A New Method of Calculating the Spin-Wave Velocity $c$ of Spin-1/2 Antiferromagnets With $O(N)$ Symmetry in a Monte Carlo Simulation

Abstract

Motivated by the so-called cubical regime in magnon chiral perturbation theory, we propose a new method to calculate the low-energy constant, namely the spin-wave velocity $c$ of spin-1/2 antiferromagnets with $O(N)$ symmetry in a Monte Carlo simulation. Specifically we suggest that $c$ can be determined by $c=L/\beta$ when the squares of the spatial and temporal winding numbers are tuned to be the same in the Monte Carlo calculations. Here $\beta$ and $L$ are the inverse temperature and the box size used in the simulations when this condition is met. We verify the validity of this idea by simulating the quantum spin-1/2 XY model. The $c$ obtained by using the squares of winding numbers is given by $c=1.1348(5)Ja$ which is consistent with the known values of $c$ in the literature. Unlike other conventional approaches, our new idea provides a direct method to measure $c$. Further, by simultaneously fitting our Monte Carlo data of susceptibilities ${\chi }_{11}$ and spin susceptibilities $\chi$ to their theoretical predictions from magnon chiral perturbation theory, we find $c$ is given by $c=1.1347(2)Ja$ which agrees with the one we obtain by the new method of using the squares of winding numbers. The low-energy constants magnetization density $\mathcal{M}$ and spin stiffenss $\rho$ of quantum spin-1/2 XY model are determined as well and are given by $\mathcal{M}=0.43561(1)/a^2$ and $\rho =0.26974(5)J$, respectively. Thanks to the prediction power of magnon chiral perturbation theory which puts a very restricted constraint among the low-energy constants for the model considered here, the accuracy of $\mathcal{M}$ we present in this study is much precise than previous Monte Carlo result.

5 pages, 7 figures

References in corpus (5)

• The ALPS project release 1.3: open source software for strongly correlated systems
• Evidence of Unconventional Universality Class in a Two-Dimensional Dimerized Quantum Heisenberg Model
• Comprehensive quantum Monte Carlo study of the quantum critical points in planar dimerized/quadrumerized Heisenberg models
• Quantum Phase Transition in a Heisenberg Antiferromagnet on a Square Lattice with Strong Plaquette Interactions
• Constraint Effective Potential of the Staggered Magnetization in an Antiferromagnet

Cited by in corpus (17)

• Level spectroscopy in a two-dimensional quantum magnet: Linearly dispersing spinons at the deconfined quantum critical point
• Detecting Goldstone Modes with Entanglement Entropy
• Velocity of excitations in ordered, disordered and critical antiferromagnets
• 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
• Multiplicative logarithmic corrections to quantum criticality in three-dimensional dimerized antiferromagnets
• Improved scaling of the entanglement entropy of quantum antiferromagnetic Heisenberg systems
• Constraint Effective Potential of the Magnetization in the Quantum XY Model
• Real-time dynamics of open quantum spin systems driven by dissipative processes
• Stochastic approximation of dynamical exponent at quantum critical point
• Universal scalings of Néel temperature, staggered magnetization density, and spinwave velocity of three-dimensional disordered and clean quantum antiferromagnets
• Universal quantum criticality at finite temperature for two-dimensional disordered and clean dimerized spin-$\frac{1}{2}$ antiferromagnets
• Pseudocriticality in antiferromagnetic spin chains
• 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