Continuous similarity transformation for critical phenomena: easy-axis antiferromagnetic XXZ model

Abstract

We apply continuous similarity transformations (CSTs) to the easy-axis antiferromagnetic XXZ-model on the square lattice. The CST flow equations are truncated in momentum space by the scaling dimension $d$ so that all contributions with $d\le 2$ are taken into account. The resulting quartic magnon-conserving effective Hamiltonian is analyzed in the zero-, one-, and two-magnon sector. In this way, a quantitative description of the ground-state energy, the one-magnon dispersion and its gap as well as of two-magnon bound states is gained for anisotropies ranging from the gapped Ising model to the gapless Heisenberg model. We discuss the critical properties of the gap closing as well as the evolution of the one-magnon roton mininum. The excitation energies of two-magnon bound states are calculated and their decay into the two-magnon continuum is determined via the inverse participation ratio.

12 pages, 8 figures

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Cited by in corpus (10)

• Switching the Magnetization in Quantum Antiferromagnets
• Quantum phases of hardcore bosons with repulsive dipolar density-density interactions on two-dimensional lattices
• Quantum melting of long-range ordered quantum antiferromagnets investigated by momentum-space continuous similarity transformations
• Quantitative description of long-range order in the anisotropic spin-1/2 Heisenberg antiferromagnet on the square lattice
• Collective modes in superconductors including Coulomb repulsion
• Anomalous enhancement of Neel order in the $S=1/2$ square lattice Heisenberg model under fictitious magnetic field
• Role of magnon-magnon interaction in optical excitation of coherent two-magnon modes
• Quantum decay of magnons in the unfrustrated honeycomb Heisenberg model
• Extracting quantum-critical properties from directly evaluated enhanced perturbative continuous unitary transformations
• Quantum effects in the magnon spectrum of 2D altermagnets via continuous similarity transformations