Massive and Massless Behavior in Dimerized Spin Ladders

Abstract

We investigate the conditions under which a gap vanishes in the spectrum of dimerized coupled spin-1/2 chains by means of Abelian bosonization and Lanczos diagonalization techniques. Although both interchain (J ′ ) and dimerization (δ) couplings favor a gapful phase, it is shown that a suitable choice of these interactions yields massless spin excitations. We also discuss the influence of different arrays of relative dimerization on the appearance of non-trivial magnetization plateaus.PACS numbers: 75.10. Jm, 75.60.Ej Published in Phys. Rev. Lett. 82, 1768(1999.Current developments in the field of spin ladders have revealed intriguing features of low-dimensional quantum antiferromagnets (AF) [1]. The appearance of plateaus in the magnetization curves of these systems has received much attention from both the theoretical and experimental side [2]. A necessary quantization condition for the appearance of such plateaus in generic ladders was derived in [2] (see also [3] for the case of 1D chains and [4][5][6][7] for other particular cases). In a very recent paper [8], an unexpected phenomenon has been observed in the magnetization curves of NH 4 CuCl 3 at high magnetic fields. The crystal structure of this material at room temperatures is known to be composed of double chains (2-leg ladders), with three different nearest neighbor interactions. Thus, from previous theoretical studies of such arrange of couplings in ladders systems, plateaus at M = 0 and 1/2 are expected to be visible at sufficiently low temperature. However, measurements performed in [8] at very low temperatures, clearly show two net plateaus at 1/4 and 3/4, while no plateaus are observed at the theoretically expected values M = 0 and 1/2.As a first step to reconcile some of these facts with the current understanding of ladder materials, in this work we study two important issues namely, (i) the possibility of closing the gap in a two-leg dimerized ladder by a combined effect of the dimerization and the interchain coupling and, (ii) the emergence of a plateau at M = 1/2 depending on the realization of the relative dimerization (see Figs. 1(a)-(b)). Though (i) was studied on a qualitative level using non-linear sigma model techniques [9], here we present a quantitative and more systematic treatment, whereas (ii) is analyzed for the first time in this work. These two issues could shed light in the study of the experimental measurements such as those performed in [8] as well as in related aspects of CuGeO chain compounds [10], in which dimerization becomes staggered between weakly coupled chains.As is well known, the isotropic spin-1/2 Heisenberg chain is already in a critical state. Thus any relevant perturbation, such as the Peierls dimerization instability [11] or a weak interchain coupling [12], [13], can drastically alter the nature of the ground state, whereas a massive spin gap excitation appears simultaneously in the energy spectrum. Interestingly, it was suggested that a combined effect could lead to a massless regime [9].In the present work ...

Ising model description of the SU(2)1 quantum critical point in a dimerized two-leg spin-1/2 ladder

“…At J ⊥ = 0 the model (58) is known as the spin-orbital chain [29] and has been recently studied by different groups (see e.g. [30,8,31]). If J ⊥ = 0 but |V | is large enough, the model (58) occurs in a non-Haldane, spontaneously dimerized phase where the spectrum is entirely incoherent and consists of pairs of topological kinks [13].…”

“…[5]), are excellent candidates for such a scenario. A nice example of this kind has been recently given by Martin-Delgado et al [6,7] (see also [8]) who considered the standard J-J ⊥ two-leg spin ladder (J, J ⊥ > 0)…”

“…The so far existing conclusion on the existence of the c = 1 critical point in the S=1/2 staggered ladder [6] and in the related model of the explicitly dimerized S=1 chain [14,15] was reached either by mapping onto an O(3) nonlinear sigma model which, strictly speaking, is valid for large S only, or using a perturbative (renormalization group) approach combined with numerical methods. In other cases [8], the c = 1 criticality of the dimerized ladder (1) was analyzed by the Abelian bosonization in the way suitable only for the XXZ-version of the model but not for the SU(2) symmetric case where the explicit dimerization field is the most relevant perturbation in the problem. Treating our QI-chain model in the strong-coupling limit and applying a nonlocal duality transformation [16,17], below we derive the effective Hamiltonian describing the low-energy sector of the dimerized spin ladder which represents a lattice spin-1/2 Heisenberg model with bond-alternating nearest-neighbor interactions.…”

Quantum magnetization plateaux of an anisotropic ferrimagnetic spin chain

“…In addition some theoretical and/or numerical analyses predicted that a magnetization plateau appears in various other systems; the polymerized chains [13][14][15][16][17][18][19][20][21][22][23], the S = 3/2 chain [24][25][26][27], the frustrated spin ladder [28][29][30][31][32], several generalized spin ladders [33][34][35][36][37][38], distorted diamond type spin chain [39][40][41] and some layered sytems [42,43]. Using the Lieb-Schultz-Mattis theorem [44], a general necessary condition for the presence of the plateau was derived [24] as…”

Plaquette order in a dimerized frustrated spin ladder

“…A number of theoretical studies have also considered the effect of an explicit dimerization term on the Heisenberg spin-ladder without frustrating (diagonal) interactions [20][21][22][23][24][25][26] . Interestingly, these works found that although a dimerization term opens a gap when added to a gapless spin-chain, adding such a term to a gapped spin ladder can lead to a gapless phase for suitably tuned dimerization and exchange couplings.…”