Phase diagram of the alternating-spin Heisenberg chain with extra isotropic three-body exchange interactions

Abstract

Abstract. For the time being isotropic three-body exchange interactions are scarcely explored and mostly used as a tool for constructing various exactly solvable one-dimensional models, although, generally speaking, such competing terms in generic Heisenberg spin systems can be expected to support specific quantum effects and phases. The Heisenberg chain constructed from alternating S = 1 and σ = 1 2 site spins defines a realistic prototype model admitting extra three-body exchange terms. Based on numerical density-matrix renormalization group (DMRG) and exact diagonalization (ED) calculations, we demonstrate that the additional isotropic three-body terms stabilize a variety of partially-polarized states as well as two specific non-magnetic states including a critical spin-liquid phase controlled by two Gaussinal conformal theories as well as a critical nematic-like phase characterized by dominant quadrupolar S-spin fluctuations. Most of the established effects are related to some specific features of the three-body interaction such as the promotion of local collinear spin configurations and the enhanced tendency towards nearest-neighbor clustering of the spins. It may be expected that most of the predicted effects of the isotropic three-body interaction persist in higher space dimensions.PACS. 75.10.Jm Quantized spin models -75.40.Mg Numerical simulation studies -75.45.+j Macroscopic quantum phenomena in magnetic systems

Alternating-spin S = 3/2 and σ = 1/2 Heisenberg chain with isotropic three-body exchange interactions

“…As in the previously studied extreme quantum case of Eq. (1) with S = 1 and σ = 1 2 [7], the basic rearrangements concern the SRC between the larger S spins, whereas -apart from the region close to the FM point θ F -the SRC between the σ = 1 2 spins remain almost constant.…”

“…1 The equation for the exact FM boundary θF for arbitrary spins S and σ reads cos θF + σ (2S + 1) sin θF = 0 [7]. chain vs θ (DMRG, OBC, L=24).…”

“…On the theoretical side, only recently some specific features of the three-body exchange interaction in Heisenberg spin models in space dimensions D=1 [1,6,7,8] and D=2 [9,13,14] have been discussed in the literature. In particular, two of us (N.B.I and J.S) recently analyzed the full quantum phase diagram of the alternating-spin Heisenberg chain [7] defined by the Hamiltonian…”

“…In particular, two of us (N.B.I and J.S) recently analyzed the full quantum phase diagram of the alternating-spin Heisenberg chain [7] defined by the Hamiltonian…”

Entanglement and quantum teleportation in a three-qubit Heisenberg chain with three-site interactions

“…But those studies only consider the nearest neighbor spin-spin interactions. The next-to-nearest neighbor interactions and multiple spin-exchange models [21][22][23][24][25][26] should gain great attention because they are closer to real situation in quasi-one-dimensional magnets than the nearest neighbor interactions. For example, optical lattices, constructed of equilateral triangles [27], always exist three-site interactions [28][29][30], with which the entanglement and quantum critical behavior in Heisenberg models are investigated carefully [31][32][33].…”