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.

arXiv comment17 pages, 8 figures

References in corpus (46)

• Macroscopic magnetization jumps due to independent magnons in frustrated quantum spin lattices
• Order-Disorder Transition in a Two-Layer Quantum Antiferromagnet
• Ladders in a magnetic field: a strong coupling approach
• High-precision finite-size scaling analysis of the quantum-critical point of S=1/2 Heisenberg antiferromagnetic bilayers
• Exact low-temperature behavior of kagome antiferromagnet at high fields
• One-Dimensional Magnetism
• Equivalence of the antiferromagnetic Heisenberg ladder to a single $S=1$ chain
• Magnetocaloric effect in one-dimensional antiferromagnets
• Magnetization plateaux and jumps in a class of frustrated ladders: A simple route to a complex behaviour
• Exact eigenstates and macroscopic magnetization jumps in strongly frustrated spin lattices
• Dimerized phase and transitions in a spatially anisotropic square lattice antiferromagnet
• Quantum magnetism in two dimensions: From semi-classical Néel order to magnetic disorder
• Universal low-temperature behavior of frustrated quantum antiferromagnets in the vicinity of the saturation field
• Independent magnon states on magnetic polytopes
• Enhanced magnetocaloric effect in frustrated magnetic molecules with icosahedral symmetry
• Finite low-temperature entropy of some strongly frustrated quantum spin lattices in the vicinity of the saturation field
• Evidence of Unconventional Universality Class in a Two-Dimensional Dimerized Quantum Heisenberg Model
• Planar lattice gases with nearest-neighbour exclusion
• Monte Carlo simulations of 2d hard core lattice gases
• High field properties of geometrically frustrated magnets
• Studies of a 2-Chain Spin Ladder with Frustrating Second Neighbor Interactions
• Low-temperature properties of the Hubbard model on highly frustrated one-dimensional lattices
• Universal properties of highly frustrated quantum magnets in strong magnetic fields
• Magnetic-field induced spin-Peierls instability in strongly frustrated quantum spin lattices
• The fate of spinons in spontaneously dimerised spin-1/2 ladders
• Topological Order, Dimerization, and Spinon Deconfinement in Frustrated Spin Ladders
• Infinite series of magnetization plateaus in the frustrated dimer-plaquette chain
• Competition between plaquette and dimer phases in Heisenberg chains
• Lattice gas description of pyrochlore and checkerboard antiferromagnets in a strong magnetic field
• Condensation of magnons and spinons in a frustrated ladder
• Linear independence of localized magnon states
• Magnetocaloric effect in quantum spin-s chains
• Finite-temperature order-disorder phase transition in a frustrated bilayer quantum Heisenberg antiferromagnet in strong magnetic fields
• Two-dimensional quantum antiferromagnets
• Phase behavior of hard-core lattice gases: A Fundamental Measure approach
• Low-temperature thermodynamics for a flat-band ferromagnet: Rigorous versus numerical results
• Localized-magnon states in strongly frustrated quantum spin lattices
• Linear energy bounds for Heisenberg spin systems
• Exact low-temperature properties of a class of highly frustrated Hubbard models
• Field Induced Spin Supersolidity in Frustrated Spin-1/2 Spin-Dimer Models
• The transition from an ordered antiferromagnet to a quantum disordered spin liquid in a solvable bilayer model
• 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
• Frustrated spin ladder with alternating spin-1 and spin-1/2 rungs
• Spin systems with dimerized ground states

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