Stripe melting, a transition between weak and strong symmetry protected topological phases

TL;DR

This paper constructs a theoretical model demonstrating a phase transition between weak and strong symmetry protected topological phases in strongly interacting bosonic systems, using a 2D Dirac fermion framework with pair density wave order.

Contribution

It introduces a novel transition mechanism between weak and strong SPT phases via melting a pair density wave in a 2D system, employing an O(4) non-linear sigma model with a topological term.

Findings

Demonstrates a transition from weak to strong SPT phase in 2D bosonic systems.

Shows the nodal line of PDW hosts a 1D boson SPT phase.

Proposes a general scheme applicable to other dimensions and topological orders.

Abstract

For a gapped disordered many-body system with both internal and translation symmetry, one can define the corresponding weak and strong Symmetry Protected Topological (SPT) phases. A strong SPT phase is protected by the internal symmetry $G$ only while a weak SPT phase, fabricated by alignment of strong SPT state in a lower dimension, requires additional discrete translation symmetry protection. In this paper, we construct a phase transition between weak and strong SPT phase in strongly interacting boson system. The starting point of our construction is the superconducting Dirac fermions with pair density wave(PDW) order in $2d$. We first demonstrate that the nodal line of the PDW contains a $1d$ boson SPT phase. We further show that melting the PDW stripe and condensing the nodal line provoke the transition from weak to strong SPT phase in $2d$. The phase transition theory contains an O(4) non-linear-$\sigma$-model(NL$\sigma$M) with topological $\Theta$-term emerging from the proliferation of domain walls bound to an SPT chain. Similar scheme also applies to weak-strong SPT transition in other dimensions and predicts possible phase transition from $2d$ to $3d$ topological order.