Very High Precision Determination of Low-Energy Parameters: The 2-d Heisenberg Quantum Antiferromagnet as a Test Case

Abstract

The 2-d spin 1/2 Heisenberg antiferromagnet with exchange coupling $J$ is investigated on a periodic square lattice of spacing $a$ at very small temperatures using the loop-cluster algorithm. Monte Carlo data for the staggered and uniform susceptibilities are compared with analytic results obtained in the systematic low-energy effective field theory for the staggered magnetization order parameter. The low-energy parameters of the effective theory, i.e.\ the staggered magnetization density ${\mathcal{M}}_s=0.30743(1)/a^2$, the spin stiffness ${\rho }_s=0.18081(11)J$, and the spin wave velocity $c=1.6586(3)Ja$ are determined with very high precision. Our study may serve as a test case for the comparison of lattice QCD Monte Carlo data with analytic predictions of the chiral effective theory for pions and nucleons, which is vital for the quantitative understanding of the strong interaction at low energies.

5 pages, 4 figures, 1 table

References in corpus (4)

• Evidence of Unconventional Universality Class in a Two-Dimensional 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
• The rotator spectrum in the delta-regime of the O(n) effective field theory in 3 and 4 dimensions

Cited by in corpus (27)

• Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
• Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions
• Pseudospin-lattice coupling in the spin-orbit Mott insulator Sr2IrO4
• Consistent scaling exponents at the deconfined quantum-critical point
• Level spectroscopy in a two-dimensional quantum magnet: Linearly dispersing spinons at the deconfined quantum critical point
• Velocity of excitations in ordered, disordered and critical antiferromagnets
• Solving the puzzle of an unconventional phase transition for a 2d dimerized quantum Heisenberg model
• Multiplicative logarithmic corrections to quantum criticality in three-dimensional dimerized antiferromagnets
• Spontaneous Magnetization of an Ideal Ferromagnet: Beyond Dyson's Analysis
• Low-Temperature Properties of Two-Dimensional Ideal Ferromagnets
• Improved scaling of the entanglement entropy of quantum antiferromagnetic Heisenberg systems
• Thermodynamics of Two-Dimensional Ideal Ferromagnets - Three-Loop Analysis
• Symmetry Analysis of Holes Localized on a Skyrmion in a Doped Antiferromagnet
• Constraint Effective Potential of the Magnetization in the Quantum XY Model
• Benchmark study of an auxiliary-field quantum Monte Carlo technique for the Hubbard model with shifted-discrete Hubbard-Stratonovich transformations
• SU(3) Quantum Spin Ladders as a Regularization of the CP(2) Model at Non-Zero Density: From Classical to Quantum Simulation
• Spontaneous symmetry breaking in correlated wave functions
• Low-Temperature Properties of Ferromagnetic Spin Chains in a Magnetic Field
• Universal scalings of Néel temperature, staggered magnetization density, and spinwave velocity of three-dimensional disordered and clean quantum antiferromagnets
• Thermodynamics of Ferromagnetic Spin Chains in a Magnetic Field: Impact of the Spin-Wave Interaction
• Combination of Tensor Network States and Green's function Monte Carlo
• Universal quantum criticality at finite temperature for two-dimensional disordered and clean dimerized spin-$\frac{1}{2}$ antiferromagnets
• Thermodynamics of the $d$=3+1 Quantum XY Model
• 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
• High-precision ground state parameters of the two-dimensional spin-1/2 Heisenberg model on the square lattice