Magnetic Phase Diagram of theS=1/2 Antiferromagnetic Zigzag Spin Chain in the Strongly Frustrated Region: Cusp and Plateau

Abstract

We determine the magnetic phase diagram of the S = 1/2 antiferromagnetic zigzag spin chain in the strongly frustrated region, using the density matrix renormalization group method. We find the magnetization plateau at 1/3 of the full moment accompanying the spontaneous symmetry breaking of the translation, the cusp singularities above and/or below the plateau, and the even-odd effect in the magnetization curve. We also discuss the formation mechanisms of the plateau and cusps briefly.KEYWORDS: frustration, cusp, 1/3 plateau, even-odd effect For the purpose of clarifying the role of the frustration in low-dimensional quantum spin systems, the S = 1/2 antiferromagnetic zigzag spin chain has been attracting considerable attention, since it minimally contains the frustrating interaction without loss of the translational invariance.1-4) The Hamiltonian of the model is given bywhere S is the S = 1/2 spin operator, H is the magnetic field, and J 1 and J 2 denote the nearest and next nearest neighbor couplings, respectively. We introduce the notation α = J 2 /J 1 for simplicity. Recently, the zigzag chain was realized as SrCuO 2 , 5) Cu(ampy)Br 2 , 6)(N 2 H 5 )CuCl 3 7) and F 2 PIMNH. 8)The Hamiltonian (1) has a very simple form, but captures a variety of behaviors induced by the frustration. In particular, the zigzag chain in a magnetic field has been studied actively [9][10][11][12][13] and it has been clarified that cusp singularities appear near the saturation field and/or in the low field region for α ≤ 0.6, in accordance with the frustration-driven shape change of the dispersion curve of the elementary excitations.12-14) However, the magnetic phase diagram including the strongly frustrated region (α > 0.6) has not been acquired yet. Here we remark that the magnetization curve of α = 0.6 is still quite different from the one in the α → ∞ limit (see Fig.2 (a)). Thus, as α is increased beyond α = 0.6, the intrinsic structural change of the magnetization curve can be expected particularly around α ≃ 1, where the most significant competition is achieved.In this paper we address the magnetization process of the zigzag chain in the strongly frustrated region(α > 0.6), using the density matrix renormalization group (DMRG) method.15) We then find that the obtained phase diagram exhibits rich physics, as is shown in Fig.1. For 0.56 < ∼ α < ∼ 1.25, the magnetization plateau appears at 1/3 of the full moment, accompanying the spontaneous breaking of the translational symmetry with the period three. Moreover, the cusp singularities in the magnetization curve show quite interesting behavior; as α is increased, the high field cusp merges into the 1/3 plateau at α ≃ 0.82. Also the low field cusp merges the 1/3 plateau at α ≃ 0.7, but it appears again when α > 0.7. In addition, we find an interesting even-odd effect in the magnetization curve for α > 0.7. In analyzing the phase diagram, an important feature of the zigzag chain is that the Hamiltonian (1) interpolates between the single Heisenberg chain(J 2 = 0) and the double Hei...

Vector chiral order in frustrated spin chains

“…The boundaries of the low-field piece of the chiral phase coincide with the low-field TL2 region of Ref. 13. Surprisingly, this is not the case for the high-field piece: While its lower boundary reasonably agrees with the transition from even-odd phase to TL2, its upper boundary lies at a finite M = M c Ӎ 0.75 and not at M = 1, as one expects from the theoretical analysis.…”

“…In such a state, the system approximately decouples into a gapped antisymmetric sector and a gapless symmetric sector, the latter being described by the Tomonaga-Luttinger liquid ͑TLL͒. An alternative two-component TLL scenario [11][12][13] assumes the existence of the Tomonaga-Luttinger liquid in both sectors and implies the absence of the chiral order.…”

Vector chiral and multipolar orders in the spin-12frustrated ferromagnetic chain in magnetic field

“…(34) and (35) coincide with Eqs. (25) and (26) by using the relation (30) and setting the exponent η = K + . That is, the two theoretical approaches, the weak-coupling bosonization theory 7 for |J 1 | ≪ J 2 and the phenomenological hard-core boson theory 6 for 1 2 − M ≪ 1, give a consistent description of the nematic and SDW 2 phases.…”

Phase diagram of hard-core bosons on a zigzag ladder

“…In particular, the one-dimensional chain with SU(2) symmetry (i.e., V = 2|t|) but different nearest-(J 1 ) and next-nearest-neighbor (J 2 ) interactions has been widely discussed, also in presence of a finite magnetic field. [14][15][16] On the other hand, here we are interested in the case with positive hopping parameters and V > 2t, in order to describe strongly interacting bosons in low-dimensional systems that are relevant for atomic gases trapped in optical lattices. However, we will show that some features of the phase diagram do not depend upon the sign of t and can be understood on the basis of the strong-coupling (classical) limit V /t → ∞.…”