Quantized and maximum entanglement from sublattice symmetry

TL;DR

This paper demonstrates that quadratic fermionic Hamiltonians with sublattice symmetry exhibit quantized entanglement between sublattices, with the ground state maximally entangled, and this property can persist even with interactions.

Contribution

It reveals that sublattice symmetry enforces quantized entanglement in eigenstates and shows this persists under interactions, without requiring translation invariance.

Findings

Eigenstates have quantized entanglement entropies between sublattices.

Ground state is maximally entangled between sublattices.

Quantization of entanglement can persist with interactions.

Abstract

We observe that the many-body eigenstates of any quadratic, fermionic Hamiltonian with sublattice symmetry have quantized entanglement entropies between the sublattices: the entanglement comes in multiple singlets. Moreover, such systems always have a ground state that is maximally entangled between the two sublattices. In fact we also show that under the same assumptions there always exists a (potentially distinct) basis of energy eigenstates that do not conserve the particle number in which each energy eigenstate is maximally entangled between the sublattices. No additional properties, such as translation invariance, are required. We also show that the quantization of ground state entanglement may persist when interactions are introduced.