Quantum phase transitions of spin chiral nanotubes

Abstract

Recently many interesting magnetic nanostructures have been fabricated and much attention is arising on the rich magnetic properties that originate in the quantum effects eminent in the nanoscale world. One of the peculiar aspects of the quantum effects is the spin excitation gap. In the spin-1/2 low-dimensional systems, the spin gap often appears when the lattice dimerization or the frustration in the spin-spin interaction are introduced. In the present study, we investigate the ground-state property of the spin-1/2 antiferromagnetic spin chiral nanotubes with the spatial modulation in the spin-spin interaction. The ground-state phase diagrams of them are determined by observing the behavior of the expectation value of the Lieb-SchultzMattis slow-twist operator calculated by the quantum Monte Carlo method with the continuous-time loop algorithm. We discuss the relation between the characteristic of the topology of the phase diagram and the chiral vector of the nanotubes.Key words: chiral nanotubes; spin gap; quantum Monte Carlo method PACS: 75.10. Jm, 75.40.Mg, 75.50.Ee, 75.75.+a MotivationThese days the experimental techniques have made a lot of progress and good experimentalists have synthesized the nanoscale magnets which realize the models that had been discussed only theoretically before. Among them are the BIP-TENO as the spin-1 twoleg ladder [1], the compound [(CuCl2tachH)3Cl]Cl2 (tach=cis,trans-1,3,5-triamino-cyclohexane) as the triangular spin nanotube [2], and the oxygen molecules adsorbed on the inner surface of the porous material as a many-leg spin tube [3]. The spin ladders [4] and tubes [5] have attracted attention in the course of the extensive studies on the low-dimensional magnets, part of which started from the discussions on the Haldane gap [6] of the one-dimensional spin chains. The appearance of the spin excitation gap is one of the interesting macroscopic quantum phenomena. In spin-1/2 systems, it occurs when the frustration in the spin-spin interaction or the lattice dimerization is introduced. A good example of the former case is the triangular spin nanotube [7] whose spontanous dimerized and gapped ground state had been theoretically investigated [8] and now got a strong possibility of an experimental realization in the near future [2]. During the course of studies on the low-dimensional systems, the huge amount of studies on the carbon nanotubes

Quantum spin nanotubes—frustration, competing orders and criticalities

“…The valence bond solid (VBS) ground states were revealed to appear in some different spin tube systems. For example, the quantum Monte Carlo simulation study [24] suggested that several different types of the VBS ground state occur in some chiral spin nanotubes without frustration. The recent non-linear σ model and DMRG approach [25] indicated some three-leg higher spin tubes exhibit several Haldane phases.…”

Twisted-order parameter applied to dimerized ladders

“…Although the SOP parameter can detect the change associated with this phase crossing, however it does not perform so well when trying to locate the position of those critical points. To this end, another order parameter called twisted-order parameter (TOP) has been introduced for spin chains [30] and some ladders [31,32]. The TOP being non-local, it can be considered as a close relative of the SOP.…”

Heat Capacity Reveals the Physics of a Frustrated Spin Tube

“…Introduction.-Spin tubes constitute a special class of quasi-one-dimensional spin ladder systems characterized by periodic boundary conditions in the rung direction [1][2][3][4][5][6][7][8][9][10][11][12][13]. The magnetic compound ½ðCuCl 2 tachHÞ 3 ClCl 2 , for sample preparation, see [14], is a geometrically frustrated triangular spin tube, the frustration being related both to the triangular arrangement of its rungs and to the twisted geometry of the legs, compare Fig.…”