Scaling of entanglement entropy across Lifshitz transitions

Abstract

We investigate the scaling of the bipartite entanglement entropy across Lifshitz quantum phase transitions, where the topology of the Fermi surface changes without any changes in symmetry. We present both numerical and analytical results which show that Lifshitz transitions are characterized by a well-defined set of critical exponents for the entanglement entropy near the phase transition. In one dimension, we show that the entanglement entropy exhibits a length scale that diverges as the system approaches a Lifshitz critical point. In two dimensions, the leading and sub-leading coefficients of the scaling of entanglement entropy show distinct power-law singularities at critical points. The effect of weak interactions is investigated using the density matrix renormalization group algorithm.

11 pages, 11 figures; v2) references added

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• Incommensurability Effects in Odd Length J_1-J_2 Quantum Spin Chains: On-site magnetization and Entanglement
• The scaling of entanglement entropy in a honeycomb lattice on a torus
• Spin-gap spectroscopy in a bosonic flux ladder
• Pivoting through the chiral-clock family
• Analytic Expression for the Entanglement Entropy of a 2D Topological Superconductor
• Orbital antiferroelectricity and higher dimensional magnetoelectric order in the spin-$1/2$ XX chain extended with three-spin interactions