Ground-state properties of two-dimensional dimerized Heisenberg models

Abstract

The purpose of this paper is to investigate the ground-state properties of two-dimensional Heisenberg models on a square lattice with a given dimerization. Our aim is threefold: First, we want to investigate the dimensional transition from two to one dimension for three models consisting of weakly coupled chains for large dimerizations. Simple scaling arguments show that the interchain coupling is always relevant. The ground states of two of these models therefore have one-dimensional nature only at the decoupling point. The third considered model is more complicated, because it contains additional relevant intrachain couplings leading to a gap as shown by scaling arguments and numerical investigations. Second, we investigate at which point the dimerization destroys the Néel ordered ground state of the isotropic model. Within a mapping to a nonlinear sigma-model and linear spinwave theory (LSWT) we conclude that the stability of the Néel ordered state depends on the microscopic details of the model. Third, the considered models also can be regarded as effective models for a spin system with spin-phonon coupling. This leads to the question if a spin-Peierls transition, i.e. a gain of total energy due to lattice distortion, is possible. LSWT shows that such a transition is possible under certain conditions leading to a coexistence of long-range order and spin-Peierls dimerization. We also find that the gain of magnetic energy is largest for a stair-like distortion of the lattice.

13 pages, 11 figures, revtex

References in corpus (9)

• Resonating Valence Bond Theory of Coupled Heisenberg Chains
• Thermodynamics of the anisotropic Heisenberg chain calculated by the density matrix renormalization group method
• The Square-Lattice Heisenberg Antiferromagnet at Very Large Correlation Lengths
• Monte Carlo Study of the S=1/2 and S=1 Heisenberg Antiferromagnet on a Spatially Anisotropic Square Lattice
• A Plane of Weakly Coupled Heisenberg Chains: Theoretical Arguments and Numerical Calculations
• On a Renormalization Group Approach to Dimensional Crossover
• Finite Temperature DMRG Investigation of the Spin-Peierls Transition in CuGeO${}_3$
• Two-Dimensional Quantum Spin Systems with Ladder and Plaquette Structure
• Quantum Phase Transitions in Two-Dimensional Spin Systems with Ladder, Plaquette and Mixed-Spin Structures

Cited by in corpus (15)

• Order-N Cluster Monte Carlo Method for Spin Systems with Long-range Interactions
• Comprehensive quantum Monte Carlo study of the quantum critical points in planar dimerized/quadrumerized Heisenberg models
• Low-energy fixed points of random Heisenberg models
• Spin stiffness and quantum fluctuations in C-type and A-type antiferromagnets
• Spin excitation spectra of the two dimensional $S=1/2$ Heisenberg model with a checkerboard structure
• Valence-Bond Order in a Honeycomb Antiferromagnet Coupled to Quantum Phonons
• Quantum phase transitions of multi-species Dirac fermions
• Topological solitons and bulk polarization switch in collinear type II multiferroics
• Anisotropic magnetic interactions and spin dynamics in the spin-chain compound Cu(py)${}_2$Br${}_2$: An experimental and theoretical study
• Simple microscopic model for magneto-electric coupling in type-II antiferromagnetic multiferroics
• A direct proof of dimerization in a family of SU(n)-invariant quantum spin chains
• Thermodynamic properties of the two-dimensional S=1/2 Heisenberg antiferromagnet coupled to bond phonons
• Deconfinement phase transition in a two-dimensional model of interacting $2\times 2$ plaquettes
• Structural and magnetic instabilities of layered magnetic systems
• Neel to spin-Peierls transition in a quasi-1D Heisenberg model coupled to bond phonons