Topological and Entanglement Properties of Resonating Valence Bond wavefunctions

Abstract

We examine in details the connections between topological and entanglement properties of short-range resonating valence bond (RVB) wave functions using Projected Entangled Pair States (PEPS) on kagome and square lattices on (quasi-)infinite cylinders with generalized boundary conditions (and perimeters with up to 20 lattice spacings). Making use of disconnected topological sectors in the space of dimer lattice coverings, we explicitly derive (orthogonal) "minimally entangled" PEPS RVB states. For the kagome lattice, we obtain, using the quantum Heisenberg antiferromagnet as a reference model, the finite size scaling of the energy separations between these states. In particular, we extract two separate (vanishing) energy scales corresponding (i) to insert a vison line between the two ends of the cylinder and (ii) to pull out and freeze a spin at either end. We also investigate the relations between bulk and boundary properties and show that, for a bipartition of the cylinder, the boundary Hamiltonian defined on the edge can be written as a product of a highly non-local projector with an emergent (local) su(2)-invariant one-dimensional (superfluid) t--J Hamiltonian, which arises due to the symmetry properties of the auxiliary spins at the edge. This multiplicative structure, a consequence of the disconnected topological sectors in the space of dimer lattice coverings, is characteristic of the topological nature of the states. For minimally entangled RVB states, it is shown that the entanglement spectrum, which reflects the properties of the edge modes, is a subset (half for kagome RVB) of the spectrum of the local Hamiltonian, providing e.g. a simple argument on the origin of the topological entanglement entropy S0=-ln 2 of Z2 spin liquids. We propose to use these features to probe topological phases in microscopic Hamiltonians and some results are compared to existing DMRG data.

15 pages, 19 figures. Large extension of the paper. Finite size scaling of the (topological) ground state energy splittings added (for the Kagome quantum antiferromagnet)

References in corpus (9)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Criticality, the area law, and the computational power of PEPS
• Quantum magnetism in the paratacamite family: towards an ideal kagome lattice
• Valence Bond Solids for Quantum Computation
• Entanglement scaling in two-dimensional gapless systems
• Critical Correlations for Short-Range Valence-Bond Wave Functions on the Square Lattice
• Rényi entanglement entropies in quantum dimer models : from criticality to topological order
• Competing Valence Bond Crystals in the Kagome Quantum Dimer Model

Cited by in corpus (107)

