Loop-Cluster Simulation of the $t$-$J$ Model on the Honeycomb Lattice

Abstract

Inspired by the lattice structure of the unhydrated variant of the superconducting material Na${}_x$CoO${}_2\cdot$yH${}_2$O at $x=1/3$, we study the $t$-$J$ model on a honeycomb lattice by using an efficient loop-cluster algorithm. The low-energy physics of the undoped system and of the single hole sector is described by a systematic low-energy effective field theory. The staggered magnetization per spin ${\tilde{\mathcal{M}}}_s=0.2688(3)$, the spin stiffness ${\rho }_s=0.102(2)J$, the spin wave velocity $c=1.297(16)Ja$, and the kinetic mass $M^{\prime }$ of a hole are obtained by fitting the numerical Monte Carlo data to the effective theory predictions.

8 pages, 10 figures, 2 tables

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• Frustrated Heisenberg antiferromagnet on the honeycomb lattice: Spin gap and low-energy parameters
• Solving the puzzle of an unconventional phase transition for a 2d dimerized quantum Heisenberg model
• Constraint Effective Potential of the Staggered Magnetization in an Antiferromagnet
• A New Method of Calculating the Spin-Wave Velocity $c$ of Spin-1/2 Antiferromagnets With $O(N)$ Symmetry in a Monte Carlo Simulation
• Subtlety of Determining the Critical Exponent $\nu$ of the Spin-1/2 Heisenberg Model with a Spatially Staggered Anisotropy on the Honeycomb Lattice
• Systematic Effective Field Theory Investigation of Spiral Phases in Hole-Doped Antiferromagnets on the Honeycomb Lattice
• Systematic Low-Energy Effective Field Theory for Magnons and Holes in an Antiferromagnet on the Honeycomb Lattice
• Microscopic Model versus Systematic Low-Energy Effective Field Theory for a Doped Quantum Ferromagnet
• Universal scalings of Néel temperature, staggered magnetization density, and spinwave velocity of three-dimensional disordered and clean quantum antiferromagnets
• Magnetic Catalysis in Antiferromagnetic Films
• Universal quantum criticality at finite temperature for two-dimensional disordered and clean dimerized spin-$\frac{1}{2}$ antiferromagnets
• Holes Localized on a Skyrmion in a Doped Antiferromagnet on the Honeycomb Lattice: Symmetry Analysis
• Square-Lattice Antiferromagnet Subjected to a Magnetic Field Aligned with the Order Parameter
• Monte Carlo determination of the low-energy constants for a two-dimensional spin-1 Heisenberg model with spatial anisotropy