Entanglement renormalization of fractonic anisotropic ${\mathbb{Z}}_N$ Laplacian models

Abstract

Gapped fracton phases constitute a new class of quantum states of matter which connects to topological orders but does not fit easily into existing paradigms. They host unconventional features such as sub-extensive and robust ground state degeneracies as well as sensitivity to lattice geometry. We investigate the anisotropic ${\mathbb{Z}}_N$ Laplacian model [1] which can describe a family of fracton phases defined on arbitrary graphs. Focusing on representative geometries where the 3D lattices are extensions of 2D square, triangular, honeycomb and Kagome lattices into the third dimension, we study their ground state degeneracies and mobility of excitations, and examine their entanglement renormalization group (ERG) flows. All models show bifurcating behaviors under ERG but have distinct ERG flows sensitive to both $N$ and lattice geometry. In particular, we show that the anisotropic ${\mathbb{Z}}_N$ Laplacian models defined on the extensions of triangular and honeycomb lattices are equivalent when $N$ is coprime to $3$. We also point out that, in contrast to previous expectations, the model defined on the extension of Kagome lattice is robust against local perturbations if and only if $N$ is coprime to $6$.

References in corpus (48)

• Fault-tolerant quantum computation by anyons
• Good Quantum Error-Correcting Codes Exist
• Multiple Particle Interference and Quantum Error Correction
• Entanglement renormalization
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Local stabilizer codes in three dimensions without string logical operators
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Quantum Glassiness
• Fractons
• A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations
• Fracton Phases of Matter
• Algorithms for entanglement renormalization
• Exotic topological order in fractal spin liquids
• Entanglement renormalization for quantum fields
• Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory
• Fracton Models on General Three-Dimensional Manifolds
• Entanglement renormalization and topological order
• Entanglement renormalization, scale invariance, and quantum criticality
• Foliated fracton order from gauging subsystem symmetries
• Topological Quantum Glassiness
• Gapped quantum liquids and topological order, stochastic local transformations and emergence of unitarity
• Fractional excitations in foliated fracton phases
• Commuting Pauli Hamiltonians as maps between free modules
• Universal topological phase of 2D stabilizer codes
• Exact entanglement renormalization for string-net models
• A class of highly entangled many-body states that can be efficiently simulated
• Structure of 2D Topological Stabilizer Codes
• Bifurcation in entanglement renormalization group flow of a gapped spin model
• Unifying variational methods for simulating quantum many-body systems
• Simulation of time evolution with the MERA
• Universal entanglement signatures of foliated fracton phases
• Foliated fracton order in the checkerboard model
• Scaling of entanglement entropy in the (branching) multi-scale entanglement renormalization ansatz
• Fractons with Twisted Boundary Conditions and Their Symmetries
• Bifurcating entanglement-renormalization group flows of fracton stabilizer models
• Jordan-Wigner Dualities for Translation-Invariant Hamiltonians in Any Dimension: Emergent Fermions in Fracton Topological Order
• Classification of translation invariant topological Pauli stabilizer codes for prime dimensional qudits on two-dimensional lattices
• FCC, Checkerboards, Fractons, and QFT
• 2+1d Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
• A real space decoupling transformation for quantum many-body systems
• Gapped Lineon and Fracton Models on Graphs
• A degeneracy bound for homogeneous topological order
• Fracton Self-Statistics
• Fractons on Graphs and Complexity
• Anisotropic higher rank ${\mathbb{Z}}_N$ topological phases on graphs
• Pascal's Triangle Fractal Symmetries
• Renormalization of Ising cage-net model and generalized foliation
• Fractal Subsystem Symmetries, 't Hooft Anomalies, and UV/IR Mixing

Cited by in corpus (1)

• Planon-modular fracton orders