gauge theory in quantum spin ice and discuss how to understand the deconfinement of the frustrated U(1) gauge theory. In particular, the systematic way to estimate the gauge field strength is argued for both electric field and magnetic field. Thus, one could understand confined vs deconfined transition between (quasi-) 2D and 3D. In addition, we discuss glassy behavior due to attractive interaction between gauge charges which results from further neighbor Ising spin exchanges. In this case, we explore relevant phase transitions and their characteristics similar to a charged colloidal particle problem.