Spurious topological entanglement entropy from subsystem symmetries

Abstract

We demonstrate that linear combinations of subregion entropies with canceling boundary terms, commonly used to calculate the topological entanglement entropy, may suffer from spurious nontopological contributions even in models with zero correlation length. These spurious contributions are due to a specific kind of long-range string order, and persist throughout certain subsystem symmetry-protected phases. We introduce an entropic quantity that measures the presence of such order, and hence should serve as an order parameter for the aforementioned phases.

5+8 pages, 2+5 figures; v2 published version

References in corpus (43)

• Good Quantum Error-Correcting Codes Exist
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Entanglement spectrum of a topological phase in one dimension
• Multiple Particle Interference and Quantum Error Correction
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Local stabilizer codes in three dimensions without string logical operators
• Identifying Topological Order by Entanglement Entropy
• Topological quantum order: stability under local perturbations
• A symmetry principle for Topological Quantum Order
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Analytic and numerical demonstration of quantum self-correction in the 3D Cubic Code
• Topological Entanglement Renyi Entropy and Reduced Density Matrix Structure
• Subsystem symmetry protected topological order
• Symmetry and Topological Order
• Fractal symmetries: Ungauging the cubic code
• Anyons and matrix product operator algebras
• Entanglement Entropy of Gapped Phases and Topological Order in Three dimensions
• Identifying phases of quantum many-body systems that are universal for quantum computation
• Generalized Elitzur's Theorem and Dimensional Reduction
• Topological Entanglement Entropy of Fracton Stabilizer Codes
• Fractal Symmetric Phases of Matter
• Commuting Pauli Hamiltonians as maps between free modules
• Classification of subsystem symmetry-protected topological phases
• A computationally universal phase of quantum matter
• On the energy landscape of 3D spin Hamiltonians with topological order
• Topological Entanglement Entropy from the Holographic Partition Function
• Universal quantum computation using fractal symmetry-protected cluster phases
• Spurious Long-range Entanglement and Replica Correlation Length
• Structure of 2D Topological Stabilizer Codes
• Recoverable Information and Emergent Conservation Laws in Fracton Stabilizer Codes
• Deciphering the nonlocal entanglement entropy of fracton topological orders
• Bifurcation in entanglement renormalization group flow of a gapped spin model
• The hidden symmetry-breaking picture of symmetry-protected topological order
• Interactions along an Entanglement Cut in 2+1D Abelian Topological Phases
• Algebraic Methods for Quantum Codes on Lattices
• Ungauging quantum error-correcting codes
• Compactifying fracton stabilizer models
• Stability of topologically invariant order parameters at finite temperature
• Perturbative analysis of topological entanglement entropy from conditional independence
• Probing topological order with Rényi entropy
• Symmetry-Protected Topological Interfaces and Entanglement Sequences
• Lattice quantum codes and exotic topological phases of matter

Cited by in corpus (64)

• Fracton Phases of Matter
• Prediction of Toric Code Topological Order from Rydberg Blockade
• Fractonic Matter in Symmetry-Enriched U(1) Gauge Theory
• Clustering of conditional mutual information for quantum Gibbs states above a threshold temperature
• Topological Defect Networks for Fractons of all Types
• Twisted foliated fracton phases
• Sorting topological stabilizer models in three dimensions
• Strong planar subsystem symmetry-protected topological phases and their dual fracton orders
• Gauging permutation symmetries as a route to non-Abelian fractons
• Fusion rules from entanglement
• Compactifying fracton stabilizer models
• Subsystem symmetry enriched topological order in three dimensions
• Ground state degeneracy on torus in a family of ${\mathbb{Z}}_N$ toric code
• Entanglement Spectra of Stabilizer Codes: A Window into Gapped Quantum Phases of Matter
• Classifying local fractal subsystem symmetry protected topological phases
• Universality Classes of Stabilizer Code Hamiltonians
• Entanglement bootstrap approach for gapped domain walls
• Magic-induced computational separation in entanglement theory
• Boson-fermion duality with subsystem symmetry
• Lieb-Schultz-Mattis type constraints on Fractonic Matter
• Universal lower bound on topological entanglement entropy
• Detecting subsystem symmetry protected topological order via entanglement entropy
• Distilling Fractons from Layered Subsystem-Symmetry Protected Phases
• Topological graph states and quantum error correction codes
• Bifurcating subsystem symmetric entanglement renormalization in two dimensions
• Seeing topological entanglement through the information convex
• Toy model of boundary states with spurious topological entanglement entropy
• Verlinde formula from entanglement
• Detecting Subsystem Symmetry Protected Topological Order Through Strange Correlators
• Quantum entanglement and non-Hermiticity in free-fermion systems
• Fractionalization of subsystem symmetries in two dimensions
• Designer non-Abelian fractons from topological layers
• Fractalizing quantum codes
• Mixed-State Entanglement Measures in Topological Order
• Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators
• Entanglement Signature of Hinge Arcs, Fermi Arcs, and Crystalline Symmetry Protection in Higher-Order Weyl Semimetals
• Topological order and Fractons from Gauging Exponential Symmetries
• An analog of topological entanglement entropy for mixed states
• Parafermions in Hierarchical Fractional Quantum Hall States
• Entropy scaling law and the quantum marginal problem
• Stability of topological purity under random local unitaries
• Universal Spreading of Conditional Mutual Information in Noisy Random Circuits
• An entropic invariant for 2D gapped quantum phases
• Many-body systems with spurious modular commutators
• Unveiling UV/IR Mixing via Symmetry Defects: A View from Topological Entanglement Entropy
• Petz map recovery for long-range entangled quantum many-body states
• Anyon Quantum Dimensions from an Arbitrary Ground State Wave Function
• Subsystem Symmetry Fractionalization and Foliated Field Theory
• Boundary topological entanglement entropy in two and three dimensions
• Bicolor loop models and their long range entanglement
• A Theorem on Extensive Spectral Degeneracy for Systems with Higher Symmetries in General Dimensions
• String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation
• Boundary anomaly detection in two-dimensional subsystem symmetry-protected topological phases
• Topological order in symmetric blockade structures
• Higher Hall conductivity from a single wave function: Obstructions to symmetry-preserving gapped edge of (2+1)D topological order
• (2+1)D topological phases with RT symmetry: many-body invariant, classification, and higher order edge modes
• Phase transitions in (2 + 1)D subsystem-symmetric monitored quantum circuits
• There and Back Again: A Gauging Nexus between Topological and Fracton Phases
• Rényi-like entanglement probe of the chiral central charge
• Higher-form entanglement asymmetry and topological order
• Holographic duality between bulk topological order and boundary mixed-state order
• Topological entanglement entropy meets holographic entropy inequalities
• Robust Mixed-State Cluster States and Spurious Topological Entanglement Negativity
• Confinement and Flux Attachment