Fingerprints of cluster-based Haldane and bound-magnon states in a spin-1 Heisenberg diamond chain

TL;DR

This study analyzes the spin-1 Heisenberg diamond chain in a magnetic field, uncovering a spectrum of unconventional ground states including uniform and cluster-based Haldane phases, monomer-dimer fragmentation, and bound-magnon crystals. By combining variational bounds, exact diagonalization, DMRG, Lanczos, and quantum Monte Carlo methods with an extended localized-magnon framework, the authors map a comprehensive ground-state phase diagram and establish a highly accurate effective monomer-dimer lattice-gas description for the frustrated regime. They demonstrate pronounced magnetocaloric effects near field-driven transitions and propose a quantum Stirling engine using the chain as the working medium, achieving near-Carnot efficiency in most regimes. The Ni$_3$(OH)$_2$(C$_4$H$_2$O$_4$)(H$_2$O)$_4$·2H$_2$O compound is discussed as a qualitative, albeit unfrustrated, experimental benchmark, while the frustrated chain offers a rich platform for magnetocalorics and quantum thermodynamics with potential technological implications.

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 [Ni3(OH)2(C4H2O4)(H2O)4].2H2O such as a at 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 Gruneisen 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.

Figures (13)

• Figure 1: A part of the crystal structure of one-dimensional coordination polymer [Ni$_3$(OH)$_2$(C$_4$H$_2$O$_4$)(H$_2$O)$_4$] $\cdot$ 2H$_2$O visualized according to crystallographic data reported in Ref. guil02. A color scheme for atom labeling: green balls - nickel, red balls - oxygen, gray balls - carbon.
• Figure 2: A schematic illustration of the spin-1 Heisenberg diamond chain with the intra-dimer interaction $J_2$ (green lines) along its vertical bonds and the monomer-dimer interaction $J_1$ (red lines) along sides of diamond plaquettes. Three spins from $i$-th unit cell are labeled.
• Figure 3: A schematic illustration of exact ground states of the spin-1 Heisenberg diamond chain: (a) the monomer-dimer (MD) phase; (b) the bound magnon crystal (BMC) phase; (c) the tetramer-dimer (TD) phase; (d) the heptamer-dimer (HD) phase; (e) the decamer-dimer (D-D) phase; (f) the Haldane phase. Green arrows correspond to the polarized monomer spins $S_{1,i}^z=+1$ [panels (a) and (b)], green ovals correspond to a dimer-singlet state [panels (a), (c), (d), and (e)], and orange ovals accompanied with orange arrows represent a triplet state of a dimer [panel (b)], a tetramer [panel (c)], a heptamer [panel (d)], or a decamer [panel (e)].
• Figure 4: Three one-magnon energy bands of the spin-1 Heisenberg diamond chain as given by Eq. (\ref{['Eq:Epsilons']}) at zero magnetic field $h=0$ and three selected values of the interaction ratio: (a) $J_2/J_1=0.5$; (b) $J_2/J_1=2$; (c) $J_2/J_1=2.5$.
• Figure 5: A schematic illustration of all fragmented ground states of the spin-1 Heisenberg diamond chain. Except the fully fragmented MD phase with unique singlet state of all dimers corresponding to a magnetic ground state with the period $p = 1$, three fragmented cluster-based Haldane phases denoted as the tetramer-dimer (TD) phase with the period $p = 2$, the heptamer-dimer (HD) phase with the period $p = 3$, and the decamer-dimer (DD) phase with the period $p = 4$ emerge. Orange arrows and zeros represent dimer-triplet and dimer-singlet states of the vertical spin-1 dimers, respectively, while green arrows correspond to the monomer spins.