Gapless Coulomb State Emerging from a Self-Dual Topological Tensor-Network State

Area of Science:

• Condensed Matter Physics
• Quantum Field Theory
• Topological Quantum Matter

Background:

• Topological states of matter exhibit exotic properties like anyonic excitations.
• Understanding topological phase transitions and their underlying models is crucial for quantum information science.

Purpose of the Study:

• To propose a tensor network representation for a deformed Z_{2} topological ground state wave function.
• To establish an exact mapping between this topological state and the two-dimensional Ashkin-Teller model.
• To investigate topological phase transitions and novel quantum phases within this framework.

Main Methods:

• Tensor network representation of topological ground states.
• Exact mapping to the two-dimensional Ashkin-Teller model.
• Analysis of quantum Kosterlitz-Thouless phase transitions.
• Derivation of scaling behavior for anyon correlations.

Main Results:

• The norm of the Z_{2} topological ground state is mapped to the Ashkin-Teller model.
• Topological (toric code) phases correspond to partial order phases of the Ashkin-Teller model.
• A gapless Coulomb state with quasi-long-range order emerges via quantum Kosterlitz-Thouless transition.
• Deformations from self-duality lead to gapped Higgs or confining phases.

Conclusions:

• The Ashkin-Teller model provides a solvable framework for understanding Z_{2} topological phases and transitions.
• The study reveals a novel gapless Coulomb state and its connection to electric-magnetic duality.
• The findings offer insights into anyon interactions, condensation, and the behavior of topological matter under perturbations.