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Springer proceedings in physics

Simulating the Euclidean Time — Schrödinger Equation Using an Intel iPSC/860 Hypercube: Application to the t — J Model of High-T c Superconductivity

Mitchel D. Kovarik, Ted Barnes

Published Jan 1, 1993• 0 citations
Publisher
DOI
10.1007/978-3-642-78448-4_27

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We describe a Monte Carlo simulation of a dynamical fermion problem in two spatial dimensions on an Intel iPSC/860 hypercube. The problem studied is the determination of the dispersion relation of a dynamical hole in the t-J model of the high temperature superconductors. Since this problem involves the motion of many fermions in more than one spatial dimensions, it is representative of the class of systems that suffer from the ``minus sign problem`` of dynamical fermions which has made Monte Carlo simulation very difficult. We demonstrate that for small values of the hole hopping parameter one can extract the entire hole dispersion relation using the GRW Monte Carlo algorithm, which is a simulation of the Euclidean time Schroedinger equation, and present results on 4 {times} 4 and 6 {times} 6 lattices. Generalization to physical hopping parameter values wig only require use of an improved trial wavefunction for importance sampling.
We describe a Monte Carlo simulation of the 2-dimensional t-J model on an Intel iPSC/860 hypercube. The problem studied is the determination of the dispersion relation of a dynamical hole in the t-J model of the high temperature superconductors. Since this problem involves the motion of many fermions in more than one spatial dimensions, it is representative of the class of systems that suffer from the ``minus sign problem`` of dynamical fermions which has made Monte Carlo simulation very difficult. We demonstrate that for small values of the hole hopping parameter one can extract the entire hole dispersion relation using the GRW Monte Carlo algorithm, which is a simulation of the Euclidean time Schroedinger equation, and present results on 4 {times} 4 and 6 {times} 6 lattices. We demonstrate that a qualitative picture at higher hopping parameters may be found by extrapolating weak hopping results where the minus sign problem is less severe. Generalization to physical hopping parameter values will only require use of an improved trial wavefunction for importance sampling.