Emergent Ising degrees of freedom in frustrated two-leg ladder and bilayer $s=1/2$ Heisenberg antiferromagnets

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.

17 pages, 8 figures

References in corpus (17)

• Exact low-temperature behavior of kagome antiferromagnet at high fields
• Magnetocaloric effect in one-dimensional antiferromagnets
• Exact eigenstates and macroscopic magnetization jumps in strongly frustrated spin lattices
• Universal low-temperature behavior of frustrated quantum antiferromagnets in the vicinity of the saturation field
• Enhanced magnetocaloric effect in frustrated magnetic molecules with icosahedral symmetry
• Evidence of Unconventional Universality Class in a Two-Dimensional Dimerized Quantum Heisenberg Model
• Monte Carlo simulations of 2d hard core lattice gases
• Universal properties of highly frustrated quantum magnets in strong magnetic fields
• Topological Order, Dimerization, and Spinon Deconfinement in Frustrated Spin Ladders
• Condensation of magnons and spinons in a frustrated ladder
• Linear independence of localized magnon states
• Finite-temperature order-disorder phase transition in a frustrated bilayer quantum Heisenberg antiferromagnet in strong magnetic fields
• Low-temperature thermodynamics for a flat-band ferromagnet: Rigorous versus numerical results
• Exact low-temperature properties of a class of highly frustrated Hubbard models
• Two-particle bound states and one-particle structure factor in a Heisenberg bilayer system
• Contractor-Renormalization approach to frustrated magnets in magnetic field
• Exact magnetization plateaus and phase transitions in spin-S Heisenberg antiferromagnets in arbitrary dimensions

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