Simulations of Discrete Quantum Systems in Continuous Euclidean Time

Abstract

Path integrals are usually formulated in discrete Euclidean time using the Trotter formula. We propose a new method to study discrete quantum systems, in which we work directly in the Euclidean time continuum. The method is of general interest and can be applied to studies of quantum spin systems, lattice fermions, and in principle also lattice gauge theories. Here it is applied to the Heisenberg quantum antiferromagnet using a continuous-time version of a loop cluster algorithm. The computational advantage of this algorithm is exploited to confirm the predictions of chiral perturbation theory in the extreme low temperature regime, down to $T=0.01J$. A fit of the low-energy parameters of chiral perturbation theory gives excellent agreement with previous results and with experiments.

The UUcoded file cluster.tar.gz contains RevTeX source and two Postscript figures. Further information available at http://ctpa02.mit.edu/~bbbeard/

References in corpus (2)

• Cluster Algorithm for Vertex Models
• Finite size and temperature effects in the AF Heisenberg model

Cited by in corpus (6)

• Testing and tuning symplectic integrators for Hybrid Monte Carlo algorithm in lattice QCD
• Efficient continuous-time quantum Monte Carlo algorithm for fermionic lattice models
• GPU-based single-cluster algorithm for the simulation of the Ising model
• Finite Size Scaling, Fisher Zeroes and N=4 Super Yang-Mills
• Lorentz Covariance and the Dimensional Crossover of 2d-Antiferromagnets
• The Lattice $\beta$-function of Quantum Spin Chains