Emergent (2+1)D topological orders from iterative (1+1)D gauging

Description

Gauging involves introducing new degrees of freedom, known as gauge fields, to localize an existing global symmetry. It is known that, following this process, the gauge fields exhibit a dual global symmetry. Subsequently, one can gauge this emergent global symmetry by creating new gauge fields that once again exhibit a global symmetry. We investigate this iterative process, wherein new degrees of freedom are created and entangled with the previous ones through local symmetries. We focus on gauging spin chains with Abelian group symmetries and arranging the new spins on a 2D lattice. The local symmetries of the emergent 2D state, which are modified by the concatenation of the following gauging maps surprisingly correspond to the stabilizer terms of the XZZX-code generalized to any Abelian group. We encode our construction in the family of tensor network states that we dub ``projected entangled pair emergent states'' (PEPES). By utilizing this representation and by considering the local symmetries as stabilizer Hamiltonian terms, we establish a connection between the condensable anyons at the boundary and the quantum phase of the initial symmetric state before the gauging process.

Period	17 Apr 2024
Held at	Universidad Complutense de Madrid, Spain
Degree of Recognition	International