Exactly solvable model for a deconfined quantum critical point in 1D

Abstract

We construct an exactly solvable lattice model for a deconfined quantum critical point (DQCP) in (1+1) dimensions. This DQCP occurs in an unusual setting, namely at the edge of a (2+1) dimensional bosonic symmetry protected topological phase (SPT) with ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ symmetry. The DQCP describes a transition between two gapped edges that break different ${\mathbb{Z}}_2$ subgroups of the full ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ symmetry. Our construction is based on an exact mapping between the SPT edge theory and a ${\mathbb{Z}}_4$ spin chain. This mapping reveals that DQCPs in this system are directly related to ordinary ${\mathbb{Z}}_4$ symmetry breaking critical points.

4.25 pages with 3 figures + 3 page supplemental material with 1 figure. References, discussion, and intro updated

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• "Deconfined" quantum critical points
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• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
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• Deconfined quantum critical point in one dimension
• Quantum phase transitions beyond Landau-Ginzburg theory in one-dimensional space revisited

Cited by in corpus (25)

• Lieb-Schultz-Mattis, Luttinger, and 't Hooft -- anomaly matching in lattice systems
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• Lieb-Schultz-Mattis anomalies and web of dualities induced by gauging in quantum spin chains
• Emergent generalized symmetries in ordered phases and applications to quantum disordering
• Gapless symmetry-protected topological phases and generalized deconfined critical points from gauging a finite subgroup
• Boundary deconfined quantum criticality at transitions between symmetry-protected topological chains
• Emergent self-duality in long range critical spin chain: from deconfined criticality to first order transition
• Average-exact mixed anomalies and compatible phases
• Deconfined Quantum Critical Point: A Review of Progress
• Symmetry fractionalization, mixed-anomalies and dualities in quantum spin models with generalized symmetries
• Deconfined Quantum Criticality in the long-range, anisotropic Heisenberg Chain
• Classical origins of Landau-incompatible transitions
• Pivoting through the chiral-clock family
• LSM and CPT
• Anyonic phase transitions in the 1D extended Hubbard model with fractional statistics
• Deconfined quantum criticality of frustrated hard-core dipolar bosons
• Deconfined criticality as intrinsically gapless topological state in one dimension
• Generalized Landau Paradigm for quantum phases and phase transitions
• Non-Landau quantum phase transition in modulated SU(N) Heisenberg spin chains
• Solvable models for 2+1D quantum critical points: Loop soups of 1+1D conformal field theories
• Deconfined quantum criticality on a triangular Rydberg array
• Analogs of deconfined quantum criticality for non-invertible symmetry breaking in 1d
• Deconfined pseudocriticality in a model spin-1 quantum antiferromagnet
• Deconfined quantum criticality with internal supersymmetry