Structure of quantum correlations in momentum space and off diagonal long range order in eta pairing and BCS states

TL;DR

This paper analyzes the structure of quantum correlations in eta pairing and BCS states in momentum space, revealing how these correlations relate to off-diagonal long-range order and their multipartite entanglement properties.

Contribution

It provides a detailed characterization of momentum-space quantum correlations in eta pairing and BCS states, linking bipartite negativity to ODLRO and exploring multipartite entanglement structure.

Findings

Negativity between paired momentum modes relates to ODLRO.

Multipartite entanglement exhibits self-similar, robust structure.

Momentum-space correlations are connected to superconducting order.

Abstract

The quantum states built with the eta paring mechanism i.e., eta pairing states, were first introduced in the context of high temperature superconductivity where they were recognized as important example of states allowing for off-diagonal long-range order (ODLRO). In this paper we describe the structure of the correlations present in these states when considered in their momentum representation and we explore the relations between the quantum bipartite/multipartite correlations exhibited in k space and the direct lattice superconducting correlations. In particular, we show how the negativity between paired momentum modes is directly related to the ODLRO. Moreover, we investigate the dependence of the block entanglement on the choice of the modes forming the block and on the ODLRO; consequently we determine the multipartite content of the entanglement through the evaluation of the generalized "Meyer Wallach" measure in the direct and reciprocal lattice. The determination of the persistency of entanglement shows how the network of correlations depicted exhibits a self-similar structure which is robust with respect to "local" measurements. Finally, we recognize how a relation between the momentum-space quantum correlations and the ODLRO can be established even in the case of BCS states.