Evidence for deconfined $U(1)$ gauge theory at the transition between toric code and double semion

Abstract

Building on quantum Monte Carlo simulations, we study the phase diagram of a one-parameter Hamiltonian interpolating between trivial and topological Ising paramagnets in two dimensions, which are dual to the toric code and the double semion. We discover an intermediate phase with stripe order which spontaneously breaks the protecting Ising symmetry. Remarkably, we find evidence that this intervening phase is gapless due to the incommensurability of the stripe pattern and that it is dual to a $U(1)$ gauge theory exhibiting Cantor deconfinement.

7 pages, 4 figures, supplemental material included (7 pages, 10 figures)

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Cited by in corpus (18)

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• Building models of topological quantum criticality from pivot Hamiltonians
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• Persistent Homology of ${\mathbb{Z}}_2$ Gauge Theories
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• Continuous phase transitions between fractional quantum Hall states and symmetry-protected topological states
• Topological physics in quantum critical systems
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• Advancing Hybrid Quantum-Classical Algorithms via Mean-Operators
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• Transition between 2D Symmetry Protected Topological Phases on a Klein Bottle
• Solvable models for 2+1D quantum critical points: Loop soups of 1+1D conformal field theories
• Twisted quantum doubles are sign problem-free