Professor Daniel Arovas
University of California San Diego

Quantum Entanglement Spectra of Gapless Spin Chains

Abstract:

We investigate the entanglement spectra of certain one-dimensional gapess spin systems. For the spin-1/2 antiferromagnetic Heisenberg chain, we show how an "entanglement gap" gap fully separates a series of generic, high-lying "entanglement energy" levels, from a nearly-flat band of levels with specific multiplicities that uniquely define the ground-state. This gap remains finite in the thermodynamic limit. This rich structure emerges only when the system is partitioned in momentum space, and not real space. Despite the fact that the Laughlin state is bulk gapped while the antiferromagnetic spin chain state is bulk gapless, we show that the S=1/2 chain has an entanglement spectrum almost identical to that of the Laughlin Fractional Quantum Hall state in two dimensions, revealing the similar field theory of their low-energy edge and bulk excitations respectively.