We probe the magnetic field-induced Tomonaga-Luttinger liquid (TLL) state in the bond-alternating spin-
1/2 antiferromagnetic (AFM) chain compound
NaVOPO4 using thermodynamic as well as local $\ensuremath{\mu}\mathrm{SR}$ and
31P NMR probes down to mK temperatures in magnetic fields up to 14 T. The $\ensuremath{\mu}\mathrm{SR}$ and NMR relaxation rates in the gapless TLL regime decay slowly following characteristic power-law behavior, enabling us to directly determine the interaction parameter
K as a function of the magnetic field. These estimates are crosschecked using magnetization and specific heat data. The field-dependent
K lies in the range of
0.4<K<1 and indicates the repulsive nature of interactions between the spinless fermions, in line with the theoretical predictions. This renders
NaVOPO4 the first experimental realization of TLL with repulsive fermionic interactions in hitherto studied
S=1/2 bond-alternating AFM-AFM chain compounds.
We consider a one-dimensional system of spinless fermions with single particle and pair hoppings in a potential on-site disorder. The pair hopping term violates integrability of the model and enhances superconducting fluctuations in the bulk of the liquid. By means of the Abelian bosonization and extensive numerical density matrix renormalization group calculations we provide evidence that sufficiently large pair hopping amplitude guarantees the survival of the Tomonaga-Luttinger liquid phase at weak disorder. Large disorder drives the system to the Bose-glass phase, realizing the Giamarchi-Schulz scenario in such a system.