Exotic phase transitions in spin ladders with discrete symmetries that emulate spin-1/2 bosons in 2D

We introduce a spin ladder with a set of discrete symmetries that is designed to emulate a two-dimensional spin-1/2 boson system at half-filling. Based on global properties such as the structure of topological defects, we establish the correspondence between the two systems and construct a dictionary of symmetries and operators. In particular, translation invariance leads to Lieb-Schultz-Mattis constraints for both systems, resulting in exotic deconfined quantum critical points. Subsequently, we study the spin ladder in detail. An exact duality transformation maps it onto a Z2 gauge theory of three partons, analogous to the U(1) gauge theory of chargons and spinons in two-dimensional spin-1/2 boson systems. With the mapping between spins and partons, we construct exactly solvable models for all pertinent symmetry-breaking phases and analyze their transitions. We complement the exact analysis with numerics and make connections to conventional parton gauge theories.