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arXiv:2610.21955

Spin-1/2 Heisenberg diamond-like decorated honeycomb lattice in a magnetic field from the perspective of localized magnons and exact diagonalization

Katarína Karľová, Malo Rouxel, Jozef Strečka, A. Honecker

Published Oct 15, 2026• 0 citations
arXivHTMLPDF

Abstract

The spin-$1/2$ 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.

DOI
10.48550/arxiv.2610.21955

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Abstract We investigate the spin-1/2 Heisenberg antiferromagnet on a distorted diamond-decorated honeycomb lattice in an external magnetic field. By combining density-matrix renormalization group, sign-problem-free quantum Monte Carlo in a mixed dimer–monomer basis, exact diagonalization, and an effective lattice-gas approach, we determine the ground-state phase diagram and analyze the finite-temperature magnetization process. The model hosts a rich variety of frustration-induced quantum phases including a quantum ferrimagnetic phase of Lieb–Mattis type, a quantum ferromagnetic phase, a spin-canted phase, a monomer–dimer phase, a dimer–tetramer liquid, a dimer-tetramer solid, and two distinct one-dimensional-crossover phases of ferromagnetic and ferrimagnetic character. Depending on the lattice distortion, we identify robust magnetization plateaus at 0, 1/4, 1/2, and 3/4 of the saturation magnetization originating from competing local dimer and tetramer singlets. Finite-temperature QMC data reveal how thermal fluctuations progressively smear the plateau structure, while the effective lattice-gas description reliably captures the corresponding low-temperature behavior.
The spin-1/2 Heisenberg antiferromagnet on the frustrated diamond-decorated square lattice is known to feature various zero-field ground-state phases, consisting of extended monomer-dimer and dimer-tetramer ground states as well as a ferrimagnetic regime. Using a combination of analytical arguments, density matrix renormalization group (DMRG), exact diagonalization as well as sign-problem-free quantum Monte Carlo (QMC) calculations, we investigate the properties of this system and the related Lieb lattice in the presence of a finite magnetic field, addressing both the ground-state phase diagram as well as several thermodynamic properties. In addition to the zero-field ground states, we find at high magnetic field a spin-canted phase with a continuously rising magnetization for increasing magnetic field strength as well as the fully polarized paramagnetic phase. At intermediate field strength, we identify a first-order quantum phase transition line between the ferrimagnetic and the monomer-dimer regime. This first-order line extends to finite temperatures, terminating in a line of critical points that belong to the universality class of the two-dimensional Ising model.
The spin-1/2 Ising-Heisenberg model on a diamond-decorated square lattice exhibits an intriguing temperature-driven phase transition in a magnetic field between a classical ferrimagnetic phase and a quantum monomer-dimer phase. A generalized decoration-iteration transformation accurately maps the considered model to an effective spin-1/2 Ising model on a square lattice with temperature-dependent effective interactions and field, whereby the effective field vanishes at the phase boundary separating the classical ferrimagnetic phase from the quantum monomer-dimer phase. Typical features of the magnetization, magnetic susceptibility and specific heat in the vicinity of discontinuous and continuous thermal phase transitions between the classical ferrimagnetic phase and the quantum monomer-dimer phase are elucidated.
The spin-1/2 Heisenberg antiferromagnet on the diamond-decorated square lattice in the presence of a magnetic field displays various quantum phases including the Lieb-Mattis ferrimagnetic, dimer-tetramer, monomer-dimer, and spin-canted phases, in addition to the trivial fully saturated state. Thermodynamic properties of this model are investigated using several complementary analytical and numerical methods such as exact diagonalization up to the systems of 40 spins, an effective monomer-dimer description, sign-problem-free quantum Monte Carlo simulations for up to 180 spins, and a decoupling approximation. Our particular attention is focused on the parameter region favoring the dimer-tetramer phase. This ground state can be represented by a classical hard-dimer model on the square lattice and retains a macroscopic degeneracy even under a magnetic field. However, the description of the low-temperature thermodynamics close to the boundary between the macroscopically degenerate dimer-tetramer and the nondegenerate monomer-dimer phases requires an extended classical monomer-dimer lattice-gas model. Anomalous thermodynamic properties emerging in the vicinity of the dimer-tetramer phase are studied in detail. Under the adiabatic demagnetization we detect an enhanced magnetocaloric effect promoting an efficient cooling to absolute zero temperature.
The thermal phase transitions of a spin-1/2 Ising-Heisenberg model on the diamond-decorated square lattice in a magnetic field are investigated using a decoration-iteration transformation and classical Monte Carlo simulations. A generalized decoration-iteration transformation maps this model exactly onto an effective classical Ising model on the square lattice with temperature-dependent effective nearest-neighbor interactions and magnetic field strength. The effective field vanishes along a ground-state phase boundary of the original model, separating a ferrimagnetic and a quantum monomer-dimer phase. At finite temperatures this phase boundary gives rise to an exactly solvable surface of discontinuous (first-order) phase transitions, which terminates in a line of Ising critical points. The existence of discontinuous reentrant phase transitions within a narrow parameter regime is reported and explained in terms of the low-energy excitations from both phases. These exact results, obtained from the mapping to the zero-field effective Ising model, are corroborated by classical Monte Carlo simulations of the effective model.
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.