Boundary deconfined quantum criticality at transitions between symmetry-protected topological chains

Abstract

Decades of research have revealed a deep understanding of topological quantum matter with protected edge modes. We report that even richer physics emerges when tuning between two topological phases of matter whose respective edge modes are incompatible. The frustration at the edge leads to novel boundary physics, such as symmetry-breaking phases with exotic non-Landau transitions -- even when the edge is zero-dimensional. As a minimal case study we consider spin chains with ${\mathbb{Z}}_3\times {\mathbb{Z}}_3$ symmetry, exhibiting two nontrivial symmetry-protected topological (SPT) phases. At the bulk 1+1D critical transition between these SPT phases, we find two stable 0+1D boundary phases, each spontaneously breaking one of the ${\mathbb{Z}}_3$ symmetries. Furthermore, we find that a single boundary parameter tunes a non-Landau boundary critical transition between these two phases. This constitutes a 0+1D version of an exotic phenomenon driven by charged vortex condensation known as deconfined quantum criticality. This work highlights the rich unexplored physics of criticality between nontrivial topological phases and provides insights into the burgeoning field of gapless topological phases.

arXiv comment4.5 pages + 2 page supplement

References in corpus (91)

• Unpaired Majorana fermions in quantum wires
• Persistent entanglement in arrays of interacting particles
• "Deconfined" quantum critical points
• Entanglement spectrum of a topological phase in one dimension
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Topological phases of fermions in one dimension
• Classifying quantum phases using Matrix Product States and PEPS
• Symmetry Protected Topological phases of Quantum Matter
• Topological Phases of One-Dimensional Fermions: An Entanglement Point of View
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
• Complete classification of 1D gapped quantum phases in interacting spin systems
• Deconfined quantum critical points: symmetries and dualities
• Detection of Symmetry Protected Topological Phases in 1D
• Generalised twisted partition functions
• Quantum criticality with two length scales
• Scaling in the Fan of an Unconventional Quantum Critical Point
• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Continuous quantum phase transition between an antiferromagnet and a valence-bond-solid in two dimensions; evidence for logarithmic corrections to scaling
• Majorana Zero Modes in 1D Quantum Wires Without Long-Ranged Superconducting Order
• Emergent $SO(5)$ Symmetry at the Néel to Valence-Bond-Solid Transition
• Putting competing orders in their place near the Mott transition
• Gapless topological phases and symmetry-enriched quantum criticality
• Topology and edge modes in quantum critical chains
• Quantum Criticality and Deconfinement in Phase Transitions Between Valence Bond Solids
• Gapless Symmetry Protected Topological Order
• Deconfined quantum criticality and Neel order via dimer disorder
• A Gapless Symmetry-Protected Topological Phase of Fermions in One Dimension
• The phase diagram of the anisotropic spin-2 XXZ model: an infinite system DMRG study
• Quantum phase transition between cluster and antiferromagnetic states
• A number conserving theory for topologically protected degeneracy in one-dimensional fermions
• Deconfined criticality flow in the Heisenberg model with ring-exchange interactions
• Dynamical Signature of Fractionalization at the Deconfined Quantum Critical Point
• Majorana Edge States in Interacting Two-chain Ladders of Fermions
• Majorana edge states in two atomic wires coupled by pair-hopping
• Many-body characterization of topological superconductivity: The Richardson-Gaudin-Kitaev chain
• Localized Majorana-like modes in a number conserving setting: An exactly solvable model
• Topological Luttinger Liquids from Decorated Domain Walls
• Deconfined quantum critical point in one dimension
• Ising ferromagnet to valence bond solid transition in a one-dimensional spin chain: Analogies to deconfined quantum critical points
• Quantum field theory for the chiral clock transition in one spatial dimension
• The Prediction of a Gapless Topological "Haldane Liquid" Phase in a One-Dimensional Cold Polar Molecular Lattice
• Topological States in a One-Dimensional Fermi Gas with Attractive Interactions
• Boundary Critical Phenomena in the Three-State Potts Model
• Quantum phase transitions beyond Landau-Ginzburg theory in one-dimensional space revisited
• Topological states in a microscopic model of interacting fermions
