Entanglement Entropy as a Portal to the Physics of Quantum Spin Liquids

Abstract

Quantum Spin Liquids (QSLs) are phases of interacting spins that do not order even at the absolute zero temperature, making it impossible to characterize them by a local order parameter. In this article, we review the unique view provided by the quantum entanglement on QSLs. We illustrate the crucial role of Topological Entanglement Entropy in diagnosing the non-local order in QSLs, using specific examples such as the Chiral Spin Liquid. We also demonstrate the detection of anyonic quasiparticles and their braiding statistics using quantum entanglement. In the context of gapless QSLs, we discuss the detection of emergent fermionic spinons in a bosonic wavefunction, by studying the size dependence of entanglement entropy.

Review article; 13 pages, 10 figures

References in corpus (19)

• Non-Abelian Anyons and Topological Quantum Computation
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• "Deconfined" quantum critical points
• Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu_3(OH)_6Cl_2
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Spin-Liquid State in the S = 1/2 Hyperkagome Antiferromagnet Na4Ir3O8
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• U(1) Gauge Theory of the Hubbard Model : Spin Liquid States and Possible Application to k-(BEDT-TTF)_2 Cu_2 (CN)_3
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Ground state entanglement and geometric entropy in the Kitaev's model
• Entanglement entropy in fermionic Laughlin states
• Universal terms for the entanglement entropy in 2+1 dimensions
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Entanglement entropy of critical spin liquids
• Bipartite entanglement entropy in fractional quantum Hall states
• Entanglement, fidelity and topological entropy in a quantum phase transition to topological order
• Topological phases and topological entropy of two-dimensional systems with finite correlation length

Cited by in corpus (20)

• Generalized Symmetries in Condensed Matter
• Unusual ordered phases of highly frustrated magnets: a review
• Quantum phases of Rydberg atoms on a kagome lattice
• Entanglement Spectra of Stabilizer Codes: A Window into Gapped Quantum Phases of Matter
• Multipartitioning topological phases by vertex states and quantum entanglement
• Universal logarithmic corrections to entanglement entropies in two dimensions with spontaneously broken continuous symmetries
• Topological spin ordering via Chern-Simons superconductivity
• Capacity of entanglement and distribution of density matrix eigenvalues in gapless systems
• Bell's Inequality and Entanglement in Qubits
• Mixed-State Entanglement Measures in Topological Order
• Chiral Broken Symmetry Descendants of the Kagomé Lattice Chiral Spin Liquid
• Identifying topological order in the Shastry-Sutherland model via entanglement entropy
• Quantum spin liquids on the diamond lattice
• Momentum space entanglement of interacting fermions
• Electron-mediated entanglement of two distant macroscopic ferromagnets within a nonequilibrium spintronic device
• Conformal geometry from entanglement
• Characterization of helical states in semiconductor quantum wells using quantum information quantities
• Spin-wave study of entanglement and Rényi entropy for coplanar and collinear magnetic orders in two-dimensional quantum Heisenberg antiferromagnets
• Single-shot quantum measurements sketch quantum many-body states
• A primer on Kitaev Model: Basic aspects, material realization, and recent experiments