Zero Modes and Entanglement Entropy

Abstract

Ultraviolet divergences are widely discussed in studies of entanglement entropy. Also present, but much less understood, are infrared divergences due to zero modes in the field theory. In this note, we discuss the importance of carefully handling zero modes in entanglement entropy. We give an explicit example for a chain of harmonic oscillators in 1D, where a mass regulator is necessary to avoid an infrared divergence due to a zero mode. We also comment on a surprising contribution of the zero mode to the UV-scaling of the entanglement entropy.

v2: 12 pages, 8 figures. Minor changes and typos fixed. Figure and details added on the UV behavior of the giant eigenvalue in the limit of large system size. Discussion added of relation to other work

References in corpus (3)

• A holographic proof of the strong subadditivity of entanglement entropy
• Zero modes and divergence of entanglement entropy
• Entanglement Entropy of Periodic Sublattices

Cited by in corpus (16)

• Complexity and entanglement for thermofield double states
• Entanglement Growth after a Global Quench in Free Scalar Field Theory
• Entanglement Evolution in Lifshitz-type Scalar Theories
• Entanglement Entropy in Causal Set Theory
• Divergence of entanglement entropy in quantum systems: Zero-modes
• Vacuum entanglement harvesting with a zero mode
• Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory -- I. Single-particle states
• Universal finite-size amplitude and anomalous entanglement entropy of $z=2$ quantum Lifshitz criticalities in topological chains
• One-to-one correspondence between entanglement mechanics and black hole thermodynamics
• Zero mode suppression of superluminal signals in light-matter interactions
• Entanglement entropies of an interval for the massless scalar field in the presence of a boundary
• Spatial entanglement in interacting Bose-Einstein condensates
• Field Space Entanglement Entropy, Zero Modes and Lifshitz Models
• Ambiguities in the local thermal behavior of the scalar radiation in one-dimensional boxes
• Euclidean Time Approach to Entanglement Entropy on Lattices and Fuzzy Spaces
• Odd Entanglement Entropy and Logarithmic Negativity for Thermofield Double States