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arXiv:0806.0694 · Physical Review B

Two-particle bound states and one-particle structure factor in a Heisenberg bilayer system

A. Collins, Chris J. Hamer

Published Aug 14, 2008• 15 citations
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Abstract

The $S=1/2$ Heisenberg bilayer spin model at zero temperature is studied in the dimerized phase using analytic triplet-wave expansions and dimer series expansions. The occurrence of two-triplon bound states in the $S=0$ and $S=1$ channels, and antibound states in the $S=2$ channel, is predicted by the triplet-wave theory and confirmed by series expansions. All bound states are found to vanish at or before the critical coupling separating the dimerized phase from the N\'eel phase. The critical behavior of the total and single-particle static transverse structure factors is also studied by series and found to conform with theoretical expectations. The single-particle state dominates the structure factor at all couplings.

DOI
10.1103/physrevb.78.054419

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The S=1/2S=1/2S=1/2 Heisenberg bilayer spin model at zero temperature is studied in the dimerized phase using analytic triplet-wave expansions and dimer series expansions. The occurrence of two-triplon bound states in the S=0S=0S=0 and S=1S=1S=1 channels, and antibound states in the S=2S=2S=2 channel, is predicted by the triplet-wave theory and confirmed by series expansions. All bound states are found to vanish at or before the critical coupling separating the dimerized phase from the N'eel phase. The critical behavior of the total and single-particle static transverse structure factors is also studied by series and found to conform with theoretical expectations. The single-particle state dominates the structure factor at all couplings.
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Series expansion studies of the J1J_1J1​-J2J_2J2​-Heisenberg bilayer
We study a bilayer of the frustrated J1J_1J1​-J2J_2J2​ Heisenberg-model on the square lattice. Starting from the dimer limit at strong interlayer coupling, we perform series expansions using the perturbative Continuous Unitary Transformation, based on the flow equation method, in order to determine the spectrum up to the two-triplon sector. From the one-triplon dispersion we obtain quantum critical lines for transitions from the dimer phase into either Néel or collinear magnetic order. For low to intermediate frustration these transitions are consistent with existing findings, based on the magnetic phases. In the region of strongest frustration, i.e. J2/J1∼0.5J_2/J_1\sim 0.5J2​/J1​∼0.5, we provide an estimate for the stability of the anticipated single-layer quantum spin-liquids against finite interlayer coupling. In the two-triplon sector we find a set of well defined (anti)bound states, which can be classified according to total spin and in-plane rotational symmetry. For vanishing frustration these states agree with previous series expansion analysis. For J2/J1≳0.5J_2/J_1\gtrsim 0.5J2​/J1​≳0.5 we provide evidence for a close-by condensation of one-triplon and two-triplon singlet bound states, suggesting that between the dimer and the collinear state, additional phases may intervene.
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We study the spectrum of a bilayer of Kitaev magnets on the honeycomb lattice, coupled by Heisenberg exchange in the quantum-dimer phase at strong interlayer coupling. Using the perturbative continuous unitary transformation we perform series expansion starting from the fully dimerized limit, to evaluate the elementary excitations, reaching up to and focusing on the two-triplon sector. In stark contrast to conventional bilayer quantum magnets, and because of the broken SU(2)SU(2)SU(2) invariance, encoded in the intralayer directional compass exchange, the bilayer Kitaev magnet is shown to exhibit a rich structure of two-triplon scattering-state continua, as well as several collective two-triplon (anti)bound states. Direct physical pictures for the occurrence of the latter are provided and the (anti)bound states are studied versus the stacking type, the spin components, and the exchange parameters. In addition to the two-triplon spectra, we investigate a corresponding experimental probe by evaluating the magnetic Raman-scattering intensity. We find a very strong sensitivity of this intensity on the two-triplon interactions and the scattering geometry, however, a signal from the (anti)bound states appears only in very close proximity to the continuum.
The two-layer Heisenberg antiferromagnet exhibits a zero temperature quantum phase transition from a disordered dimer phase to a collinear Neel phase, with long range order in the ground state. The spin-wave gap vanishes as ? ? ( J ? – J ? c ) &ngr; approaching the transition point. To account for strong correlations, the S = 1 elementary excitations triplets are described as a dilute Bose gas with infinite on-site repulsion. We apply the Brueckner diagram approach which gives the critical index &ngr; ˜ 0 . 5. We demonstrate also that the linearised in density Brueckner equations give the mean field result &ngr; = 1. Finally, an expansion of the Brueckner equations in powers of the density, combined with the scaling hypothesis, gives &ngr; ˜ 0 . 67. This value agrees reasonably with that of the nonlinear O(3) s model. Our approach demonstrates that for other quantum spin models the critical index can be different from that in the nonlinear s model. We discuss the conditions for this to occur.
Motivated by experiments on nonmagnetic triangular-lattice Mott insulators, we study one candidate paramagnetic phase, namely the columnar dimer (or valence-bond) phase. We apply variants of the bond-operator theory to a dimerized and spatially anisotropic spin-1/2 Heisenberg model and determine its zero-temperature phase diagram and the spectrum of elementary triplet excitations (triplons). Depending on model parameters, we find that the minimum of the triplon energy is located at either a commensurate or an incommensurate wave vector. Condensation of triplons at this commensurate-incommensurate transition defines a quantum Lifshitz point, with effective dimensional reduction that possibly leads to nontrivial paramagnetic (e.g., spin-liquid) states near the closing of the triplet gap. We also discuss the two-particle decay of high-energy triplons, and we comment on the relevance of our results for the organic Mott insulator EtMe3{}_{3}3​P[Pd(dmit)2{}_{2}2​]2{}_{2}2​.