Identifying Topological Order by Entanglement Entropy

Abstract

Topological phases are unique states of matter incorporating long-range quantum entanglement, hosting exotic excitations with fractional quantum statistics. We report a practical method to identify topological phases in arbitrary realistic models by accurately calculating the Topological Entanglement Entropy (TEE) using the Density Matrix Renormalization Group (DMRG). We argue that the DMRG algorithm naturally produces a minimally entangled state, from amongst the quasi-degenerate ground states in a topological phase. This proposal both explains the success of this method, and the absence of ground state degeneracy found in prior DMRG sightings of topological phases. We demonstrate the effectiveness of the calculational procedure by obtaining the TEE for several microscopic models, with an accuracy of order $10^{-3}$ when the circumference of the cylinder is around ten times the correlation length. As an example, we definitively show the ground state of the quantum $S=1/2$ antiferromagnet on the kagomé lattice is a topological spin liquid, and strongly constrain the full identification of this phase of matter.

20 pages, 6 figures

References in corpus (2)

• Non-Abelian Anyons and Topological Quantum Computation
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension

Cited by in corpus (67)

• A classification of symmetry enriched topological phases with exactly solvable models
• Unusual ordered phases of highly frustrated magnets: a review
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Experimental identification of quantum spin liquids
• Characterizing topological order by studying the ground states of an infinite cylinder
• Correlation effects in two-dimensional topological insulators
• Global Phase Diagram of Competing Ordered and Quantum Spin Liquid Phases on the Kagomé Lattice
• Tensor Networks for Lattice Gauge Theories with continuous groups
• Weak plaquette valence bond order in the $S=1/2$ honeycomb $J_1-J_2$ Heisenberg model
• Matrix Product State applications for the ALPS project
• Distinct Spin Liquids and their Transitions in Spin-1/2 XXZ Kagome Antiferromagnets
• One-Third Magnetization Plateau with a Preceding Novel Phase in Volborthite
• Variational Monte Carlo study of chiral spin liquid in the extended Heisenberg model on the Kagome lattice
• Phase diagram of the J1-J2 Heisenberg model on the kagome lattice
• Entanglement entropy scaling in the bilayer Heisenberg spin system
• Constraints on topological order in Mott Insulators
• Factorization and Criticality in the Anisotropic XY Chain via Correlations
• Unifying approach to the quantification of bipartite correlations by Bures distance
• Assembling Fibonacci Anyons From a ${\mathbb{Z}}_3$ Parafermion Lattice Model
• Chiral projected entangled-pair state with topological order
• Symmetry Reduction in the Quantum Kagome Antiferromagnet Herbertsmithite
• Haydeeite: a spin-1/2 kagome ferromagnet
• Competing magnetic orders and spin liquids in two- and three-dimensional kagome systems: A pseudo-fermion functional renormalization group perspective
• Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet
• Detecting edge degeneracy in interacting topological insulators through entanglement entropy
• Renyi Entanglement Entropy of Interacting Fermions Calculated Using Continuous-Time Quantum Monte Carlo Method
• Critical behavior of the QED${}_3$-Gross-Neveu model: Duality and deconfined criticality
• Renyi Entropies of Interacting Fermions from Determinantal Quantum Monte Carlo Simulations
• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• Detecting crystal symmetry fractionalization from the ground state: Application to ${\mathbb{Z}}_2$ spin liquids on the kagome lattice
• Excited state entanglement in one dimensional quantum critical systems: Extensivity and the role of microscopic details
• Genuine Multipartite Entanglement in the Cluster-Ising Model
• Crystalline Kitaev spin liquids
• Phase diagrams of one-dimensional half-filled two-orbital SU(N) cold fermions systems
• End states in a 1-D topological Kondo insulator
• Efficient Continuous-time Quantum Monte Carlo Method for the Ground State of Correlated Fermions
• Anyon braiding in semi-analytical fractional quantum Hall lattice models
• Finite-temperature crossover phenomenon in the $S=1/2$ antiferromagnetic Heisenberg model on the kagome lattice
• Kagome-Triangular Lattice Antiferromagnet NaBa2Mn3F11
• Anyonic Entanglement and Topological Entanglement Entropy
• Scaling of entanglement entropy across Lifshitz transitions
• Stability of the spin-$1/2$ kagome ground state with breathing anisotropy
• Double Semion Phase in an Exactly Solvable Quantum Dimer Model on the Kagome Lattice
• Scaling of the entanglement spectrum in driving critical dynamics
• On Enriching the Levin-Wen model with Symmetry
• Staircase of crystal phases of hard-core bosons on the Kagome lattice
• Hexagon-singlet solid ansatz for the spin-1 kagome antiferromagnet
• Quantum Critical Universality and Singular Corner Entanglement Entropy of Bilayer Heisenberg-Ising model
• Fermionic algebraic quantum spin liquid in an octa-kagome frustrated antiferromagnet
• Structure Factors of the Kagome-Lattice Heisenberg antiferromagnets at finite temperatures
• Quantum phases of the frustrated XY models on the honeycomb lattice
• Entanglement properties of the antiferromagnetic-singlet transition in the Hubbard model on bilayer square lattices
• Numerical study of magnetization plateaux in the spin-1/2 Heisenberg antiferromagnet on the checkerboard lattice
• Statistics of holes and nature of superfluid phases in Quantum dimer models
• Finite Size Scaling of Topological Entanglement Entropy
• Selection of factorizable ground state in a frustrated spin tube: Order by disorder and hidden ferromagnetism
• Gauge field entanglement of Kitaev's honeycomb model
• Entanglement Entropy at Generalized Rokhsar-Kivelson Points of Quantum Dimer Models
• Destroying a topological quantum bit by condensing Ising vortices
• The scaling of entanglement entropy in a honeycomb lattice on a torus
• Nuclear relaxation rates in the Herbertsmithite Kagome antiferromagnets ZnCu3(OH)6Cl2
• Phase diagram and sweep dynamics of a one-dimensional generalized cluster model
• Theory of quantum kagome ice and vison zero modes
• Phase diagram of the frustrated quantum-XY model on the honeycomb lattice studied by series expansions: Evidence for proximity to a bicritical point
• Quantum dissection of a covalent bond with the entanglement spectrum
• Energy gap of neutral excitations implies vanishing charge susceptibility
• Self-consistent spin-wave analysis of the 1/3 magnetization plateau in the kagome antiferromagnet