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The low-energy, finite-volume spectrum of the two-nucleon system at a quark mass corresponding to a pion mass of $m_{\pi }\approx 806\mathrm{MeV}$is studied with lattice quantum chromodynamics (LQCD) using variational methods. The interpolating-operator sets used in [Variational study of two-nucleon systems with lattice QCD, .] are extended by including a complete basis of local hexaquark operators, as well as plane-wave dibaryon operators built from products of both positive- and negative-parity nucleon operators. Results are presented for the isosinglet and isotriplet two-nucleon channels. In both channels, noticeably weaker variational bounds on the lowest few energy eigenvalues are obtained from operator sets which contain only hexaquark operators or operators constructed from the product of two negative-parity nucleons, while other operator sets produce low-energy variational bounds which are consistent within statistical uncertainties. The consequences of these studies for the LQCD understanding of the two-nucleon spectrum are investigated. Published by the American Physical Society2025 

Understanding the behavior of dense hadronic matter is a central goal in nuclear physics as it governs the nature and dynamics of astrophysical objects such as supernovae and neutron stars. Because of the nonperturbative nature of quantum chromodynamics (QCD), little is known rigorously about hadronic matter in these extreme conditions. Here, lattice QCD calculations are used to compute thermodynamic quantities and the equation of state of QCD over a wide range of isospin chemical potentials with controlled systematic uncertainties. Agreement is seen with chiral perturbation theory when the chemical potential is small. Comparison to perturbative QCD at large chemical potential allows for an estimate of the gap in the superconducting phase, and this quantity is seen to agree with perturbative determinations. Since the partition function for an isospin chemical potential ${\mu }_I$bounds the partition function for a baryon chemical potential ${\mu }_B=3{\mu }_I/2$, these calculations also provide rigorous nonperturbative QCD bounds on the symmetric nuclear matter equation of state over a wide range of baryon densities for the first time. Published by the American Physical Society2025