Imbalance Entanglement: Symmetry Decomposition of Negativity

TL;DR

This paper explores how negativity, an entanglement measure in quantum systems, can be decomposed into charge-imbalance contributions, revealing new insights into symmetry effects on entanglement.

Contribution

It introduces a charge-imbalance decomposition of negativity and demonstrates how to measure and compute it in critical one-dimensional systems.

Findings

Negativity decomposes into charge-imbalance contributions.

The decomposed negativity distribution matches charge-imbalance distribution.

Numerical confirmation aligns with conformal field theory predictions.

Abstract

In the presence of symmetry, entanglement measures of quantum many-body states can be decomposed into contributions arising from distinct symmetry sectors. Here we investigate the decomposability of negativity, a measure of entanglement between two parts of a generally open system in a mixed state. While the entanglement entropy of a subsystem within a closed system can be resolved according to its total preserved charge, we find that negativity of two subsystems may be decomposed into contributions associated with their charge imbalance. We show that this charge-imbalance decomposition of the negativity may be measured by employing existing techniques based on creation and manipulation of many-body twin or triple states in cold atomic setups. Next, using a geometrical construction in terms of an Aharonov-Bohm-like flux inserted in a Riemann geometry, we compute this decomposed negativity in critical one-dimensional systems described by conformal field theory. We show that it shares the same distribution as the charge-imbalance between the two subsystems. We numerically confirm our field theory results via an exact calculations for non-interacting particles based on a double-gaussian representation of the partially transposed density matrix.