• Phases of the (2+1) dimensional SO(5) non-linear sigma model with topological term
• Topological degeneracy and pairing in a one-dimensional gas of spinless Fermions
• Emergent Symmetry and Conserved Current at a One Dimensional Incarnation of Deconfined Quantum Critical Point
• Emmy Noether looks at the deconfined quantum critical point
• Pivot Hamiltonians as generators of symmetry and entanglement
• Emergent SO(5) symmetry at the columnar ordering transition in the classical cubic dimer model
• Topological quantum critical points in the extended Bose-Hubbard model
• Quantum spin nematics, dimerization, and deconfined criticality in quasi-one dimensional spin-1 magnets
• The phase transitions between $Z_n\times Z_n$ bosonic topological phases in 1+1 D, and a constraint on the central charge for the critical points between bosonic symmetry protected topological phases
• Symmetry protected topological phases of 1D interacting fermions with spin-charge separation
• Rokhsar-Kivelson Models of Bosonic Symmetry-Protected Topological States
• Universal Entanglement Spectra of Gapped One-dimensional Field Theories
• Exactly solvable model for a deconfined quantum critical point in 1D
• Emergent topological properties in interacting one-dimensional systems with spin-orbit coupling
• Topological and symmetry-enriched random quantum critical points
• Bulk Renormalization Group Flows and Boundary States in Conformal Field Theories
• Non-local Order in Elongated Dipolar Gases
• Neel order, quantum spin liquids and quantum criticality in two dimensions
• Topologically-Protected Long Edge Coherence Times in Symmetry-Broken Phases
• Defect flows in minimal models
• Boundary Conformal Field Theory and Tunneling of Edge Quasiparticles in non-Abelian Topological States
• Evidence for deconfined $U(1)$ gauge theory at the transition between toric code and double semion
• Quantum Phase Transitions Between a Class of Symmetry Protected Topological States
• From one-dimensional charge conserving superconductors to the gapless Haldane phase
• Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet
• Fidelity as a probe for a deconfined quantum critical point
• From trivial to topological paramagnets: The case of ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_2^3$ symmetries in two dimensions
• Relationship between Symmetry Protected Topological Phases and Boundary Conformal Field Theories via the Entanglement Spectrum
• Crystalline Symmetry-Protected Majorana Mode in Number-Conserving Dirac Semimetal Nanowires
• What is a particle-conserving Topological Superfluid?
• Topological aspects of the critical three-state Potts model
• Building models of topological quantum criticality from pivot Hamiltonians
• Interaction induced topological protection in one-dimensional conductors
• Number-conserving interacting fermion models with exact topological superconducting ground states
• One-dimensional model for deconfined criticality with ${\mathbb{Z}}_3\times {\mathbb{Z}}_3$ symmetry
• Continuous phase transition between Neel and valence bond solid phases in a J-Q-like spin ladder system
• Flux-Stabilized Majorana Zero Modes in Coupled One-Dimensional Fermi Wires
• A UV perspective on mixed anomalies at critical points between bosonic symmetry-protected phases
• Topology of critical chiral phases: multiband insulators and superconductors
• Symmetry-protected topological phases in two-leg SU(N) spin ladder with unequal spins
• Ising anyonic topological phase of interacting Fermions in one dimension
• Quantization of topological indices in critical chains at low temperatures
• "Haldane" phases with ultracold fermionic atoms in double-well optical lattices

Cited by in corpus (12)

• Topological holography, quantum criticality, and boundary states
• Universal entanglement spectrum in gapless symmetry protected topological states
• Quantum phase transition between topologically distinct quantum critical points
• Topological edge modes and phase transition in the critical fermionic chain with long-range interaction
• Gapless higher-order topology and corner states in Floquet systems
• Topological physics in quantum critical systems
• Incommensurate gapless ferromagnetism connecting competing symmetry-enriched deconfined quantum phase transitions
• Deconfined criticality as intrinsically gapless topological state in one dimension
• Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems
• Emergent gapless spiral phases and conformal Lifshitz criticality in the cluster Ising model with off-diagonal interactions
• Anomalous Dynamical Scaling at Topological Quantum Criticality
• Topology and edge modes surviving criticality in non-Hermitian Floquet systems