• Quantum entanglement in condensed matter systems
• Quantum phases of Rydberg atoms on a kagome lattice
• Lecture Notes of Tensor Network Contractions
• Loop optimization for tensor network renormalization
• Resonating valence bond states in the PEPS formalism
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• Tensor renormalization of quantum many-body systems using projected entangled simplex states
• Constructing gapless spin liquid state for the spin-1/2 J1-J2 Heisenberg model on a square lattice
• Vanishing spin gap in a competing spin-liquid phase in the kagome Heisenberg antiferromagnet
• Topological order in PEPS: Transfer operator and boundary Hamiltonians
• How universal is the entanglement spectrum?
• Spin-S Kagome quantum antiferromagnets in a field with tensor networks
• Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions
• Entanglement spectrum of the two dimensional Bose-Hubbard model
• Variational Approach to Projected Entangled Pair States at Finite Temperature
• Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study
• Phase diagram of the J1-J2 Heisenberg model on the kagome lattice
• Quantum critical phase with infinite projected entangled paired states
• Twisted and untwisted negativity spectrum of free fermions
• Negativity spectrum of one-dimensional conformal field theories
• Entanglement spectrum degeneracy and Cardy formula in 1+1 dimensional conformal field theories
• Variational tensor network renormalization in imaginary time: benchmark results in the Hubbard model at finite temperature
• Entanglement spectroscopy of non-Abelian anyons: Reading off quantum dimensions of individual anyons
• Chiral topological spin liquids with projected entangled pair states
• Chiral projected entangled-pair state with topological order
• Investigation of the Néel phase of the frustrated Heisenberg antiferromagnet by differentiable symmetric tensor networks
• Bound states and entanglement in the excited states of quantum spin chains
• Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry
• Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet
• Symmetric tensor networks and practical simulation algorithms to sharply identify classes of quantum phases distinguishable by short-range physics
• Optimized contraction scheme for tensor-network states
• Simplex Z_2 spin liquids on the Kagome lattice with Entangled Pair States: spinon and vison coherence lengths, topological entropy and gapless edge modes
• Edge theories in Projected Entangled Pair State models
• Investigation of the chiral antiferromagnetic Heisenberg model using PEPS
• Entanglement spectroscopy of SU(2)-broken phases in two dimensions
• Obtaining topological degenerate ground states by the density matrix renormalization group
• SU(2)${}_1$ chiral edge modes of a critical spin liquid
• Persistence of the gapless spin liquid in the breathing kagome Heisenberg antiferromagnet
• Valence-bond crystals in the kagome spin-1/2 Heisenberg antiferromagnet: a symmetry classification and projected wave function study
• Topology and Criticality in Resonating Affleck-Kennedy-Lieb-Tasaki loop Spin Liquid States
• Projected Entangled Pair States at Finite Temperature: Iterative Self-Consistent Bond Renormalization for Exact Imaginary Time Evolution
• Variational tensor network renormalization in imaginary time: Two-dimensional quantum compass model at finite temperature
• Abelian SU$(N{)}_1$ Chiral Spin Liquids on the Square Lattice
• Entanglement in gapless resonating valence bond states
• Negativity Spectrum in the Random Singlet Phase
• Global symmetries in tensor network states: symmetric tensors versus minimal bond dimension
• Fermionic Projected Entangled Pair States at Finite Temperature
• RVB superconductors with fermionic projected entangled pair states
• Competing Spin Liquid Phases in the S=$\frac{1}{2}$ Heisenberg Model on the Kagome Lattice
• Topological Order in an Entangled SU(2)$\otimes$XY Spin-Orbital Ring
• A beginner's guide to non-abelian iPEPS for correlated fermions
• Gapless Kitaev Spin Liquid to Classical String Gas through Tensor Networks
• Topological ${\mathbb{Z}}_2$ Resonating-Valence-Bond Spin Liquid on the Square Lattice
• Geometric Entanglement in Topologically Ordered States
• Mutual information area laws for thermal free fermions
• Overcoming the Sign Problem at Finite Temperature: Quantum Tensor Network for the Orbital $e_g$ Model on an Infinite Square Lattice
• Preparing topological PEPS on a quantum computer
• The spin-1/2 Kagome XXZ model in a field: competition between lattice nematic and solid orders
• Hubbard Model on the Pyrochlore Lattice: a 3D Quantum Spin Liquid
• Single-layer tensor network study of the Heisenberg model with chiral interactions on a kagome lattice
• Spinon confinement and deconfinement in spin-1 chains
• A class of two-dimensional AKLT models with a gap
• Detecting and identifying 2D symmetry-protected topological, symmetry-breaking and intrinsic topological phases with modular matrices via tensor-network methods
• Coexistence of long-range and algebraic correlations for short-range valence-bond wave functions in three dimensions
• Enhancing Detection of Topological Order by Local Error Correction
• Featureless quantum spin liquid, 1/3-magnetization plateau state and exotic thermodynamic properties of spin-1/2 frustrated Heisenberg antiferromagnet on an infinite Husimi lattice
• Approximating local observables on projected entangled pair states
• Entanglement Spectrum and Entanglement Hamiltonian of a Chern insulator with open boundaries
• Quantifying entanglement with scattering experiments
• Chiral spin liquids on the kagome lattice with projected entangled simplex states
• Interplay of $SU(2)$, point group and translation symmetry for PEPS: application to a chiral spin liquid
• Semionic resonating valence bond states
• Long range order and symmetry breaking in Projected Entangled Pair State models
• Tensor network representations from the geometry of entangled states
• Locality at the boundary implies gap in the bulk for 2D PEPS
• Critical colored-RVB states in the frustrated quantum Heisenberg model on the square lattice
• Phase diagram of the chiral SU(3) antiferromagnet on the kagome lattice
• Topological ${\mathbb{Z}}_2$ RVB quantum spin liquid on the ruby lattice
• iPEPS study of spin symmetry in the doped $t$-$J$ model
• Resonating Valence Bond States with Trimer Motifs
• Field-induced superfluids and Bose liquids in Projected Entangled Pair States
• Criticality in Two-Dimensional Quantum Systems: Tensor Network Approach
• Gapped $Z_2$ spin liquid in the breathing kagome Heisenberg antiferromagnet
• Entanglement Hamiltonian of the quantum Néel state
• SU(3) trimer resonating-valence-bond state on the square lattice
• Numerical detection of symmetry enriched topological phases with space group symmetry
• Real-time dynamics of a critical Resonating Valence Bond spin liquid
• Abelian and non-Abelian chiral spin liquids in a compact tensor network representation
• Projected d-wave superconducting state: a fermionic projected entangled pair state study
• Edge--Entanglement correspondence for gapped topological phases with symmetry
• Correspondence between many-particle excitations and the entanglement spectrum of disordered ballistic one-dimensional systems
• Quantum state preparation of topological chiral spin liquids via Floquet engineering
• SU(4) topological RVB spin liquid on the square lattice
• Entanglement properties of the two-dimensional SU(3) AKLT state
• Generating resonating valence bond states through Dicke subradiance
• Projected Entangled Pair States with flexible geometry
• Chiral spin liquids with projected Gaussian fermionic entangled pair states
• Entanglement Continuous Unitary Transformations
• Striped critical spin liquid in a spin-orbital entangled RVB state in a projected entangled-pair state representation
• Universal Renyi mutual information in classical systems: the case of kagome ice
• Probing a quantum spin liquid with equilibrium and nonequilibrium hole dynamics
• Tensor network variational optimizations for real-time dynamics: application to the time-evolution of spin liquids
• Simulating chiral spin liquids with projected entangled-pair states
• Entanglement spectra of superconductivity ground states on the honeycomb lattice
• Matrix Product Wave Function of the Ground State and Elementary Excitation in the Spin-1/2 Chain
• Tensor network states for the description of quantum many-body systems
• Detuning the Floquet anomalous chiral spin liquid