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Journal of Physics Condensed Matter

Manifestations of bound-magnon crystal, uniform and cluster-based Haldane states in a spin-1 Heisenberg diamond chain *

Azam Zoshki, Hamid Arian Zad, Jozef Strečka

Published May 27, 2026• 0 citations
Publisher

Abstract

Magnetic and thermodynamic properties of the antiferromagnetic spin-1 Heisenberg diamond chain in an external magnetic field are explored using an extended localized-magnon theory complemented by exact diagonalization. We focus on the low-temperature magnetization process, thermodynamic quantities, and magnetocaloric effect in a moderately frustrated regime, where the system hosts a rich variety of unconventional quantum phases including the uniform and cluster-based Haldane states, the fully fragmented monomer-dimer phase, and the bound-magnon crystal preceding the full magnetic saturation. The localized-magnon approach elaborated in our recent work is extended here to account for the uniform Haldane phase, thereby allowing the lattice-gas description to be generalized from the highly frustrated to the moderately frustrated regime. The resulting monomer-dimer lattice-gas model captures anomalous features of the magnetization, susceptibility, entropy, specific heat, and magnetic Grüneisen parameter near field-driven transitions between the quantum phases manifested as zero, one-sixth, one-third, and two-thirds magnetization plateaus.

DOI
10.1088/1361-648x/ae73d8

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Magnetic and thermodynamic properties of the antiferromagnetic spin-1 Heisenberg diamond chain in an external magnetic field are explored using an extended localized-magnon theory complemented by exact diagonalization. We focus on the low-temperature magnetization process, thermodynamic quantities, and magnetocaloric effect in a moderately frustrated regime, where the system hosts a rich variety of unconventional quantum phases including the uniform and cluster-based Haldane states, the fully fragmented monomer-dimer phase, and the bound-magnon crystal preceding the full magnetic saturation. The localized-magnon approach elaborated in our recent work is extended here to account for the uniform Haldane phase, thereby allowing the lattice-gas description to be generalized from the highly frustrated to the moderately frustrated regime. The resulting monomer-dimer lattice-gas model captures anomalous features of the magnetization, susceptibility, entropy, specific heat, and magnetic Grüneisen parameter near field-driven transitions between the quantum phases manifested as zero, one-sixth, one-third, and two-thirds magnetization plateaus.
Abstract We investigate magnetic and thermodynamic properties of a spin-1 Heisenberg diamond chain in a magnetic field using a combination of analytical and numerical methods including the variational approach, exact diagonalization, density-matrix renormalization group, localized-magnon theory, and quantum Monte Carlo simulations. In the unfrustrated regime, the model exhibits a quantum ferrimagnetic phase that captures key magnetic features of the nickel-based polymeric compound [Ni 3 (OH) 2 (C 4 H 2 O 4 )(H 2 O) 4 ] · 2H 2 O such as a flat minimum in the temperature dependence of the susceptibility times temperature product and an intermediate one-third magnetization plateau. In the frustrated regime, we uncover a rich variety of unconventional quantum phases including uniform and cluster-based Haldane states, fragmented monomer-dimer phase, and bound-magnon crystals. Analysis of the adiabatic temperature change and magnetic Grüneisen parameter reveals an enhanced magnetocaloric effect near field-induced transitions between these exotic quantum phases. Additionally, we demonstrate that the frustrated spin-1 diamond chain can operate as an efficient working medium of a quantum Stirling engine, which approaches near-optimal efficiency when driven into these unconventional quantum states.
The mixed spin-1 and spin-1/2 Heisenberg octahedral chain with regularly alternating monomeric spin-1 sites and square-plaquette spin-1/2 sites is investigated using a variational technique, localized-magnon approach, exact diagonalization, and density-matrix renormalization-group method. The investigated model has, in a magnetic field, an extraordinarily rich ground-state phase diagram, which includes the uniform and cluster-based Haldane phases, two ferrimagnetic phases of Lieb-Mattis type, two quantum spin liquids, two bound magnon crystals, in addition to the fully polarized ferromagnetic phase. The lowest-energy eigenstates in a highly frustrated parameter region belong to flatbands and, hence, low-temperature thermodynamics above the bound magnon-crystal ground states can be satisfactorily described within the localized-magnon approach. The variational method provides exact evidence for the magnon-crystal phase with a character of the monomer-tetramer ground state at zero field, whereas another magnon-crystal phase with a single bound magnon at each square plaquette is found in a high-field region. A diversity of quantum ground states gives rise to manifold zero-temperature magnetization curves, which may involve up to four wide intermediate plateaus at zero, one-sixth, one-third, and two-thirds of the saturation magnetization, two quantum spin-liquid regions, and two tiny plateaus at one-ninth and one-twelfth of the saturation magnetization corresponding to the fragmentized cluster-based Haldane phases.
