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arXiv:2504.00095 · npj Quantum Materials

Spin order and spin excitation spectra of spin-1/2 tetramer chains

Junli Li, Jun-Qing Cheng, Trinanjan Datta, Dao‐Xin Yao

Published Mar 18, 2026• 0 citations
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Abstract

Abstract We investigate the spin dynamics of a 1D spin-1/2 Heisenberg tetramer chain. Employing a combination of density matrix renormalization group, quantum renormalization group, and perturbation theory techniques, we compute the energy levels and the quantum phase diagram, analyze the phase transitions, and evaluate the dynamical structure factor (DSF), which is related to the inelastic neutron scattering (INS) spectrum and the resonant inelastic x-ray scattering (RIXS) spectrum of fractionalized and collective excitations. Our calculations suggest that the chain can transition between a hidden Z 2 × Z 2 discrete symmetry preserving tetramer phase and a Haldane phase with non-vanishing string order that breaks the hidden symmetry. These two gapped phases are intervened by an intermediate deconfined quantum critical state comprising of free spins and three-site doublets, which is a gapless critical phase with deconfined spinons that can be detected either by INS or L -edge RIXS. We find that the tetramer chain can support fractionalized (spinon) and collective (triplon and quinton) excitations. In the ferromagnetic intra-tetramer limit, the chain can support a quinton excitation which has a five-fold degenerate excited state. String order parameter calculations suggest CuInVO 5 should be in a Haldane-like phase whose INS or L -edge RIXS spectrum can support observable single-spin excitations including triplon and quinton excitations. We also identify possible two-particle excitations (two-singlon, two-triplon, triplon-quinton, and two-quinton excitations) resulting from the double spin-flip effect in the K -edge RIXS spectrum.

DOI
10.1038/s41535-026-00855-x

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Abstract We investigate the spin dynamics of a 1D spin-1/2 Heisenberg tetramer chain. Employing a combination of density matrix renormalization group, quantum renormalization group, and perturbation theory techniques, we compute the energy levels and the quantum phase diagram, analyze the phase transitions, and evaluate the dynamical structure factor (DSF), which is related to the inelastic neutron scattering (INS) spectrum and the resonant inelastic x-ray scattering (RIXS) spectrum of fractionalized and collective excitations. Our calculations suggest that the chain can transition between a hidden Z 2 × Z 2 discrete symmetry preserving tetramer phase and a Haldane phase with non-vanishing string order that breaks the hidden symmetry. These two gapped phases are intervened by an intermediate deconfined quantum critical state comprising of free spins and three-site doublets, which is a gapless critical phase with deconfined spinons that can be detected either by INS or L -edge RIXS. We find that the tetramer chain can support fractionalized (spinon) and collective (triplon and quinton) excitations. In the ferromagnetic intra-tetramer limit, the chain can support a quinton excitation which has a five-fold degenerate excited state. String order parameter calculations suggest CuInVO 5 should be in a Haldane-like phase whose INS or L -edge RIXS spectrum can support observable single-spin excitations including triplon and quinton excitations. We also identify possible two-particle excitations (two-singlon, two-triplon, triplon-quinton, and two-quinton excitations) resulting from the double spin-flip effect in the K -edge RIXS spectrum.
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We determine the spin-exchange dynamical structure factor of the Heisenberg spin chain, as is measured by indirect resonant inelastic x-ray scattering (RIXS). We find that two-spin RIXS excitations nearly entirely fractionalize into two-spinon states. These share the same continuum lower bound as single-spin neutron scattering excitations, even if the relevant final states belong to orthogonal symmetry sectors. The RIXS spectral weight is mainly carried by higher-energy excitations, and is beyond the reach of the low-energy effective theories of Luttinger liquid type.
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A KKK and L3L_{3}L3​ -edge RIXS study of the columnar and the staggered quantum dimer phases of the square lattice Heisenberg model
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Frustrated spin systems can show phases with spontaneous breaking of spin-rotational symmetry without the formation of local magnetic order. We study the dynamic response of the spin-nematic phase of one-dimensional spin-1/21/21/2 systems, characterized by slow large-distance decay of quadrupolar correlations, by numerically computing one-spin and two-spin dynamical structure factors at zero temperature using time-dependent density matrix renormalization group methods. We interpret the results in terms of an effective theory of gapped magnon excitations interacting with a quasicondensate of bound magnon pairs. This employs an extension of the well-known Tomonaga-Luttinger liquid theory which includes the magnon states as a mobile impurity. A good qualitative understanding of the characteristic thresholds and their intensity in the structure factors is obtained this way. Our results are useful in the interpretation of inelastic neutron scattering and resonant inelastic x-ray scattering experiments.