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arXiv:1609.00198 · Physical Review Letters

Bound States and Field-Polarized Haldane Modes in a Quantum Spin Ladder

Simon Ward, Mattia Mena, Pierre Bouillot, Corinna Kollath, Thierry Giamarchi, Kai Phillip Schmidt, Bruce Normand, Karl W. Krämer, Daniel A. Biner, Robert Bewley, T. Guidi, Martin Boehm, MCMORROW Desmond Francis, Christian Rüegg

Published Apr 28, 2017• 22 citations
arXivHTMLPDF

Abstract

The challenge of one-dimensional systems is to understand their physics beyond the level of known elementary excitations. By high-resolution neutron spectroscopy in a quantum spin-ladder material, we probe the leading multiparticle excitation by characterizing the two-magnon bound state at zero field. By applying high magnetic fields, we create and select the singlet (longitudinal) and triplet (transverse) excitations of the fully spin-polarized ladder, which have not been observed previously and are close analogs of the modes anticipated in a polarized Haldane chain. Theoretical modeling of the dynamical response demonstrates our complete quantitative understanding of these states.

DOI
10.1103/physrevlett.118.177202

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The challenge of one-dimensional systems is to understand their physics beyond the level of known elementary excitations. By high-resolution neutron spectroscopy in a quantum spin-ladder material, we probe the leading multiparticle excitation by characterizing the two-magnon bound state at zero field. By applying high magnetic fields, we create and select the singlet (longitudinal) and triplet (transverse) excitations of the fully spin-polarized ladder, which have not been observed previously and are close analogs of the modes anticipated in a polarized Haldane chain. Theoretical modeling of the dynamical response demonstrates our complete quantitative understanding of these states.
Motivated by the recently observed intriguing mode splittings in a magnetic field with inelastic neutron scattering in the spin ladder compound (C_{5}H_{12}N)_{2}CuBr_{4} (BPCB), we investigate the nature of the spin ladder excitations using a density matrix renormalization group and analytical arguments. Starting from the fully frustrated ladder, for which we derive the low-energy spectrum, we show that bound states are generically present close to k=0 in the dynamical structure factor of spin ladders above H_{c1}, and that they are characterized by a field-independent binding energy and an intensity that grows with H-H_{c1}. These predictions are shown to explain quantitatively the split modes observed in BPCB.
This thesis describes the neutron scattering measurements of magnetic excitations in \nspin-chains and ladders. The first part discusses an experimental investigation of the copper oxide family Srâ â Cuâ â Oâ â composed of edge-sharing chains and spin-ladders. \nThe study of Laâ Srâ â Cuâ â Oâ â comprises a slightly hole-doped chain and an undoped ladder structure where the chain can be modeled by a ferromagnetic nearest and an \nantiferromagnetic next-nearest neighbor coupling. The hole effects are apparent in gaps in the dispersion relation and can be described by a charge-density wave agreeing with the commensuration of the dispersion. Investigating the undoped ladder establishes \nthe exchange constants including a cyclic exchange manifested by the two-magnon \ncontinuum and the suppression of the S = 1 bound mode. An orbital consideration \nprovides an explanation for the exchanges including the different sizes of rung and \nleg coupling. The excitation spectrum of the doped ladder in Caâ .â Srâ â .â Cuâ â Oâ â can be \ndescribed by a direct comparison with the undoped ladder and the differences consisting \nof a higher energy mode and subgap scattering can be successfully modeled by the charge spectrum of the ladder calculated from the free electron model. The second part of the thesis investigates the alternating chain material Cu(NOâ )â · 2.5D2O and establishes the gapped one-magnon dispersion, the two-magnon continuum and for the first time the S =1 bound mode. Applying magnetic field drives the system through two critical field transitions, condensation of magnons into the ground state and saturation. The modes beyond saturation can be modeled by spin wave theory and the excitations at the first critical field follow Luttinger Liquid behavior. Additionally investigated are the temperature effects with the excitations being of a different nature but containing the signature of a strong correlated system. For an outlook the measurements including temperature and field are provided with further theoretical descriptions necessary.
Supersymmetry is an algebraic property of a quantum Hamiltonian that, by giving every boson a fermionic superpartner and vice versa, may underpin physics beyond the Standard Model. Fractional bosonic and fermionic quasiparticles are familiar in condensed matter, as in the spin and charge excitations of the ttt-JJJ model describing electron dynamics in one-dimensional materials, but this type of symmetry is almost unknown. However, the triplet excitations of a quantum spin ladder in an applied magnetic field provide a supersymmetric analogue of the ttt-JJJ chain. Here we perform neutron spectroscopy on the spin-ladder compounds (C5_55​D12_{12}12​N)2_22​CuBr4_44​ and (C5_55​D12_{12}12​N)2_22​CuCl4_44​ over a range of applied fields and temperatures, and apply matrix-product-state methods to the ladder and equivalent chain models. From the momentum-resolved dynamics of a single charge-like excitation in a bath of fractional spins, we find essential differences in thermal broadening between the supersymmetric and non-supersymmetric sectors. The persistence of a strict zone-centre pole at all temperatures constitutes an observable consequence of supersymmetry that marks the beginning of supersymmetric studies in experimental condensed matter.
Inelastic neutron scattering experiments on the S=1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9D24N4)(NO2)ClO4 have been performed under magnetic fields below and above a critical field Hc at which the energy gap closes. Normal field dependece of Zeeman splitting of the excited triplet modes below Hc has been observed, but the highest mode is unusually small and smears out with increasing field. This can be explained by an interaction with a low-lying two magnon continuum at q=pi that is present in dimerized chains but absent in uniform ones. Above Hc, we find only one excited mode, in stark contrast with three massive excitations previously observed in the structurally similar Haldane-gap material NDMAP [A. Zheludev et al., Phys. Rev. B 68, 134438 (2003)].
The excitation spectrum of the two-chain Heisenberg ladder with antiferromagnetic interactions is studied. Our approach is based on the description of the excitations as triplets above a strong-coupling singlet ground state. The quasiparticle spectrum is calculated by treating the excitations as a dilute Bose gas with infinite on-site repulsion. Additional singlet ( S=0S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0S=0) and triplet ( S=1S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1S=1) excitations are found as quasiparticle bound states. Thus it is demonstrated that the spectrum consists of one elementary triplet, one composite triplet, and one composite singlet.