Momentum-Space Entanglement in Heisenberg Spin-Half Ladders

TL;DR

This paper analytically investigates momentum-space entanglement in Heisenberg spin-half ladders, revealing distinct behaviors in gapped and gapless phases and showing a volume law for entanglement entropy.

Contribution

It provides a field theoretical analysis of momentum-space entanglement in spin ladders, highlighting differences from real-space entanglement and characterizing the entanglement Hamiltonian in various phases.

Findings

Entanglement Hamiltonian in gapped phase has central charge two.

In gapless phase, entanglement Hamiltonian has one gapless mode and one flat mode.

Momentum-space entanglement entropy follows a volume law.

Abstract

We analytically study momentum-space entanglement in quantum spin-half ladders consisting of two coupled critical XXZ spin-half chains using field theoretical methods. When the system is gapped, the momentum-space entanglement Hamiltonian is described by a conformal field theory with a central charge of two. This is in contrast to entanglement Hamiltonians of various real-space partitions of gapped-spin ladders that have a central charge of one. When the system is gapless, we interestingly find that the entanglement Hamiltonian consist of one gapless mode linear in subsystem momentum and one mode with a flat dispersion relation. We also find that the momentum-space entanglement entropy obeys a volume law.