Hybrid Quantum-Classical Simulation of Pairing and Luttinger-Liquid Behavior in a 1D Spin Chain

We study a one-dimensional spin chain combining XX-type hopping with density-density interactions as a minimal model relevant to nuclear pairing phenomena and low-density neutron matter. Classically, we compute ground-state wavefunctions within fixed-particle-number sectors using density matrix renormalization group (DMRG) techniques, characterizing pairing correlations through two-particle correlation functions. Quantum computations utilize the Trotter-Suzuki product formula and rodeo algorithm, employing controlled reversal gates and a generalized superiteration technique to facilitate efficient convergence. This hybrid quantum-classical approach provides insights into quasi-long-range pairing order characteristic of Tomonaga-Luttinger liquids, serving as a scalable testbed for quantum many-body methods applicable to nuclear physics.