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arXiv:0712.3050 · Physical Review B

Vector chiral order in frustrated spin chains

Ian P. McCulloch, R. Kube, M. Kurz, Adrian Kleine, U. Schollwöck, Alexei K. Kolezhuk

Published Mar 6, 2008• 54 citations
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Abstract

By means of a numerical analysis using a non-Abelian symmetry realization of the density matrix renormalization group, we study the behavior of vector chirality correlations in isotropic frustrated chains of spin $S=1$ and $S=1∕2$, subject to a strong external magnetic field. It is shown that the field induces a phase with spontaneously broken chiral symmetry, in line with earlier theoretical predictions. We present results on the field dependence of the order parameter and the critical exponents.

DOI
10.1103/physrevb.77.094404

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By means of a numerical analysis using a non-Abelian symmetry realization of the density matrix renormalization group, we study the behavior of vector chirality correlations in isotropic frustrated chains of spin S=1S=1S=1 and S=1∕2S=1∕2S=1∕2, subject to a strong external magnetic field. It is shown that the field induces a phase with spontaneously broken chiral symmetry, in line with earlier theoretical predictions. We present results on the field dependence of the order parameter and the critical exponents.
The frustrated isotropic J1−J2J_1-J_2J1​−J2​ model with ferromagnetic J1J_1J1​ and anti-ferromagnetic J2J_2J2​ interactions in presence of an axial magnetic field shows many exotic phases, such as vector chiral and multipolar phases. The existing studies of the phase boundaries of these systems are based on the indirect evidences such as correlation functions {\it etc}. In this paper, the phase boundaries of these exotic phases are calculated based on order parameters and jumps in the magnetization. In the strong magnetic field, Z2Z_2Z2​ symmetry is broken, therefore, order parameter of the vector chiral phase is calculated using the broken symmetry states. Our results obtained using the modified density matrix renormalization group and exact diagonalization methods, suggest that the vector chiral phase exist only in narrow range of parameter space J2/J1J_2/J_1J2​/J1​.
We calculate the vector spin chirality for S=1/2S=1/2S=1/2 zigzag spin chains having U(1) symmetry, using the density matrix renormalization group combined with unitary transformation. We then demonstrate the occurrence of the chiral order for the zigzag XY chain and discuss the associated phase transition. The results are consistent with the analysis based on the bosonization and the long distance behaviour of the chirality correlation function. For the S=1/2S=1/2S=1/2 zigzag Heisenberg chain in a magnetic field, we also verify the chiral order that is predicted by the effective field theory and the chirality correlation function, and then determine its magnetic phase diagram.
We study the one-dimensional spin-1/2 Heisenberg chain with competing ferromagnetic nearest-neighbor J_1 and antiferromagnetic next-nearest-neighbor J_2 exchange couplings in the presence of magnetic field. We use both numerical approaches (the density matrix renormalization group method and exact diagonalization) and effective field-theory approach, and obtain the ground-state phase diagram for wide parameter range of the coupling ratio J_1/J_2. The phase diagram is rich and has a variety of phases, including the vector chiral phase, the nematic phase, and other multipolar phases. In the vector chiral phase, which appears in relatively weak magnetic field, the ground state exhibits long-range order (LRO) of vector chirality which spontaneously breaks a parity symmetry. The nematic phase shows a quasi-LRO of antiferro-nematic spin correlation, and arises as a result of formation of two-magnon bound states in high magnetic fields. Similarly, the higher multipolar phases, such as triatic (p=3) and quartic (p=4) phases, are formed through binding of p magnons near the saturation fields, showing quasi-LRO of antiferro-multipolar spin correlations. The multipolar phases cross over to spin density wave phases as the magnetic field is decreased, before encountering a phase transition to the vector chiral phase at a lower field. The implications of our results to quasi-one-dimensional frustrated magnets (e.g., LiCuVO_4) are discussed.
Ordering of frustrated S=1/2 and 1 XY and Heisenberg spin chains with the competing nearest- and next-nearest-neighbor antiferromagnetic couplings is studied by exact diagonalization and density-matrix renormalization-group methods. It is found that the S=1 XY chain exhibits both gapless and gapped `chiral' phases characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, κi=SixSi+1y−SiySi+1xκ_i = S_i^xS_{i+1}^y-S_i^yS_{i+1}^xκi​=Six​Si+1y​−Siy​Si+1x​, whereas the spin correlation decays either algebraically or exponentially. Such chiral phases are not realized in the S=1/2 XY chain nor in the Heisenberg chains.