Gapless Coulomb state emerging from a self-dual topological tensor-network state

Abstract

In the tensor network representation, a deformed $Z_2$ topological ground state wave function is proposed and its norm can be exactly mapped to the two-dimensional solvable Ashkin-Teller (AT) model. Then the topological (toric code) phase with anyonic excitations corresponds to the partial order phase of the AT model, and possible topological phase transitions are precisely determined. With the electric-magnetic self-duality, a novel gapless Coulomb state with quasi-long-range order is obtained via a quantum Kosterlitz-Thouless phase transition. The corresponding ground state is a condensate of pairs of logarithmically confined electric charges and magnetic fluxes, and the scaling behavior of various anyon correlations can be exactly derived, revealing the effective interaction between anyons and their condensation. Deformations away from the self-duality drive the Coulomb state into either the gapped Higgs phase or confining phase.

4.5 pages 4 figures, and 5 appendices, the published version

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Cited by in corpus (5)

• Multicritical point of the three-dimensional Z_2 gauge Higgs model
• Characterization of topological phase transitions from a non-Abelian topological state and its Galois conjugate through condensation and confinement order parameters
• Complete characterization of non-Abelian topological phase transitions and detection of anyon splitting with projected entangled pair states
• Determining topological order from infinite projected entangled pair states
• Self-dual criticality in three-dimensional ${\mathbb{Z}}_2$ gauge theory with matter