Shape dependence of two-cylinder Renyi entropies for free bosons on a lattice
arXiv:1607.05311 · doi:10.1103/PhysRevB.94.165136
Abstract
Universal scaling terms occurring in Renyi entanglement entropies have the potential to bring new understanding to quantum critical points in free and interacting systems. Quantitative comparisons between analytical continuum theories and numerical calculations on lattice models play a crucial role in advancing such studies. In this paper, we exactly calculate the universal two-cylinder shape dependence of entanglement entropies for free bosons on finite-size square lattices, and compare to approximate functions derived in the continuum using several different ansatzes. Although none of these ansatzes are exact in the thermodynamic limit, we find that numerical fits are in good agreement with continuum functions derived using the AdS/CFT correspondence, an extensive mutual information model, and a quantum Lifshitz model. We use fits of our lattice data to these functions to calculate universal scalars defined in the thin-cylinder limit, and compare to values previously obtained for the free boson field theory in the continuum.
7 pages, 5 figures, 1 table
References in corpus (10)
- Towards a derivation of holographic entanglement entropy
- Universal terms for the entanglement entropy in 2+1 dimensions
- Remarks on the entanglement entropy for disconnected regions
- Universality of corner entanglement in conformal field theories
- On Shape Dependence and RG Flow of Entanglement Entropy
- Entanglement entropy scaling in the bilayer Heisenberg spin system
- Corner contribution to the entanglement entropy of strongly-interacting O(2) quantum critical systems in 2+1 dimensions
- Thermodynamic singularities in the entanglement entropy at a 2D quantum critical point
- Scaling of entanglement in -dimensional scale-invariant field theories
- Entanglement Entropy and Mutual Information of Circular Entangling Surfaces in 2 + 1-dimensional Quantum Lifshitz Model