Middle-field cusp singularities in the magnetization process of one-dimensional quantum antiferromagnets

Abstract

We study the zero-temperature magnetization process (M −H curve) of one-dimensional quantum antiferromagnets using a variant of the density-matrix renormalization group method. For both the S = 1/2 zig-zag spin ladder and the S = 1 bilinear-biquadratic chain, we find clear cusp-type singularities in the middle-field region of the M − H curve. These singularities are successfully explained in terms of the double-minimum shape of the energy dispersion of the low-lying excitations. For the S = 1/2 zig-zag spin ladder, we find that the cusp formation accompanies the Fermi-liquid to non-Fermi-liquid transition.PACS numbers: 75.10. Jm, 75.40.Cx, 75.30.Cr Low-dimensional antiferromagnetic (AF) quantum spin systems with various spin magnitude S and various spatial structures, have been a field of active researches, both experimentally and theoretically. In particular, the magnetization process (M − H curve, M : magnetization, H: magnetic field) of AF spin chain at low-temperatures have recently drawn much attention, because it exhibits various phase-transition-like behaviors: e.g., the critical phenomena ∆M ∼ √ H − H c associated with the gapped excitation (excitation gap ∝ H c ) [1][2][3] or with the saturated magnetization (at the saturation field H s ), [2][3][4][5][6][7] magnetization plateau, [8] and, the first-order transition.[9] These are field-induced phase transitions of the ground state, which reflect non-trivial energy-level structure at zero field.What we consider in this Letter is another type of singularity which has not been discussed so much: the cusp singularity at H = H cusp in the middle-field region (H c < H cusp < H s ). Existence this type of singularity was first demonstrated by Parkinson [10] for the integrable Uimin-Lai-Sutherland (or, SU(3)) chain, [11] and has also been known for some other integrable spin chains, [12][13][14][15] and ladders. [16,17] Derivation of the magnetization cusp for each model, however, relies on the model's integrability in an essential manner, restricting the Hamiltonian to be of somewhat unrealistic form. Hence, whether or not this type of singularity can be found in realistic systems is a highly non-trivial question. In the present Letter, we make the first systematic numerical study of the "middle-field cusp singularity" (MFCS, for short) in the zero-temperature M − H curve for non-integrable systems, through which we give a positive answer for the above question. Namely, we show that the S = 1/2 zig-zag spin ladder and the S = 1 bilinear-biquadratic chain actually exhibit MFCS in the M − H curve.The numerical method we employ is the productwavefunction renormalization group (PWFRG), [18] which is a variant of the density-matrix renormalization group (DMRG).[19] Efficiency of the PWFRG in calculation of the M − H curve has been demonstrated in previous studies; [3,20] the PWFRG will allow us to obtain the M − H curve in the thermodynamic limit with enough accuracy to detect "weak" (non-divergent) singularity like the MFCS.Consider the S = 1/2 zig-zag spin la...

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

“…However, in the bosonization theory the dimerization operator is proportional to cos( √ 8πφ − + πM ), whose average vanishes because of Eq. (24). We thus conclude that the nematic phase does not have a spontaneous dimerization.…”

“…It has been established that in zero magnetic field the ground state of the antiferromagnetic J 1 -J 2 spin chain undergoes a phase transition from a critical phase with gapless excitations for J 2 < J 2c = 0.2411J 1 to a gapped phase with spontaneous dimerization for J 2 > J 2c as J 2 increases. 17,18,19,20,21,22,23 It has also been revealed that the model exhibits cusp singularities and a 1/3-plateau in the magnetization curve 24,25 as well as a vector chiral order in the case of anisotropic exchange couplings 26,27,28 or under magnetic field. 29,30,31,32 In this paper we concentrate on the ferromagnetic case (J 1 < 0) of the J 1 -J 2 spin chain (1) in magnetic field which partially polarizes spins to the +z direction.…”

Vector chiral order in frustrated spin chains

“…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.…”

Lifshitz Transition Induced by Magnetic Field in Frustrated Two-Leg Spin-Ladder Systems

“…[16] In addition, this singularity has also been reported for other quantum spin systems: the zigzag spin chain and the frustrated Kondo necklace. [17][18][19][20] …”