Thermodynamic singularities in the entanglement entropy at a 2D quantum critical point

Abstract

We study the bipartite entanglement entropy of the two-dimensional (2D) transverse-field Ising model in the thermodynamic limit using series expansion methods. Expansions are developed for the Renyi entropy around both the small-field and large-field limits, allowing the separate calculation of the entanglement associated with lines and corners at the boundary between sub-systems. Series extrapolations are used to extract subleading power laws and logarithmic singularities as the quantum critical point is approached. In 1D, we find excellent agreement with exact results as well as quantum Monte Carlo simulations. In 2D, we find compelling evidence that the entanglement at a corner is significantly different from a free boson field theory. These results demonstrate the power of the series expansion method for calculating entanglement entropy in interacting systems, a fact that will be particularly useful in future searches for exotic quantum criticality in models with and without the sign problem.

4 pages, plus references and supplement

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• A generalized perspective on non-perturbative linked cluster expansions
• Quantum critical behavior of entanglement in lattice bosons with cavity-mediated long-range interactions
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• Closure of the entanglement gap at quantum criticality: The case of the Quantum Spherical Model
• Shape dependence of two-cylinder Renyi entropies for free bosons on a lattice
• Entanglement gap, corners, and symmetry breaking
• Quantum Criticality in the infinite-range Transverse Field Ising Model
• Universal entanglement correction induced by relevant deformations at the quantum critical point