Strong-coupling approach to the magnetization process of polymerized quantum spin chains

Abstract

Polymerized quantum spin chains (i.e. spin chains with a periodic modulation of the coupling constants) exhibit plateaux in their magnetization curves when subjected to homogeneous external magnetic fields. We argue that the strong-coupling limit yields a simple but general explanation for the appearance of plateaux as well as of the associated quantization condition on the magnetization. We then proceed to explicitly compute series for the plateau boundaries of trimerized and quadrumerized spin-1/2 chains. The picture is completed by a discussion how the universality classes associated to the transitions at the boundaries of magnetization plateaux arise in many cases from a first order strong-coupling effective Hamiltonian.PACS numbers: 75.10. Jm, 75.40.Cx, 75.45.+j, 75.60.Ej Quantum spin systems at low (or zero) temperatures can exhibit plateaux in their magnetization curves when subjected to strong external fields. Such phenomena in quasi-one-dimensional systems have recently been the subject of intense interest. In one dimension, there is an intriguing interplay between theoretical progress on a systematic understanding of the underlying mechanisms (see e.g. [1]) and an increasing number of experiments (see e.g. [2,3]) on materials which are believed to be predominantly one-dimensional.Here we study polymerized spin-S quantum spin chains in a magnetic field. Their Hamiltonian is given bywhere we assume periodicity of the coupling constants with period p, i.e.We will mostly concentrate on spin S = 1/2 and the antiferromagnetic regime J x ≥ 0. The zero-temperature magnetization process of the S = 1/2 polymerized chains (1) was studied in [4] using finite-size diagonalization and a perturbative bosonization analysis around the case of equal coupling constants J x = J (apart from this and the dimerized case, only some trimerized [5,6] and quadrumerized [7] cases seem to have been studied in the literature). Here we wish to complete the picture by discussing the 'strong-coupling' limit where at least one coupling constant is small with respect to the others, i.e. J x0 → 0. As is known e.g. from studies of spin-ladders [8,9], the magnetization process is easy to understand if some J x0 = 0. In this limit, the chain (1) decouples into clusters of p spins. These 'strongly coupled' clusters magnetize independently such that at zero temperature the magnetization M can only take finitely many values. For spin S they are subject to the quantization conditionwith a normalization such that the magnetization has saturation values M = ±1. This quantization condition was obtained (for S = 1/2) in [4] and is a special case of a more general condition written down in [9]. In particular the latter was also motivated by considering a limit in which the system decouples into clusters of finitely many spins. In fact, this counting argument is completely independent of the internal coupling inside the cluster of the p spins. The quantization condition (3) is therefore insensitive to details of the model. However, not only the tr...

Magnetic properties of theS 1/2 distorted diamond chain atT 0

“…Since the Hamiltonian has the trimer nature, as is shown in figure 6, the mechanism for the M = M s /3 plateau is just the same as that for the trimerized chain ( Figure 7) investigated by Okamoto and Kitazawa [22] and by Honecker [23]. Here we explain the mechanism for the M = M s /3 plateau of the S = 1/2 trimerized chain.…”

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…”

Massive and Massless Behavior in Dimerized Spin Ladders

“…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.…”

“…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].…”