Melting of ferromagnetic order on a trellis ladder

Abstract

The ground state properties of a frustrated spin-1/2 system is studied on a trellis ladder which is composed of two zigzag ladders interacting through rung interactions. The presence of rung interaction between the zigzag ladders induces a non-magnetic ground state, although, each of zigzag ladders has ferromagnetic order in weak anti-ferromagnetic leg interaction limit. The rung interaction also generates rung dimers and opens spin gap which increases rapidly with rung interaction strength. The correlation between spins decreases exponentially with the distance between them. Figure 1: Two coupled zigzag ladders form trellis ladder. The broken lines show the extension of trellis ladder to trellis lattice structure. The arrows show respective spin arrangements. The reference site is labeled by '0' and the distances of all other sites are shown with respect to it. The distance of the sites in the same zigzag ladder as the reference site are written in bold numbers, and the sites on the other ladder are written in normal numbers.and rung couplings of a normal ladder, respectively and J 1 is inter-ladder coupling through zigzag bonds.There are several theoretical studies for two coupled zigzag ladders, e.g. a two-leg honeycomb ladder is considered in Ref. [19], where both J 1 and J 2 are AFM, but J 3 can be either FM or AFM. This system shows two types of Haldane phases for the FM J 3 and, columnar dimer and rung singlet phases for the AFM J 3 . Normand et al. considered the similar coupled ladders with all three AFM J 1 , J 2 and J 3 interactions. They find dimerized chains for large J 2 and small J 3 limit, spiral long range order for both large J 2 and J 3 limit, Néel long range order in the small J 2 < 0.4 and for all J 3 [20]. Ronald et al. have shown the effect of inter-chain coupling on spiral ground state of J 1 − J 2 model [21]. The effect of inter-ladder coupling on spin gap and magnon dispersion has been discussed in [22] exploiting a theoretical model which has also been

Quantum phase diagram of a frustrated spin- 12 system on a trellis ladder

“…The details of this phase have been discussed already in the ref. [34]. At higher J 3 value, even for J 2 < 0.25, NC phase emerges but with small amplitude and ξ in spin spin correlation.…”

“…Higher value of J 2 needs more strength in J 3 to keep the same correlation length in NC(SRO) phase. Surprisingly, this behavior is completely opposite in the case of CS(SRO) phase, where higher J 2 requires lower J 3 to sustain the same correlation length [34]. When ξ ≤ 1, dominant correlation strengths become confined within the three nearest neighbors among which the rung bond correlation is dominant over other two bond strengths.…”

“…The nature of ξ in CS(SRO) phase is discussed in ref. [34]. In NC(SRO) regime ξ are plotted as function of J 2 for J 3 = 0.5, 0.6, 0.7, 0.8, 0.9 in Fig.…”

“…Our main focus of this paper is to construct the quantum phase diagram (QPD) and also understand the effect of rung interaction J 3 on the various exotic phases of zigzag ladder [5]. We notice that in small J 2 /|J 1 | limit, gs has collinear striped (CS) SRO on each zigzag ladder; however, spins on one zigzag ladder are aligned antiferromagnetically with respect to the spins on the other zigzag ladder [34]. The NC spin order sets in for moderate value of J 2 .…”