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

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.

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• Signatures of a Deconfined Phase Transition on the Shastry-Sutherland Lattice: Applications to Quantum Critical SrCu${}_2$(BO${}_3$)${}_2$
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• Bulk characterization of topological crystalline insulators: stability under interactions and relations to symmetry enriched U(1) quantum spin liquids
• Topological density-wave states in a particle-hole symmetric Weyl metal
• Topological Electromagnetic Responses of Bosonic Quantum Hall, Topological Insulator, and Chiral Semi-Metal phases in All Dimensions
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• Duality viewpoint of criticality
• Field theory of symmetry-protected valence bond solid states in (2+1) dimensions
• Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
• Decorated defect condensate, a window to unconventional quantum phase transitions in Weyl semimetals
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond
• Canonical quantization of nonlinear sigma models with theta term, with applications to symmetry-protected topological phases
• Transition between 2D Symmetry Protected Topological Phases on a Klein Bottle
• Perturbative and global anomalies in bosonic analogues of integer quantum Hall and topological insulator phases