Duality viewpoint of criticality

Abstract

In this work, we study quantum many-body systems which are self-dual under duality transformation connecting different symmetry protected topological (SPT) phases. We provide a geometric explanation of the criticality of these self-dual models. More precisely, we show a ground state (quasi-)degeneracy under the periodic boundary conditions,i.e., the ingappability of the bulk spectrum. Equivalently, the symmetry group at criticality, including the duality symmetry, has a mixed 't Hooft anomaly. This approach can not only predict the spectrum of the self-dual model with ordinary 0-form symmetry, but also be applied to that with generalized symmetry, such as higher form and subsystem symmetry. As an application, we illustrate our results with several examples in one and two dimensions, which separate two different SPTs.

References in corpus (53)

• Generalized Global Symmetries
• Entanglement spectrum of a topological phase in one dimension
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Topological phases of fermions in one dimension
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Classifying quantum phases using Matrix Product States and PEPS
• Magnetization plateaus in spin chains: ``Haldane gap'' for half-integer spins
• Lieb-Schultz-Mattis in Higher Dimensions
• Coupling a QFT to a TQFT and Duality
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
• A symmetry principle for Topological Quantum Order
• Emergent Photons and New Transitions in the O(3) Sigma Model with Hedgehog Suppression
• Symmetry protected topological phases from decorated domain walls
• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
• Subsystem symmetry protected topological order
• Symmetry and Topological Order
• Intrinsic and emergent anomalies at deconfined critical points
• Topological phases with generalized global symmetries
• Intrinsically Gapless Topological Phases
• Gapless Symmetry Protected Topological Order
• Generalized Elitzur's Theorem and Dimensional Reduction
• Random Matrix Theory and Entanglement in Quantum Spin Chains
• Duality between $(2+1)d$ Quantum Critical Points
• Strong-weak coupling self-duality in the two-dimensional quantum phase transition of $p+ip$ superconducting arrays
• Classification of subsystem symmetry-protected topological phases
• First order phase transition in the anisotropic quantum orbital compass model
• Quantum Phase Transition between Integer Quantum Hall States of Bosons
• Symmetry protection of critical phases and global anomaly in $1+1$ dimensions
• All Majorana Models with Translation Symmetry are Supersymmetric
• An Adventure in Topological Phase Transitions in 3 + 1-D: Non-abelian Deconfined Quantum Criticalities and a Possible Duality
• Quantum phase transitions beyond Landau-Ginzburg theory in one-dimensional space revisited
• Quantum phase transitions between bosonic symmetry protected topological phases in two dimensions: emergent $QE{D}_3$ and anyon superfluid
• Twisted boundary condition and Lieb-Schultz-Mattis ingappability for discrete symmetries
• Anomaly matching and symmetry-protected critical phases in $SU(N)$ spin systems in 1+1 dimensions
• Insensitivity of bulk properties to the twisted boundary condition
• From Bosonic Topological Transition to Symmetric Fermion Mass Generation
• Strong planar subsystem symmetry-protected topological phases and their dual fracton orders
• Fate of the cluster state on the square lattice in a magnetic field
• Deconfined Quantum Critical Point on the Triangular Lattice
• Realizing all $so(N{)}_1$ quantum criticalities in symmetry protected cluster models
• Effective and exact holographies from symmetries and dualities
• Frustration and Multicriticality in the Antiferromagnetic Spin-1 Chain
• Quantum Phase Transitions Between a Class of Symmetry Protected Topological States
• Quantum Phase Transitions Between Bosonic Symmetry Protected Topological States Without Sign Problem: Nonlinear Sigma Model with a Topological Term
• Lieb-Schultz-Mattis type theorems for Majorana models with discrete symmetries
• Stripe melting, a transition between weak and strong symmetry protected topological phases
• Fracton Topological Order at Finite Temperature
• A UV perspective on mixed anomalies at critical points between bosonic symmetry-protected phases
• Geometric approach to Lieb-Schultz-Mattis theorem without translation symmetry under inversion or rotation symmetry
• Stability against contact interactions of a topological superconductor in two-dimensional space protected by time-reversal and reflection symmetries

Cited by in corpus (9)

• Non-Invertible Duality Transformation Between SPT and SSB Phases
• Subsystem Non-Invertible Symmetry Operators and Defects
• Intrinsically/Purely Gapless-SPT from Non-Invertible Duality Transformations
• Generating Lattice Non-invertible Symmetries
• Strong-to-weak spontaneous symmetry breaking meets average symmetry-protected topological order
• Boundary conditions and anomalies of conformal field theories in 1+1 dimensions
• Generalized Kramers-Wannier Duality from Bilinear Phase Map
• Self-$G$-ality in 1+1 dimensions
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution