Topological Edge and Interface states at Bulk disorder-to-order Quantum Critical Points

Abstract

We study the interplay between two nontrivial boundary effects: (1) the two dimensional ($2d$) edge states of three dimensional ($3d$) strongly interacting bosonic symmetry protected topological states, and (2) the boundary fluctuations of $3d$ bulk disorder-to-order phase transitions. We then generalize our study to $2d$ gapless states localized at an interface embedded in a $3d$ bulk, when the bulk undergoes a quantum phase transition. Our study is based on generic long wavelength descriptions of these systems and controlled analytic calculations. Our results are summarized as follows: ($i.$) The edge state of a prototype bosonic symmetry protected states can be driven to a new fixed point by coupling to the boundary fluctuations of a bulk quantum phase transition; ($ii.$) the states localized at a $2d$ interface of a $3d$ SU(N) quantum antiferromagnet may be driven to a new fixed point by coupling to the bulk quantum critical modes. Properties of the new fixed points identified are also studied.

arXiv comment8 pages, 7 figures

References in corpus (45)

• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Topological Insulators in Three Dimensions
• Topological invariants of time-reversal-invariant band structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Quantized Electric Multipole Insulators
• Periodic table for topological insulators and superconductors
• "Deconfined" quantum critical points
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Helical Metal Inside a Topological Band Insulator
• Deconfined quantum critical points: symmetries and dualities
• The Theory of Boundary Critical Phenomena
• Level/rank Duality and Chern-Simons-Matter Theories
• Classification of Topological Insulators and Superconductors
• Algebraic spin liquid as the mother of many competing orders
• Emergent Photons and New Transitions in the O(3) Sigma Model with Hedgehog Suppression
• Boson topological insulators: A window into highly entangled quantum phases
• Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface
• Electron spectral function and algebraic spin liquid for the normal state of underdoped high $T_c$ superconductors
• Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator
• A Time-Reversal Invariant Topological Phase at the Surface of a 3D Topological Insulator
• Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator
• A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators
• Topology and edge modes in quantum critical chains
• Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions
• Gapless Symmetry Protected Topological Order
• Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions
• Phases of one-dimensional SU(N) cold atomic Fermi gases --from molecular Luttinger liquids to topological phases
• Duality between $(2+1)d$ Quantum Critical Points
• Classification and Description of Bosonic Symmetry Protected Topological Phases with semiclassical Nonlinear Sigma models
• Self-dual Quantum Electrodynamics as Boundary State of the three dimensional Bosonic Topological Insulator
• Unconventional Surface Critical Behaviors Induced by Quantum Phase Transition from Two-Dimensional Affleck-Kennedy-Lieb-Tasaki Phase to Néel Order
• On topological phases of spin chains
• Symmetry-protected topological phases of alkaline-earth cold fermionic atoms in one dimension
• Nonordinary criticality at the edges of planar spin-1 Heisenberg antiferromagnets
• Nonordinary edge criticaliy of two-dimensional quantum critical magnets
• Three dimensional Symmetry Protected Topological Phase close to Antiferromagnetic Neel order
• Phase diagrams of one-dimensional half-filled two-orbital SU(N) cold fermions systems
• Realizing topological surface states in a lower-dimensional flat band
• Easy-plane QED${}_3$'s in the large $N_f$ limit
• A square lattice algebraic spin liquid with SO(5) symmetry

Cited by in corpus (11)

• Quantum criticality under decoherence or weak measurement
• Gapless topological phases and symmetry-enriched quantum criticality
• Symmetry protected topological phases under decoherence
• Continuous Néel-VBS Quantum Phase Transition in Non-Local one-dimensional systems with SO(3) Symmetry
• Gauge Enhanced Quantum Criticality Between Grand Unifications: Categorical Higher Symmetry Retraction
• Quantum phase transition between topologically distinct quantum critical points
• Metal-Insulator Transition with Charge Fractionalization
• Conformal boundary conditions for a 4d scalar field
• Continuous phase transitions between fractional quantum Hall states and symmetry-protected topological states
• Deconfined Quantum Critical Point with Non-locality
• Deep Boundary Perturbations at a Quantum Critical Point