Quantum phase transitions between bosonic symmetry protected topological phases in two dimensions: emergent $QED_3$ and anyon superfluid

TL;DR

This paper develops a lattice wavefunction construction for 2D bosonic SPT phases, analyzes their phase transitions via emergent QED3 theory, and introduces an intermediate anyon superfluid phase.

Contribution

It provides a systematic projective construction method for 2D bosonic SPT wavefunctions and characterizes the phase transitions and intermediate phases between SPT states.

Findings

Emergent QED3 describes critical points between SPT phases.

Intermediate phase exhibits anyon superfluid properties.

Constructed explicit lattice wavefunctions for bosonic SPT phases.

Abstract

Inspired by Chern-Simons effective theory description of symmetry protected topological (SPT) phases in two dimensions, we present a projective construction for many-body wavefunctions of SPT phases. Using this projective construction we can systematically write down trial wavefunctions of SPT phases on a lattice. An explicit example of SPT phase with $U(1)$ symmetry is constructed for two types of bosons with filling $\nu_{b_1}=\nu_{b_2}=\frac12$ per site on square lattice. We study continuous phase transitions between different $U(1)$-SPT phases based on projective construction. The effective theory around the critical point is emergent $QED_3$ with fermion number $N_f=2$. Such a continuous phase transition however needs fine tuning, and in general there are intermediate phases between different $U(1)$-SPT phases. We show that such an intermediate phase has the same response as an anyon superconductor, and hence dub it "anyon superfluid". A schematic phase diagram of interacting bosons with $U(1)$ symmetry is depicted.