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arXiv:1211.1676 · Physical Review B

Ground states of spin- 1 2 triangular antiferromagnets in a magnetic field

Ru Chen, Hyejin Ju, Hong‐Chen Jiang, Oleg A. Starykh, Leon Balents

Published Apr 17, 2013• 60 citations
arXivHTMLPDF

Abstract

We use a combination of numerical density matrix renormalization group calculations and several analytical approaches to comprehensively study a simplified model for a spatially anisotropic spin-$\frac{1}{2}$ triangular lattice Heisenberg antiferromagnet: the three-leg triangular spin tube (TST). The model is described by three Heisenberg chains, with exchange constant $J$, coupled antiferromagnetically with exchange constant ${J}^{\ensuremath{'}}$ along the diagonals of the ladder system, with periodic boundary conditions in the shorter direction. Here, we determine the full phase diagram of this model as a function of both spatial anisotropy (between the isotropic and decoupled chain limits) and magnetic field. We find a rich phase diagram, which is remarkably dominated by quantum states: the phase corresponding to the classical ground state appears only in an exceedingly small region. Among the dominant phases generated by quantum effects are commensurate and incommensurate coplanar quasiordered states, which appear in the vicinity of the isotropic region for most fields, and in the high-field region for most anisotropies. The coplanar states, while not classical ground states, can at least be understood semiclassically. Even more strikingly, the largest region of phase space is occupied by a spin density wave phase, which has incommensurate collinear correlations along the field. This phase has no semiclassical analog, and may be ascribed to enhanced one-dimensional fluctuations due to frustration. Cutting across the phase diagram is a magnetization plateau, with a gap to all excitations and ``up-up-down'' spin order, with a quantized magnetization equal to $\frac{1}{3}$ of the saturation value. In the TST, this plateau extends almost but not quite to the decoupled chains limit. Most of the above features are expected to carry over to the two-dimensional system, which we also discuss. At low field, a dimerized phase appears, which is particular to the one-dimensional nature of the TST, and which can be understood from quantum Berry phase arguments.

DOI
10.1103/physrevb.87.165123

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We study the ground-state phase diagram of a frustrated spin-1/2 four-leg tube. Using a variety of complementary techniques, namely, density matrix renormalization group, exact diagonalization, Schwinger boson mean-field theory, quantum Monte Carlo, and series expansion, we explore the parameter space of this model in the regime of all-antiferromagnetic exchange. In contrast to unfrustrated four-leg tubes, we uncover a rich phase diagram. Apart from the Luttinger liquid fixed point in the limit of decoupled legs, this comprises several gapped ground states, namely, a plaquette, an incommensurate, and an antiferromagnetic quasispin-2 chain phase. The transitions between these phases are analyzed in terms of total energy and static structure factor calculations and are found to be of (weak) first order. Despite the absence of long-range order in the quantum case, remarkable similarities to the classical phase diagram are uncovered, with the exception of the icommensurate regime, which is strongly renormalized by quantum fluctuations. In the limit of large leg exchange, the tube exhibits a deconfinement crossover from gapped magnon-like excitations to spinons.
We study the ground state phase diagram of the twisted three-leg spin tube in magnetic fields by the density matrix renormalization group (DMRG) method. The twisted spin tube is composed of triangular unit cells and possesses strong quantum fluctuations under geometrical frustration. We apply the sine square deformation method to remove the strong boundary effects and obtain smooth magnetization curves without steps of finite systems. With the analysis of the magnetization curves and correlation functions we determine the ground state phase diagram consisting of (a) a Tomonaga-Luttinger (TL) liquid characterized by spin-32\frac{3}{2}23​ Heisenberg model, (b) 3-sublattice state named UUD with 1/3 magnetization and (c) TL-liquid of massless chirality with 1/3 magnetization plateau, (d) TL-liquid of massless spin mode with or without chirality quasi long-range order.
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