From trivial to topological paramagnets: The case of ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_2^3$ symmetries in two dimensions

Abstract

Using quantum Monte Carlo simulations, we map out the phase diagram of Hamiltonians interpolating between trivial and non-trivial bosonic symmetry-protected topological phases, protected by ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_2^3$ symmetries, in two dimensions. In all cases, we find that the trivial and the topological phases are separated by an intermediate phase in which the protecting symmetry is spontaneously broken. Depending on the model, we identify a variety of magnetic orders on the triangular lattice, including ferromagnetism, $\sqrt{3}\times \sqrt{3}$ order, and stripe orders (both commensurate and incommensurate). Critical properties are determined through a finite-size scaling analysis. Possible scenarios regarding the nature of the phase transitions are discussed.

14 pages, 12 figures

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Cited by in corpus (13)

• Pivot Hamiltonians as generators of symmetry and entanglement
• Symmetry-protected sign problem and magic in quantum phases of matter
• Evidence for deconfined $U(1)$ gauge theory at the transition between toric code and double semion
• Building models of topological quantum criticality from pivot Hamiltonians
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• Boundary deconfined quantum criticality at transitions between symmetry-protected topological chains
• Average-exact mixed anomalies and compatible phases
• Continuous phase transitions between fractional quantum Hall states and symmetry-protected topological states
• Incommensurate gapless ferromagnetism connecting competing symmetry-enriched deconfined quantum phase transitions
• Continuous topological phase transition between ${\mathbb{Z}}_2$ topologically ordered phases
• 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