Rokhsar-Kivelson Models of Bosonic Symmetry-Protected Topological States

Abstract

A platform for constructing microscopic Hamiltonians describing bosonic symmetry-protected topological (SPT) states is presented. The Hamiltonians we consider are examples of frustration-free Rokhsar-Kivelson models, which are known to be in one-to-one correspondence with classical stochastic systems in the same spatial dimensionality. By exploring this classical-quantum mapping, we are able to construct a large class of microscopic models which, in a closed manifold, have a non-degenerate gapped symmetric ground state describing the universal properties of SPT states. Examples of one and two dimensional SPT states which illustrate our approach are discussed.

12 pages; 3 figures

References in corpus (3)

• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Topological Order and Conformal Quantum Critical Points
• Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge

Cited by in corpus (17)

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• Lieb-Schultz-Mattis anomalies and web of dualities induced by gauging in quantum spin chains
• Classifying One-Dimensional Quantum States Prepared by a Single Round of Measurements
• Boundary deconfined quantum criticality at transitions between symmetry-protected topological chains
• Boundary conditions and anomalies of conformal field theories in 1+1 dimensions
• Noninvertible symmetry and topological holography for modulated SPT in one dimension
• Detecting topological order from modular transformations of ground states on the torus
• Incommensurate gapless ferromagnetism connecting competing symmetry-enriched deconfined quantum phase transitions
• Measurement-Driven Transitions between Area Law Phases
• Charge pumps, pivot Hamiltonians and symmetry-protected topological phases
• Bridging Rokhsar-Kivelson Type and Generic Quantum Phase Transitions via Thermofield Double States
• Intertwined order of generalized global symmetries
• Parafermionic representation of Potts-based cluster chain