Cluster-based Haldane phases, bound magnon crystals and quantum spin liquids of a mixed spin-1 and spin-1/2 Heisenberg octahedral chain

Abstract

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 variational technique, localizedmagnon approach, exact diagonalization ( ED) and density-matrix renormalization group ( DMRG) 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 and two bound magnon crystals in addition to the fully polarized ferromagnetic phase. The lowest-energy eigenstates in a highly-frustrated parameter region belong to flat bands and hence, low-temperature thermodynamics above the bound magnoncrystal ground states can be satisfactorily described within the localized-magnon approach. The variational method provides an exact evidence for the magnon-crystal phase with a character of the monomer-tetramer ground state at zero field, while 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.

Towards lattice-gas description of low-temperature properties above the Haldane and cluster-based Haldane ground states of a mixed spin-(1,1/2) Heisenberg octahedral chain

“…In our recent papers, we have provided a proper description of the low-temperature thermodynamics of the spin-1/2 Heisenberg octahedral chain [25,27] in the full range of the magnetic fields within the highly frustrated parameter region, because this frustrated quantum spin chain exhibits at sufficiently low magnetic fields another exact ground state with the character of the monomertetramer phase being composed from a localized twomagnon state. Exactly the same ground state with the character of monomer-tetramer phase appears in the ground-state phase diagram of the mixed spin-(1,1/2) Heisenberg octahedral chain, for which we have also found a consistent description of the low-temperature thermodynamics in the full range of the magnetic fields in a highly frustrated parameter region [32]. It should be mentioned that a less frustrated parameter region of the mixed spin-(1,1/2) Heisenberg octahedral chain involves besides the monomer-tetramer phase three additional fragmentized cluster-based Haldane phases, which are manifested in the zero-temperature magnetization curve as fractional magnetization plateaus at 1/6, 1/9 and 1/12 of the saturation magnetization.…”

Frustrated magnetism of spin-1/2 Heisenberg diamond and octahedral chains as a statistical-mechanical monomer-dimer problem

“…We are convinced that the proposed calculation scheme has opened the route to a low-temperature magnetic behavior of several frustrated Heisenberg spin models, which have at least two tensor-product ground states with a magnetic unit spread over one and two unit cells, respectively. The mixed spin-(1,1/2) Heisenberg octahedral chain affords a suitable platform for implementation of the lattice-gas model of hard-core monomers and dimers, which would extend a legitimacy of the previous calculations based on the lattice-gas model of hardcore monomers [27]. Note furthermore that the suggested calculation procedure is also compatible with recent extension enabling a straightforward computation of entanglement measures [28].…”

“…The other factor 1 4 d j entering into the partition function (27) is the correction term for the singlet-hexamer state (25), which avoids fourfold counting of this eigenstate when performing the summation over spin states of two monomeric spins S 1,j and S 1,j+1 . As in Sec.…”

“…One may fortunately avoid this shortcoming in a special subclass of the frustrated quantum Heisenberg spin models satisfying local spinconservation laws. It has been actually verified that an additional counting of the lowest-energy bound twomagnon eigenstate paves the way towards a complete description of low-temperature magnetization curves and thermodynamics of highly frustrated Heisenberg octahedral chains from zero up to the saturation field [25][26][27][28].…”

Quantum Phase Transition of a Quantum Mixed Spin Chain by Employing Density Matrix Renormalization Group Method

“…In general, quantum mixed spin chains possess two types of inhomogeneities, [ 16,17 ] the alternation of coupling strengths and spin magnitudes within a unit cell, and have attracted a great interest for their exotic low‐energy physics, like the magnetization plateau and Luttinger liquid shown in various ferrimagnetic Heisenberg chains, [ 18–20 ] the Kosterlitz‐Thouless and Gaussian criticalities recently studied in the mixed spin‐(1/2, 5/2, 1/2) Heisenberg branched chain, [ 21,22 ] and the quantum spin liquid phases appeared in the mixed spin‐1 and spin‐1/2 Heisenberg octahedral chain. [ 23 ] Additionally, these mixed spin chains are also of experimental interest and have several realistic realizations. [ 24–26 ] From the theoretical point of view, however, due to the complexity induced by inhomogeneities, analytical methods may fail to extract the ground‐state properties of mixed spin chains and numerical calculations become necessary.…”