Entanglement entropy of critical spin liquids

Abstract

Quantum spin liquids are phases of matter whose internal structure is not captured by a local order parameter. Particularly intriguing are critical spin liquids, where strongly interacting excitations control low energy properties. Here we calculate their bipartite entanglement entropy that characterize their quantum structure. In particular we calculate the Renyi entropy $S_2$, on model wavefunctions obtained by Gutzwiller projection of a Fermi sea. Although the wavefunctions are not sign positive, $S_2$ can be calculated on relatively large systems (>324 spins), using the variational Monte Carlo technique. On the triangular lattice we find that entanglement entropy of the projected Fermi-sea state violates the boundary law, with $S_2$ enhanced by a logarithmic factor. This is an unusual result for a bosonic wave-function reflecting the presence of emergent fermions. These techniques can be extended to study a wide class of other phases.

4+ pages, 2 figures, to be published in PRL

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• Thermodynamic singularities in the entanglement entropy at a 2D quantum critical point
• Renyi Entanglement Entropy of Interacting Fermions Calculated Using Continuous-Time Quantum Monte Carlo Method
• Quantum Fluctuations in Holographic Theories with Hyperscaling Violation
• A Wang-Landau method for calculating Renyi entropies in finite-temperature quantum Monte Carlo simulations
• Projected BCS states and spin Hamiltonians for the SO(n)_1 Wess-Zumino-Witten model
• Topological and nematic ordered phases in many-body cluster-Ising models
• $U(1)\times U(1)$ Symmetry Protected Topological Order in Gutzwiller Wave Functions
• Establishing non-Abelian topological order in Gutzwiller projected Chern insulators via Entanglement Entropy and Modular S-matrix
• Entangled Dilaton Dyons
• Scaling of entanglement entropy across Lifshitz transitions
• Correlated metallic state in honeycomb lattice: Orthogonal Dirac semimetal
• The scaling of entanglement entropy in a honeycomb lattice on a torus
• Density-matrix based numerical methods for discovering order and correlations in interacting systems