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arXiv:1104.4570 · Journal of Physics Condensed Matter

Effects of a space modulation on the behavior of a 1D alternating Heisenberg spin-1/2 model

S. Mahdavifar, Jahanfar Abouie

Published May 26, 2011• 10 citations
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Abstract

The effects of a magnetic field (h) and a space modulation (δ) on the magnetic properties of a one-dimensional antiferromagnetic-ferromagnetic Heisenberg spin-1/2 model have been studied by means of numerical exact diagonalization of finite size systems, the nonlinear σ model, and a bosonization approach. The space modulation is considered on the antiferromagnetic couplings. At δ = 0, the model is mapped to a gapless Lüttinger liquid phase by increasing the magnetic field. However, the space modulation induces a new gap in the spectrum of the system and the system experiences different quantum phases which are separated by four critical fields. By opening the new gap, a magnetization plateau appears at ½M(sat). The effects of the space modulation are reflected in the emergence of a plateau in other physical functions such as the F-dimer and the bond-dimer order parameters, and the pair-wise entanglement.

DOI
10.1088/0953-8984/23/24/246002

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The effects of a magnetic field (h) and a space modulation (δ) on the magnetic properties of a one-dimensional antiferromagnetic-ferromagnetic Heisenberg spin-1/2 model have been studied by means of numerical exact diagonalization of finite size systems, the nonlinear σ model, and a bosonization approach. The space modulation is considered on the antiferromagnetic couplings. At δ = 0, the model is mapped to a gapless Lüttinger liquid phase by increasing the magnetic field. However, the space modulation induces a new gap in the spectrum of the system and the system experiences different quantum phases which are separated by four critical fields. By opening the new gap, a magnetization plateau appears at ½M(sat). The effects of the space modulation are reflected in the emergence of a plateau in other physical functions such as the F-dimer and the bond-dimer order parameters, and the pair-wise entanglement.
The effects of a magnetic field (h) and a space modu-lation (δ) on the magnetic properties of a one dimensional antiferromagnetic-ferromagnetic Heisenberg spin-1/2 model have been studied by means of numerical exact diagonal-ization of finite size systems, nonlinear sigma model and bosonization approach. The space modulation is considered on the antiferromagnetic couplings. At δ = 0, the model is mapped to a gapless Lüttinger liquid phase by increasing the magnetic field. However, the space modulation induces a new gap in the spectrum of the system and the system ex-periences different quantum phases which are separated by four critical fields. By opening the new gap a magnetization plateau appears at 12Msat. The effects of the space modu-lation are reflected in the emergence of a plateau in other physical functions such as the F-dimer and the bond dimer order parameters, and the pair-wise entanglement. PACS numbers: 75.10.Jm, 75.10.Pq ‡ The authors have the same contributions in the work. ar
We consider the spin-1/2 Heisenberg chain with alternating spin exchange in the presence of additional modulation of exchange on odd bonds with period 3. We study the ground state magnetic phase diagram of this hexamer spin chain in the limit of very strong antiferromagnetic (AF) exchange on odd bonds using the numerical Lanczos method and bosonization approach. In the limit of strong magnetic field commensurate with the dominating AF exchange, the model is mapped onto an effective XXZ Heisenberg chain in the presence of uniform and spatially modulated fields, which is studied using the standard continuum-limit bosonization approach. In the absence of additional hexamer modulation, the model undergoes a quantum phase transition from a gapped phase into the only one gapless Lüttinger liquid (LL) phase by increasing the magnetic field. In the presence of hexamer modulation, two new gapped phases are identified in the ground state at magnetization equal to [Formula: see text] and [Formula: see text] of the saturation value. These phases reveal themselves also in the magnetization curve as plateaus at corresponding values of magnetization. As a result, the magnetic phase diagram of the hexamer chain shows seven different quantum phases, four gapped and three gapless, and the system is characterized by six critical fields which mark quantum phase transitions between the ordered gapped and the LL gapless phases.
We consider the ground-state phase diagram of a one-dimensional spin-1/2 XXZ chain with a spatially modulated Dzyaloshinskii-Moriya interaction in the presence of an alternating magnetic field applied along the z[over ̂] axis. The model is studied using the continuum-limit bosonization approach and the finite system exact numerical technique. In the absence of a magnetic field, the ground-state phase diagram of the model includes, besides the ferromagnetic and gapless Luttinger-liquid phases, two gapped phases: the composite (C1) phase characterized by the coexistence of long-range-ordered (LRO) alternating dimerization and spin chirality patterns, and the composite (C2) phase characterized by, in addition to the coexisting spin dimerization and alternating chirality patterns, the presence of LRO antiferromagnetic order. In the case of mentioned composite gapped phases, and in the case of a uniform magnetic field, the commensurate-incommensurate type quantum phase transitions from a gapful phase into a gapless phase have been identified and described using the bosonization treatment and finite chain exact diagonalization studies. The upper critical magnetic field corresponding to the transition into a fully polarized state has been also determined. It has been shown that the very presence of a staggered component of the magnetic field vapes the composite (C1) in favor of the composite gapped (C2) phase.
The S =1/2 bond alternating Heisenberg spin chain in a magnetic field is studied by the numerical diagonalization and the finite size scaling based on the conformal field theory. It is found that the magnetic state (0< m <1) is gapless (the central charge c =1) and described by the Luttinger liquid, which corresponds to a spinless Fermion system with repulsive interaction for antiferromagnetic-antiferromagnetic alternating chains, but attractive one for ferromagnetic-antiferromagnetic chains. The critical exponents δ and η are determined at the critical fields. The results suggest that the phase transitions belong to the same universality class as the S =1 antiferromagnetic chain for both alternating cases.
One dimensional S =1 antiferromagnetic Heisenberg chains with bond alternation and uniaxial single-ion-type anisotropy are studied by numerical exact diagonalization of finite size systems. We calculate the ground state phase diagram using the twisted boundary condition method for D ≥0. The ground states of this model contain the Haldane state, large- D state and the dimer state. Using conformal field theory and the level spectroscopy method, we calculate the D and δ-dependence of the Luttinger liquid paraments K and the critical exponent ν of the energy gap.
We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (J1FJ_1^FJ1F​) and antiferromagnetic (J1AJ_1^AJ1A​) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction (J2FJ_2^FJ2F​). In this model frustration is induced by the non-zero J2FJ_2^FJ2F​ and the effect of dimerization is realized by changing the strength of J1AJ_1^AJ1A​ for a fixed value of J1FJ_1^FJ1F​. The model with site spin sss behaves like a Haldane spin chain with site spin 2sss in the limit of vanishing J2FJ_2^FJ2F​ and large J1F/J1AJ_1^F/J_1^AJ1F​/J1A​. We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of J1A−J2FJ_1^A-J_2^FJ1A​−J2F​ is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.