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arXiv:1210.8199 · Physical Review B

Quantum phases of a frustrated four-leg spin tube

Marcelo Arlego, W. Brenig, Yousef Rahnavard, B. Willenberg, H. D. Rosales, G. L. Rossini

Published Jan 9, 2013• 9 citations
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Abstract

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.

DOI
10.1103/physrevb.87.014412

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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 a frustrated spin-1/2 four-leg tube in an external magnetic field. We explore the parameter space of this model in the regime of all-antiferromagnetic exchange couplings by means of three different approaches: density matrix renormalization group (DMRG), a low-energy effective Hamiltonian (LEH) and a Hartree variational approach (HVA). We find that in the limit of weakly interacting plaquettes, singlet and triplet states play an important role in the formation of magnetization plateaux. We study the transition regions numerically and analytically, and find that they are described, at first order in a strong- coupling expansion, by an XXZ spin-1/2 chain in a magnetic field. These results are consistent with the DMRG and HVA calculations.
We study the ground state phase diagram of a frustrated spin-1/2 four-leg spin tube in an external magnetic field. We explore the parameter space of this model in the regime of all-antiferromagnetic exchange couplings by means of three different approaches: analysis of low-energy effective Hamiltonian, a Hartree variational approach, and density matrix renormalization group for finite clusters. We find that in the limit of weakly interacting plaquettes, low-energy singlet, triplet, and quintuplet states play an important role in the formation of fractional magnetization plateaus. We study the transition regions numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an XXZXXZXXZ spin-1/2 chain in a magnetic field; the second-order terms give corrections to the XXZXXZXXZ model. All techniques provide consistent results which allow us to predict the existence of fractional plateaus in an important region in the space of parameters of the model.
We develop a real space quantum renormalization group (QRG) to explore a frustrated anisotropic four-leg spin-1/2 nanotube in the thermodynamic limit. We obtain the phase diagram, fixed points, critical points, the scaling of coupling constants and magnetization curves. Our investigation points out that, in the case of strong leg coupling, the diagonal frustrating interaction is marginal under QRG transformations and does not affect the universality class of the model. Remarkably, the renormalization equations express that the spin nanotube prepared in the strong leg coupling case goes to the strong plaquette coupling limit (weakly interacting plaquettes). Subsequently, in the limit of weakly interacting plaquettes, the model is mapped onto a 1D spin-1/2 XXZ chain in a longitudinal magnetic field under QRG transformation. Furthermore, the effective Hamiltonian of the spin nanotube inspires both first and second order phase transitions accompanied by the fractional magnetization plateaus. Our results show that the anisotropy changes the magnetization curve and the phase transition points, significantly. Finally, we report the numerical exact diagonalization results to compare the ground state phase diagram with our analytical visions.
We study the magnetism of a frustrated four-leg spin-1/21/21/2 ladder with transverse periodic boundary conditions: the frustrated four-spin tube (FFST). Using a combination of series expansion (SE), based on the continuous unitary transformation method and density-matrix renormalization group (DMRG) we analyze the ground-state, the one-, and the two-particle excitations in the regime of strong rung coupling. We find several marked differences of the FFST with respect to standard two-leg ladders. First, we show that frustration destabilizes the spin-gap phase of the FFST, which is adiabatically connected to the limit of decoupled rung singlets, leading to a first-order quantum phase transition at finite interrung coupling. Second, we show that apart from the well-known triplon branch of spin ladders, the FFST sustains additional elementary excitations, including a singlon and additional triplons. Finally, we find that in the two-particle sector, the FFST exhibits collective (anti)bound states similar to two-leg ladders, however, with a different ordering of the spin-quantum numbers. We show that frustration has significant impact on the FFST leading to a flattening of the ground-state energy landscape, a mass-enhancement of the excitations, and to a relative enhancement of the (anti)binding strength. Where possible, we use DMRG to benchmark the findings from our SE calculations, showing excellent agreement.
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-12\frac{1}{2}21​ triangular lattice Heisenberg antiferromagnet: the three-leg triangular spin tube (TST). The model is described by three Heisenberg chains, with exchange constant JJJ, 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 13\frac{1}{3}31​ 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.
The ground state, magnetization curves, low-temperature thermodynamics, and heat-engine performance of the fully frustrated spin-1/21/21/2 Heisenberg four-leg tube with antiferromagnetic inter- and intra-plaquette coupling constants J1 and J2 are examined using exact diagonalization, density matrix renormalization group, and localized-magnon theory. In the unfrustrated to weakly frustrated regime J2/J1 << 2, the system exhibits a continuous field-driven quantum phase transition between the gapped Haldane phase and a gapless Tomonaga-Luttinger quantum spin liquid. In the highly frustrated regime J2/J1 > 2, the system contrarily displays discontinuous field-driven quantum phase transitions between the Wigner magnon crystals, which are manifested in zero-temperature magnetization curves as intermediate plateaus at zero, one-quarter, one-half, and three-quarters of the saturation magnetization. The low-temperature magnetic and thermodynamic properties in this regime are accurately captured by an effective interacting lattice-gas model of two monomer quasi-particle species constructed from localized one- and two-magnon states. Finally, we explore a quantum Stirling heat engine using the fully frustrated four-leg tube as the working medium. The work output and efficiency are strongly suppressed near discontinuous field-induced transitions and reach pronounced local maxima well inside the stability regions of the Wigner magnon crystals.