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Emergent Ising degrees of freedom in frustrated two-leg ladder and bilayer s=12 Heisenberg antiferromagnets

Oleg Derzhko, Taras Krokhmalskii, and Johannes Richter
Phys. Rev. B 82, 214412 – Published 10 December 2010
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  • INTRODUCTION
  • MODEL
  • PRODUCT EIGENSTATES
  • DEGENERACY OF LOCALIZED-MAGNON STATES
  • LATTICE-GAS MODELS WITH NEAREST-NEIGHBOR…
  • LATTICE-GAS MODELS WITH FINITE REPULSION
  • CONCLUSIONS
  • ACKNOWLEDGEMENTS
  • APPENDICES
    • References

    Abstract

    Based on exact diagonalization data for finite quantum Heisenberg antiferromagnets on two frustrated lattices (two-leg ladder and bilayer) and analytical arguments we map low-energy degrees of freedom of the spin models in a magnetic field on classical lattice-gas models. Further we use transfer-matrix calculations and classical Monte Carlo simulations to give a quantitative description of low-temperature thermodynamics of the quantum spin models. The classical lattice-gas model yields an excellent description of the quantum spin models up to quite large temperatures. The main peculiarity of the considered frustrated bilayer is a phase transition which occurs at low temperatures for a wide range of magnetic fields below the saturation magnetic field and belongs to the two-dimensional Ising model universality class.

      • Received 20 September 2010

      DOI:https://doi.org/10.1103/PhysRevB.82.214412

      ©2010 The American Physical Society

      Authors & Affiliations

      Oleg Derzhko1,2, Taras Krokhmalskii1, and Johannes Richter2

      • 1Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, 1 Svientsitskii Street, L’viv-11, 79011, Ukraine
      • 2Institut für Theoretische Physik, Universität Magdeburg, P.O. Box 4120, 39016 Magdeburg, Germany

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      Vol. 82, Iss. 21 — 1 December 2010

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      Images

      • Figure 1
        (Color online) Lattices considered in this paper: (a) the frustrated two-leg ladder and (b) the frustrated bilayer. The vertical bonds have the strength J2>0 whereas all other bonds have the strength J1>0.Reuse & Permissions
      • Figure 2
        (Color online) Ground-state magnetization curves for the frustrated ladder (thin solid) and bilayer (thick broken) in the considered strong-coupling regime. We set J1=1, J2=4 (ladder) and J1=1, J2=5 (bilayer), i.e., we have h1=6 and h2=4 for the ladder, and h1=9 and h2=5 for the bilayer.Reuse & Permissions
      • Figure 3
        (Color online) Hard-dimer description of the localized-magnon states of the frustrated two-leg ladder. (a) Independent localized-magnon states (nonoverlapping hard-dimer states). (b) Interacting localized-magnon states (overlapping hard-dimer states).Reuse & Permissions
      • Figure 4
        (Color online) Specific heat C for the frustrated bilayer with J1=1, J2=5 (h1=9 and h2=5): exact diagonalization data versus hard-square predictions. Upper panel: C in dependence on the hard-core parameter (h−h1)/T, cf. Eq. (5.1) [symbols: spin system with N=20 (N=10), double-dashed line: hard-square model with N=10]. Lower panel: C in dependence on the temperature T for various values of magnetic field h [open symbols: spin system with N=16 (N=8), lines: hard-square model with N=8, and black filled up-triangles: Monte Carlo results for the hard-square model for large N up to 800×800 for h=8.9].Reuse & Permissions
      • Figure 5
        (Color online) Specific heat C for the frustrated two-leg ladder with J1=1, J2=4 (h1=6,h2=4) and J1=1, J2=10 (h1=12,h2=10): exact diagonalization data for N=16 (N=8) versus lattice-gas predictions for N=8. Upper panel: C in dependence on the hard-core parameter (h−h1)/T for T=0.5 and T=1 [open symbols: spin system with J2=4, filled pentagons: spin system with J2=10, long-dashed and dotted lines: lattice-gas model, and double-dashed line: hard-dimer model]. Lower panel: C in dependence on the temperature T for various values of magnetic field h [symbols: spin system with J2=4 and lines: lattice-gas model]. Note that the short-dashed (h=4.5) and the double-dashed line (h=5.5) coincide because of the particle-hole symmetry inherent in the lattice-gas model. For the spin model the corresponding symbols (up-triangles and circles) also coincide at lower temperatures.Reuse & Permissions
      • Figure 6
        (Color online) Phase diagram of the s=12 Heisenberg antiferromagnet in a magnetic field on the frustrated bilayer lattice with J1=1, J2=5 (i.e., h1=9, h2=5) in the half-plane “magnetic field h—temperature T”. The critical line Tc(h) (solid line) separates the long-range ordered phase, in which the localized magnons occupy one sublattice and the other one is empty (below the curve) and the disordered phase with a random distribution of localized magnons (above the curve). The dashed line corresponds to the critical line according to the hard-square description.Reuse & Permissions
      • Figure 7
        (Color online) Specific heat C for the frustrated bilayer with J1=1, J2=5 (h1=9,h2=5) and J1=1, J2=10 (h1=14,h2=10): exact diagonalization data versus lattice-gas predictions. Upper panel: C in dependence on the hard-core parameter (h−h1)/T for N=20 (N=10) and T=0.5 and T=1 [open symbols: spin system with J2=5, filled pentagons: spin system with J2=10, long-dashed and dotted lines: lattice-gas model, and double-dashed line: hard-square model]. Lower panel: C in dependence on the temperature T for various values of magnetic field h for N=16 (N=8) [symbols: spin system with J2=5 and lines: lattice-gas model]. The lines for h=6 and h=8 coincide because of the particle-hole symmetry of the lattice-gas model.Reuse & Permissions
      • Figure 8
        (Color online) Specific heat (upper panel), staggered susceptibility (middle panel), and entropy (lower panel) versus temperature for the frustrated bilayer with J1=1 and J2=5 (h1=9 and h2=5) for different magnetic fields obtained from Monte Carlo simulations for the effective lattice-gas model with finite repulsion V=J1.Reuse & Permissions
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