Nature of the singlet phase beyond the ferrimagnetic transition

Characterize the nature of the total-spin-zero ground state of the frustrated alternating spin-(1,1/2) Heisenberg chain above the discontinuous transition from the Lieb–Mattis ferrimagnetic phase.

Background

The alternating spin-(1,1/2) Heisenberg chain loses its Lieb–Mattis ferrimagnetic moment when frustration from the next-nearest-neighbor coupling drives a discontinuous transition to a singlet. Earlier work established the transition and estimated its location but did not determine the physical character of the singlet state.

The paper addresses this problem using SU(2)-symmetric DMRG and concludes that the singlet phase is critical, commensurate, and characterized by a modulation wavevector near 3π/4, a vanishing singlet–triplet gap, and an effective central charge near 1.8.

References

What the singlet state above the transition actually is was left open, and stated as such: the nature of the $S_g=0$ ground states established beyond the ferrimagnetic phase is named there as one of the important remaining questions.

— A rigid commensurate host and a defect that switches: vacancies in the frustrated alternating spin-(1, 1/2) Heisenberg chain  (2610.22140 - Silva et al., 15 Oct 2026) in Section 1, Introduction

The rule holds at all seven positions, and we have no explanation for it; a test of the natural candidate, a dimerization in pairs of cells, on clean chains with an odd number of cells ($L=78$, $82$) found gaps of the same order as at $L=80$ and rules it out.

— A rigid commensurate host and a defect that switches: vacancies in the frustrated alternating spin-(1, 1/2) Heisenberg chain  (2610.22140 - Silva et al., 15 Oct 2026) in Section 5, The vacancy, subsection “$J_2^{\ast}$ depends on where the vacancy sits”

Sizes up to $L=200$ therefore do not decide whether the singlet-side transmission goes to a small plateau or to zero as a power law; we report both and claim neither.

— A rigid commensurate host and a defect that switches: vacancies in the frustrated alternating spin-(1, 1/2) Heisenberg chain  (2610.22140 - Silva et al., 15 Oct 2026) in Section 5, subsection “Transmission through the vacancy”; Section 6, Discussion