Monte Carlo Study of the S=1/2 and S=1 Heisenberg Antiferromagnet on a Spatially Anisotropic Square Lattice

Abstract

We present a quantum Monte Carlo study of a Heisenberg antiferromagnet on a spatially anisotropic square lattice, where the coupling strength in the x-direction ($J_x$) is different from that in the y-direction ($J_y$). By varying the anisotropy $\alpha$ from 0 to 1, we interpolate between the one-dimensional chain and the two-dimensional isotropic square lattice. Both $S=1/2$ and S=1 systems are considered separately in order to facilitate comparison. The temperature dependence of the uniform susceptibility and the spin-spin correlation length are computed down to very low temperatures for various values of $\alpha$. For S=1, the existence of a quantum critical point at ${\alpha }_c^{S=1}=0.040(5)$ as well as the scaling of the spin gap is confirmed. Universal quantities predicted from the $\mathcal{O}(3)$ nonlinear $\sigma$ model agree with our results at $\alpha =0.04$ without any adjustable parameters. On the other hand, the $S=1/2$ results are consistent with ${\alpha }_c^{S=1/2}=0$, as discussed by a number of previous theoretical studies. Experimental implications for $S=1/2$ compounds such as Sr${}_2$CuO${}_3$ are also discussed.

8 pages, 7 figures, to be published in Phys. Rev. B

References in corpus (2)

• Multi-Chain Mean-Field Theory of Quasi One-Dimensional Quantum Spin Systems
• 63Cu NQR evidence of dimensional crossover to anisotropic 2d regime in S= 1/2 three-leg ladder Sr2Cu3O5

Cited by in corpus (45)

• Ground-State Phase Diagram of Quantum Heisenberg Antiferromagnets on the Anisotropic Dimerized Square Lattice
• Topological phases in ultracold polar-molecule quantum magnets
• Quenching the Haldane gap in spin-1 Heisenberg antiferromagnets
• Kitaev honeycomb and other exotic spin models with polar molecules
• Phase diagram of the frustrated, spatially anisotropic S=1 antiferromagnet on a square lattice
• Characterizing the Haldane phase in quasi-one-dimensional spin-1 Heisenberg antiferromagnets
• Surface critical behaviors of coupled Haldane chains
• Emergent Haldane phase in the $S=1$ bilinear-biquadratic Heisenberg model on the square lattice
• Influence of an inter-chain coupling on spiral ground-state correlations in frustrated spin-1/2 J1-J2 Heisenberg chains
• Magnetic order in coupled spin-half and spin-one Heisenberg chains in anisotropic triangular-lattice geometry
• Magnetic properties of the quasi-two-dimensional S = 1/2 Heisenberg antiferromagnet [Cu(pyz)2(HF2)]PF6
• Solving the puzzle of an unconventional phase transition for a 2d dimerized quantum Heisenberg model
• Very High Precision Determination of Low-Energy Parameters: The 2-d Heisenberg Quantum Antiferromagnet as a Test Case
• Spinon confinement: dynamics of weakly coupled Hubbard chains
• Numerically exploring the 1D-2D dimensional crossover on spin dynamics in the doped Hubbard model
• A New Method of Calculating the Spin-Wave Velocity $c$ of Spin-1/2 Antiferromagnets With $O(N)$ Symmetry in a Monte Carlo Simulation
• Quenching of the Haldane gap in LiVSi2O6 and related compounds
• Ground-state properties of two-dimensional dimerized Heisenberg models
• Subtlety of Determining the Critical Exponent $\nu$ of the Spin-1/2 Heisenberg Model with a Spatially Staggered Anisotropy on the Honeycomb Lattice
• Monte Carlo Determination of the Low-Energy Constants of a Spin 1/2 Heisenberg Model with Spatial Anisotropy
• Effective spin-1 breathing kagome Hamiltonian induced by the exchange hierarchy in the maple leaf mineral bluebellite
• Spin and charge dynamics of a quasi-one-dimensional antiferromagnetic metal
• Ground-state long-range order in quasi-one-dimensional Heisenberg quantum antiferromagnets: High-order coupled-cluster calculations
• Hidden magnetic order in CuNCN
• NMR and dc-susceptibility studies of NaVGe2O6
• Magnetization process for a quasi-one-dimensional S=1 antiferromagnet
• Mott Transition in Quasi-One-Dimensional Systems
• Quantum Monte Carlo Study on the Spin-1/2 Honeycomb Heisenberg Model with Mixing Antiferromagnetic and Ferromagnetic Interactions in External Magnetic Fields
• Quantum phase transitions of the S=1 Shastry-Sutherland model
• Stripe order and magnetic anisotropy in the $S=1$ antiferromagnet BaMoP${}_2$O${}_8$
• A microscopic model for a class of mixed-spin quantum antiferromagnets
• Classification for the universal scaling of Néel temperature and staggered magnetization density of three-dimensional dimerized spin-1/2 antiferromagnets
• Magnetism study on a frustration-free spatially anisotropic $S$ = 1 square lattice antiferromagnet Ni[SC(NH${}_2$)${}_2$]${}_6$Br${}_2$
• Low-temperature thermal conductivity and magnetic transitions of the kagomé-staircase compound Ni${}_3$V${}_2$O${}_8$
• Phase diagram of spin-$1$ chains with Dzyaloshinskii-Moriya interaction
• Universal scaling of three-dimensional dimerized quantum antiferromagnets on bipartite lattices
• Self-adapting method for the localization of quantum critical points using Quantum Monte Carlo techniques
• Universal quantum criticality at finite temperature for two-dimensional disordered and clean dimerized spin-$\frac{1}{2}$ antiferromagnets
• Mott insulating phases and magnetism of fermions in a double-well optical lattice
• Haldane phases and phase diagrams of the S = 3/2, 1 bilinear-biquadratic Heisenberg model on the orthogonal dimer chain
• Dimensional Crossover in Quasi-one-dimensional Spin-1 Heisenberg Antiferromagnets
• Quantum criticality at finite temperature for two-dimensional $J{Q}_3$ models on the square and the honeycomb lattices
• Ground state energy density, susceptibility, and Wilson ratio of a two-dimensional disordered quantum spin system
• Monte Carlo determination of the low-energy constants for a two-dimensional spin-1 Heisenberg model with spatial anisotropy
• Quantum magnetism of ferromagnetic spin dimers in $\alpha$-KVOPO${}_4$