Partons from stabilizer codes

TL;DR

This paper explores the conditions under which fermionic parton wave functions, especially from Majorana stabilizer codes, exhibit topological order after Gutzwiller projection, revealing phase transitions not apparent in unprojected states.

Contribution

It provides a rigorous framework for identifying topological order in projected fermionic wave functions and demonstrates phase transitions in interpolated Majorana codes using matrix product states.

Findings

Projected Majorana stabilizer codes can exhibit topological order.

Interpolated states show a phase transition detected by topological entanglement entropy.

Free-fermion states are adiabatically connected, but their projections can differ significantly.

Abstract

The Gutzwiller projection of fermionic wave functions is a well-established method for generating variational wave functions describing exotic states of matter, such as quantum spin liquids. We investigate the conditions under which a projected wave function constructed from fermionic partons can be rigorously shown to possess topological order. We demonstrate that these conditions can be precisely determined in the case of projected Majorana stabilizer codes. We then use matrix product states to study states that interpolate between two distinct Majorana fermion codes, one yielding a $\mathbb Z_2$ spin liquid and the other a trivial polarized state upon projection. While the free-fermion states are adiabatically connected, we find that the projected states undergo a phase transition detected by the topological entanglement entropy. Our work underscores the profound impact of the Gutzwiller projection and cautions against inferring properties of quantum spin liquids solely from their unprojected counterparts.