Two fluid model of IQH bosons

Symmetry protected topological (SPT) phases are a class of interacting quantum systems which have a global symmetry but nevertheless possess a gapped energy spectrum. These states are distinct from typical topological phases in which the bulk gap is due to some broken symmetry (parity, time reversal, U(1), etc). Of interest are 2D systems such as quantum spin Hall states, topological insulators, and integer quantum Hall states of bosons. A key feature of these phases is the gapless edge states, which are robust against any perturbation that preserve the underlying symmetry. Typically the edge dynamics are studied from a stand alone edge theory, and connections to the bulk are encorporated through a bulk edge correspondence. Alternatively, if these systems are recast in terms of hydrodynamic variables, the details of the edge dynamics can be studied by means of hydrodynamic boundary layers. In this work we adapt the fluid description of FQH states seen in (arXiv:2203.06516) to model a system of interacting two component bosons. In particular, we show how the boundary conditions of a two fluid model naturally give rise to the two counter propagating boundary modes expected in these type of SPT phases. This work further justifies fluid descriptions of quantum phases, and opens the door to a more general study of the hydrodynamics of SPT phases.