A rigid commensurate host and a defect that switches: vacancies in the frustrated alternating spin-(1, 1/2) Heisenberg chain

The alternating spin- (1, 12) Heisenberg chain with a frustrating next-nearest-neighbor coupling J 2 loses its Lieb--Mattis moment through a discontinuous transition to a singlet whose nature was left open. Using an SU(2)-symmetric density-matrix renormalization group, in which the total spin is a quantum-number label, we identify that phase and follow a single vacancy through it. The total spin collapses directly from S=L/4 to S=0, with no partially polarized window. The singlet phase is critical: its singlet--triplet gap closes as 1/L, its entanglement entropy grows logarithmically with a central charge c 1.8, and its modulation wavevector, extrapolated from L=80 to 200, is commensurate at 3π/4 and independent of J 2 to 5 times10-5. Removing the central S=1 site switches the ground state of the doped chain from a triplet to a singlet at J 2=0.3068(3), where the host shows no feature; the triplet is not bound to the vacancy but spread over one of the two segments it leaves. The transmission of correlations through the vacancy saturates at a finite value below J 2, T(infinity)=0.102(15) and 0.036(9) at J 2=0.28 and 0.30, and the cut-chain law T proportional to L-1 is excluded on both sides. We also show that the longitudinal correlator is not an observable in a triplet sector.