The rich ground-state phase diagram of the mixed spin-(1,1/2) Heisenberg octahedral chain was previously elaborated from effective mixed-spin Heisenberg chains, which were derived by employing a local conservation of a total spin on square plaquettes of an octahedral chain. Here we present a comprehensive analysis of the thermodynamic properties of this model. In the highly frustrated parameter region the lowest-energy eigenstates of the mixed-spin Heisenberg octahedral chain belong to flat bands, which allow a precise description of low-temperature magnetic properties within the localized-magnon approach exploiting a classical lattice-gas model of hard-core monomers. The present article provides a more comprehensive version of the localized-magnon approach, which extends the range of its validity down to a less frustrated parameter region involving the Haldane and cluster-based Haldane ground states. A comparison between results of the developed localized-magnon theory and accurate numerical methods such as full exact diagonalization and finite-temperature Lanczos technique convincingly evidence that the low-temperature magnetic properties above the Haldane and the cluster-based Haldane ground states can be extracted from a classical lattice-gas model of hard-core monomers and dimers, which is additionally supplemented by a hard-core particle spanned over the whole lattice representing the gapped Haldane phase.
Abstract Magnetic, thermodynamic, and magnetocaloric properties of a spin- 1 2 12\frac{1}{2}21​ Heisenberg octahedral chain with three distinct exchange interactions are investigated in an external magnetic field using the variational method, extended localized-magnon approach, and exact diagonalization. Variational arguments rigorously establish two distinct fragmented phases in the frustrated regime. In the former phase, all four spins of each square plaquette form a collective plaquette singlet, whereas in the latter phase, two dimer singlets are formed along diagonals of each square plaquette. These bound two-magnon states, supplemented with three localized one-magnon states, enable us to elaborate a generalized localized-magnon theory that is applicable in a frustrated regime across the entire field range as confirmed by comparison with exact diagonalization data. The concept of localized magnons provides a consistent description of low-temperature magnetization curves featuring intermediate one-fifth and three-fifths plateaus, which intersect each other at temperature-independent crossing points determined by the relative degeneracies of competing bound-magnon phases. Field variations of the specific heat reveal a pronounced double-peak structure near each field-driven transition with peak heights depending on the relative degeneracies of the respective bound-magnon states. Our results demonstrate that the system supports highly efficient cooling via adiabatic demagnetization, making it a promising candidate for magnetocaloric refrigeration.
It is evidenced that effective lattice-gas models of hard-core monomers and dimers afford a proper description of low-temperature features of spin-12\frac{1}{2}21​ Heisenberg diamond and octahedral chains. In addition to monomeric particles assigned within the localized-magnon theory to bound one- and two-magnon eigenstates, the effective monomer-dimer lattice-gas model includes dimeric particles assigned to a singlet-tetramer (singlet-hexamer) state as a cornerstone of dimer-tetramer (tetramer-hexamer) ground state of a spin-12\frac{1}{2}21​ Heisenberg diamond (octahedral) chain. The feasibility of the effective description is confirmed through the exact diagonalization and finite-temperature Lanczos methods. Both quantum spin chains display rich ground-state phase diagrams including discontinuous as well as continuous field-driven phase transitions, whereby the specific heat shows in vicinity of the former phase transitions an extraordinary low-temperature peak coming from a highly degenerate manifold of low-lying excitations.
The spin-1/21/21/2 quantum Heisenberg model on the diamond-decorated honeycomb lattice in a magnetic field is investigated using complementary analytical and numerical methods. The ground-state phase diagram comprises Lieb-Mattis ferrimagnetic, dimer-tetramer, monomer-dimer, spin-canted, and saturated paramagnetic phases, giving rise to characteristic magnetization plateaus, continuous and discontinuous field-induced transitions. In the highly frustrated regime, a localized-magnon approach based on an effective classical lattice-gas model provides an accurate description of the low-temperature magnetism and thermodynamics in agreement with numerical results. At intermediate frustration, finite-temperature calculations reveal characteristic specific-heat signatures of the field-induced transitions including the development of Ising critical behavior at the field-induced transition between the monomer-dimer and Lieb-Mattis ferrimagnetic phase.