Quantum Criticality Correlations in a Transverse-Field Anisotropic Cluster-XX Chain

Abstract We investigate the spin-1/2 XX chain with an anisotropic three-spin interaction in a transverse magnetic field, a model in which cluster interactions provide a tunable route to unconventional quantum phases and low-energy spectral reconstructions. We focus on how the anisotropy of the three-spin coupling modifies the field-driven evolution of gapless phases and their quantum correlations beyond the conventional gap-closing scenario. We find a rich phase structure containing both gapped and gapless regimes, including a Lifshitz-type gapless–gapless transition associated with a reconstruction of the low-energy Fermi points while the excitation gap remains closed. For β < 0, the field can drive a sequence of two gapless phases followed by a gapped phase, whereas for β > 0 the system is gapless at zero field, becomes gapped immediately upon applying a finite field, and undergoes a further transition at h = 1 between distinct gapped regimes. The anisotropy also produces distinct chiral and chiral-nematic correlation patterns, while concurrence and quantum discord reveal qualitatively different distributions of bipartite entanglement and more general nonclassical correlations across the phase diagram. These results show that anisotropic three-spin interactions provide a distinct extension of previously studied cluster-XX chains, in which external fields can reorganize the topology of gapless excitations and the associated correlation structure. The model therefore offers an exactly solvable framework for studying unconventional quantum criticality arising from the interplay of cluster interactions, field control, and quantum correlations.