Anyon condensation web and multipartite entanglement in 2D modulated gauge theories

Abstract

In this work, we introduce an anyon condensation web that interconnects a broad class of 2D fracton gauge theories with multipolar conservation laws at a microscopic level. We find that condensation of anyons triggers the emergence of additional spatially modulated symmetries, which has the general effect of increasing the number of super-selection anyon sectors, as well as the ground state degeneracy for systems with periodic boundary conditions. As explicit examples, we start with the rank-2 toric code model and implement various anyon condensation protocols, resulting in a range of 2D fracton-like theories, each with a distinct gauge structure. We also expand the scope of anyon condensation by introducing lattice defects into spatially modulated gauge theories and demonstrate that these geometric defects can be viewed as effective anyon condensations along the branch cut. Furthermore, we introduce the Multipartite Entanglement Mutual Information measure as a diagnostic tool to differentiate among various distinct multipole conserving phases. A captivating observation is the UV sensitivity of the mutual information sourced from multipartite entanglement in such spatially modulated gauge theories, which depends on the geometric cut and the system size, and exhibits periodic oscillations at large distances.

arXiv comment19 pages, 15 figures. v2: changed "fracton-like" to "modulated"; added references; added Sec. IV.F

References in corpus (63)

• Fault-tolerant quantum computation by anyons
• Detecting topological order in a ground state wave function
• String-net condensation: A physical mechanism for topological phases
• Local stabilizer codes in three dimensions without string logical operators
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Quantum Glassiness
• Quantum orders in an exact soluble model
• A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations
• Generalized Electromagnetism of Subdimensional Particles: A Spin Liquid Story
• The Fracton Gauge Principle
• Ring exchange, the Bose metal, and bosonization in two dimensions
• Exotic $U(1)$ Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory
• Fracton Models on General Three-Dimensional Manifolds
• Fracton topological order via coupled layers
• Anyon condensation and its applications
• Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor
• Entanglement and topological entropy of the toric code at finite temperature
• Preparing random states and benchmarking with many-body quantum chaos
• Towards classification of Fracton phases: the multipole algebra
• The Higgs Mechanism in Higher-Rank Symmetric $U(1)$ Gauge Theories
• On thermalization in Kitaev's 2D model
• Fracton topological order from Higgs and partial confinement mechanisms of rank-two gauge theory
• Measurement as a shortcut to long-range entangled quantum matter
• Emergent (anomalous) higher symmetries from topological orders and from dynamical electromagnetic field in condensed matter systems
• Topological Entanglement Entropy of Fracton Stabilizer Codes
• Fractional excitations in foliated fracton phases
• Mutual Chern-Simons theory for Z_2 topological order
• Fractonic Matter in Symmetry-Enriched U(1) Gauge Theory
• Cage-Net Fracton Models
• Symmetric Fracton Matter: Twisted and Enriched
• Multipolar Topological Field Theories: Bridging Higher Order Topological Insulators and Fractons
• Entanglement Entropy From Tensor Network States for Stabilizer Codes
• Topological Defect Networks for Fractons of all Types
• Symmetric Tensor Gauge Theories on Curved Spaces
• Construction of bosonic symmetry-protected-trivial states and their topological invariants via $G\times SO(\infty )$ non-linear $\sigma$-models
• Fractons from vector gauge theory
• Bond algebraic liquid phase in strongly correlated multiflavor cold atom systems
• Synthetic Topological Degeneracy by Anyon Condensation
• Deciphering the nonlocal entanglement entropy of fracton topological orders
• Bifurcation in entanglement renormalization group flow of a gapped spin model
• Fractonic Chern-Simons and BF theories
• Universal entanglement signatures of foliated fracton phases
• Fracton-elasticity duality of two-dimensional superfluid vortex crystals: defect interactions and quantum melting
• Topological Route to New and Unusual Coulomb Spin Liquids
• Emergent fractons and algebraic quantum liquid from plaquette melting transitions
• Position-Dependent Excitations and UV/IR Mixing in the ${\mathbb{Z}}_N$ Rank-2 Toric Code and its Low-Energy Effective Field Theory
• Bifurcating entanglement-renormalization group flows of fracton stabilizer models
• Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions
• Rank-2 Toric Code in Two Dimensions
• Ground state degeneracy on torus in a family of ${\mathbb{Z}}_N$ toric code
• Effective Fractonic Behavior in a Two-Dimensional Exactly Solvable Spin Liquid
• Higher-Order Entanglement and Many-Body Invariants for Higher-Order Topological Phases
• Study of a hard-core boson model with ring-only interactions
• A symmetry principle for gauge theories with fractons
• Aspects of ${\mathbb{Z}}_N$ rank-2 gauge theory in $(2+1)$ dimensions: construction schemes, holonomies, and sublattice one-form symmetries
• Effective Field Theory of Dipolar Braiding Statistics in Two Dimensions
• Bosonic symmetry protected topological phases with reflection symmetry
• Symmetric higher rank topological phases on generic graphs
• Multipartite entanglement in two-dimensional chiral topological liquids
• Topological defect network representations of fracton stabilizer codes
• Non-Abelian defects in Fracton phase of matter
• Screw dislocations in the X-cube fracton model
• No Strings Attached: Boundaries and Defects in the Cubic Code

Cited by in corpus (9)

• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections
• Anomaly inflow for dipole symmetry and higher form foliated field theories
• Topological order and Fractons from Gauging Exponential Symmetries
• Hall-like behaviour of higher rank Chern-Simons theory of fractons
• Unveiling UV/IR Mixing via Symmetry Defects: A View from Topological Entanglement Entropy
• Generalized Modulated Symmetries in ${\mathbb{Z}}_2$ Topological Ordered Phases
• Infinite-component $BF$ field theory: Connection of fracton order, Toeplitz braiding, and non-Hermitian amplification
• Preparing Code States via Seed-Entangler-Enriched Sequential Quantum Circuits: Application to Tetra-Digit Topological Error-Correcting Codes
• Symmetry-enriched topological order and quasifractonic behavior in ${\mathbb{Z}}_N$ stabilizer codes