Superfluid Neutron Matter with a Twist

• Main Authors: Georgios Palkanoglou, Alexandros Gezerlis
• Format: Article
• Language: English
• Published: MDPI AG 2021-01-01
• Series: Universe
• Subjects: pairing; superfluidity; neutron matter; BCS theory; finite-size effects
• Online Access: https://www.mdpi.com/2218-1997/7/2/24

Superfluid neutron matter is a key ingredient in the composition of neutron stars. The physics of the inner crust are largely dependent on those of its <i>S</i>-wave neutron superfluid, which has made its presence known through pulsar glitches and modifications in neutron star cooling. Moreover, with recent gravitational-wave observations of neutron star mergers, the need for an equation of state for the matter of these compact stars is further accentuated and a model-independent treatment of neutron superfluidity is important. Ab initio techniques developed for finite systems can be guided to perform extrapolations to the thermodynamic limit and attain this model-independent extraction of various quantities of infinite superfluid neutron matter. To inform such an extrapolation scheme, we performed calculations of the neutron <inline-formula><math display="inline"><semantics><mrow><msup><mrow></mrow><mn>1</mn></msup><msub><mi>S</mi><mn>0</mn></msub></mrow></semantics></math></inline-formula> pairing gap using model-independent odd–even staggering in the context of the particle-conserving, projected Bardeen–Cooper–Schrieffer (BCS) theory under twisted boundary conditions. While the practice of twisted boundary conditions is standard in solid-state physics and has been used repeatedly in the past to reduce finite-size effects, this is the first time that it has been employed in the context of pairing. We find that a twist-averaging approach results in a substantial reduction of the finite-size effects, bringing systems with <inline-formula><math display="inline"><semantics><mrow><mi>N</mi><mo>⪆</mo><mn>50</mn></mrow></semantics></math></inline-formula> within a <inline-formula><math display="inline"><semantics><mrow><mn>2</mn><mo>%</mo></mrow></semantics></math></inline-formula> error margin from the infinite system. This can significantly reduce extrapolation-related errors in the extraction of superfluid neutron matter quantities.