Topological holography, quantum criticality, and boundary states

Abstract

Topological holography is a holographic principle that describes the generalized global symmetry of a local quantum system in terms of a topological order in one higher dimension. This framework separates the topological data from the local dynamics of a theory and provides a unified description of the symmetry and duality in gapped and gapless phases of matter. In this work, we develop the topological holographic picture for (1+1)d quantum phases, including both gapped phases as well as a wide range of quantum critical points, including phase transitions between symmetry protected topological (SPT) phases, symmetry enriched quantum critical points, deconfined quantum critical points, and intrinsically gapless SPT phases. Topological holography puts a strong constraint on the emergent symmetry and the anomaly for these critical theories. We show how the partition functions of these critical points can be obtained from dualizing (orbifolding) more familiar critical theories. The topological responses of the defect operators are also discussed in this framework. We further develop a topological holographic picture for conformal boundary states of (1+1)d rational conformal field theories. This framework provides a simple physical picture to understand conformal boundary states and also uncovers the nature of the gapped phases corresponding to the boundary states.

43 pages, 10 figures, 3 tables. v2: references added. v3: Added a conclusion section and minor revision. v4: Minor correction

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Cited by in corpus (34)

• Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries
• Gapped Phases in (2+1)d with Non-Invertible Symmetries: Part I
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• Quantum entanglement of fermionic symmetry-enriched quantum critical points in one dimension
• Entanglement and the density matrix renormalisation group in the generalised Landau paradigm
• Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
• Duality via Sequential Quantum Circuit in the Topological Holography Formalism
• Quantum Cluster State Model with Haagerup Fusion Category Symmetry
• Topological physics in quantum critical systems
• Noninvertible symmetry and topological holography for modulated SPT in one dimension
• Weak Hopf non-invertible symmetry-protected topological spin liquid and lattice realization of (1+1)D symmetry topological field theory
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Gauge theory and mixed state criticality
• Incommensurate gapless ferromagnetism connecting competing symmetry-enriched deconfined quantum phase transitions
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• Generalized Modulated Symmetries in ${\mathbb{Z}}_2$ Topological Ordered Phases
• Deconfined criticality as intrinsically gapless topological state in one dimension
• (2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
• Exploring nontrivial topology at quantum criticality in a superconducting processor
• Generalized Landau Paradigm for quantum phases and phase transitions
• Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems
• Dualities between 2+1d fusion surface models from braided fusion categories
• Subsystem Symmetry-Protected Topological Phases from Subsystem SymTFT of 2-Foliated Exotic Tensor Gauge Theory
• A non-semisimple non-invertible symmetry
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
• Emergent gapless spiral phases and conformal Lifshitz criticality in the cluster Ising model with off-diagonal interactions
• Exploring two dimensional ${\mathbb{Z}}_2$ invariant phases with time reversal symmetry and their transitions with topological operations
• Non-onsite symmetry breaking: topological phase coexistence and criticality
• Impurity screening by defects in (1+1)$d$ quantum critical systems
• Transition between 2D Symmetry Protected Topological Phases on a Klein Bottle
• Entropic order parameters and topological holography
• Higher-form anomalies and state-operator correspondence beyond conformal invariance
• Anomalous Dynamical Scaling at Topological Quantum Criticality
• Topology and edge modes surviving criticality in non-Hermitian Floquet systems