Quantum Heisenberg antiferromagnet on low-dimensional frustrated lattices

Abstract

Using a lattice-gas description of the low-energy degrees of freedom of the quantum Heisenberg antiferromagnet on the frustrated two-leg ladder and bilayer lattices we examine the magnetization process at low temperatures for these spin models. In both cases the emergent discrete degrees of freedom implicate a close relation of the frustrated quantum Heisenberg antiferromagnet to the classical lattice gas with finite nearest-neighbor repulsion or, equivalently, to the Ising antiferromagnet in a uniform magnetic field. Using this relation we obtain analytical results for thermodynamically large systems in the one-dimensional case. In the two-dimensional case we perform classical Monte Carlo simulations for systems of up to $100\times 100$ sites.

Submitted to Teoreticheskaya i Matematicheskaya Fizika (special issue dedicated to the 90th anniversary of Professor Sergei Vladimirovich Tyablikov)

References in corpus (7)

• Exact low-temperature behavior of kagome antiferromagnet at high fields
• High-Order Coupled Cluster Method Study of Frustrated and Unfrustrated Quantum Magnets in External Magnetic Fields
• Condensation of magnons and spinons in a frustrated ladder
• Linear independence of localized magnon states
• Emergent Ising degrees of freedom in frustrated two-leg ladder and bilayer $s=1/2$ Heisenberg antiferromagnets
• Finite-temperature order-disorder phase transition in a frustrated bilayer quantum Heisenberg antiferromagnet in strong magnetic fields
• Field Induced Spin Supersolidity in Frustrated Spin-1/2 Spin-Dimer Models

Cited by in corpus (5)

• Frustrated honeycomb-lattice bilayer quantum antiferromagnet in a magnetic field: Unconventional phase transitions in a two-dimensional isotropic Heisenberg model
• Ising versus Potts criticality in a low-temperature magnetothermodynamics of a frustrated spin-1/2 Heisenberg triangular bilayer
• Magnetization plateaus, spin-canted orders and field-induced transitions in a spin-1/2 Heisenberg antiferromagnet on a distorted diamond-decorated honeycomb lattice
• Unveiling the degeneracy of bound magnon crystals from magnetic and thermodynamic features of the spin-1/2 Heisenberg octahedral chain
• Quantum Heisenberg antiferromagnet in a field on the Tasaki square lattice