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arXiv:1904.02240 · Physical review. B./Physical review. B

Frustrated quantum Heisenberg double-tetrahedral and octahedral chains at high magnetic fields

Olesia Krupnitska

Published Aug 5, 2020• 6 citations
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Abstract

We consider the spin-1/2 antiferromagnetic Heisenberg model on two one-dimensional frustrated lattices, a double-tetrahedral chain and an octahedral chain, with almost dispersionless (flat) lowest magnon band in a strong magnetic field. Using the localized-magnon picture, we construct an effective description of the one-dimensional chains with triangle and square traps within the strong-coupling approximation. We perform extensive exact diagonalization and density matrix renormalization group calculations to check the validity of the obtained effective Hamiltonians by comparison with the initial models with special focus on the magnetization and specific heat at high magnetic fields.

DOI
10.1103/physrevb.102.064403

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We consider the spin-1/2 antiferromagnetic Heisenberg model on two one-dimensional frustrated lattices, a double-tetrahedral chain and an octahedral chain, with almost dispersionless (flat) lowest magnon band in a strong magnetic field. Using the localized-magnon picture, we construct an effective description of the one-dimensional chains with triangle and square traps within the strong-coupling approximation. We perform extensive exact diagonalization and density matrix renormalization group calculations to check the validity of the obtained effective Hamiltonians by comparison with the initial models with special focus on the magnetization and specific heat at high magnetic fields.
We consider the spin-1/2 antiferromagnetic Heisenberg model on the two-dimensional square-kagome lattice with almost dispersionless lowest magnon band. For a general exchange coupling geometry we elaborate low-energy effective Hamiltonians which emerge at high magnetic fields. The effective model to describe the low-energy degrees of freedom of the initial frustrated quantum spin model is the (unfrustrated) square-lattice spin-1/2 XXZ model in a z-aligned magnetic field. For the effective model we perform quantum Monte Carlo simulations to discuss the low-temperature properties of the square-kagome quantum Heisenberg antiferromagnet at high magnetic fields. We pay special attention to a magnetic-field driven Berezinskii-Kosterlitz-Thouless phase transition which occurs at low temperatures.
We consider the spin-1/2 antiferromagnetic Heisenberg model on the two-dimensional square-kagome lattice with almost dispersionless lowest magnon band. For a general exchange coupling geometry we elaborate low-energy effective Hamiltonians which emerge at high magnetic fields. The effective model to describe the low-energy degrees of freedom of the initial frustrated quantum spin model is the (unfrustrated) square-lattice spin-1/2 XXZ model in a z-aligned magnetic field. For the effective model we perform quantum Monte Carlo simulations to discuss the low-temperature properties of the square-kagome quantum Heisenberg antiferromagnet at high magnetic fields. We pay special attention to a magnetic-field driven Berezinskii–Kosterlitz– Thouless phase transition which occurs at low temperatures.
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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-12\frac{1}{2}21​ Heisenberg octahedral chain with regularly alternating monomeric and square-plaquette sites is investigated using various analytical and numerical methods: variational technique, localized-magnon approach, exact diagonalization (ED), and density-matrix renormalization group (DMRG) methods. The model belongs to the class of flatband systems and it has a rich ground-state phase diagram including phases with spontaneously broken translational symmetry. Moreover, it exhibits an anomalous low-temperature thermodynamics close to continuous or discontinuous field-driven quantum phase transitions between three quantum ferrimagnetic phases, tetramer-hexamer phase, monomer-tetramer phase, localized-magnon phase, and two different spin-liquid phases. If the intraplaquette coupling is at least twice as strong as the monomer-plaquette coupling, the variational method furnishes a rigorous proof of the monomer-tetramer ground state in a low-field region and the localized-magnon approach provides exact evidence of a single magnon trapped at each square plaquette in a high-field region. In the rest of the parameter space we have numerically studied the ground-state phase diagram and magnetization process using DMRG and ED methods. It is shown that the zero-temperature magnetization curve may involve up to four intermediate plateaus at zero, one-fifth, two-fifths, and three-fifths of the saturation magnetization, while the specific heat exhibits a striking low-temperature peak in the vicinity of discontinuous quantum phase transitions.
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.