Quantum Monte Carlo simulations of one hole in the t-J model

Fumiko Yamaguchi, Y. Yamamoto

Matthias Troyer

I compute the properties of a mobile hole or a static impurity injected into a quantum critical two-dimensional antiferromagnet by quantum Monte Carlo simulations. Using field-theoretical results by Sachdev et al. the mobile hole problem is mapped to the static impurity one and can thus also be treated in quantum Monte Carlo simulations without a negative sign problem.

Brian Rost, James K. Freericks

Nikolaos G. Diamantis, Efstratios Manousakis

We discuss that flat-histogram techniques can be appropriately applied in the sampling of quantum Monte Carlo simulation in order to improve the statistical quality of the results at long imaginary time or low excitation energy. Typical imaginary-time correlation functions calculated in quantum Monte Carlo are subject to exponentially growing errors as the range of imaginary time grows and this smears the information on the low energy excitations. We show that we can extract the low energy physics by modifying the Monte Carlo sampling technique to one in which configurations which contribute to making the histogram of certain quantities flat are promoted. We apply the diagrammatic Monte Carlo (diag-MC) method to the motion of a single hole in the t-J model and we show that the implementation of flat-histogram techniques allows us to calculate the Green's function in a wide range of imaginary-time. In addition, we show that applying the flat-histogram technique alleviates the "sign"-problem associated with the simulation of the single-hole Green's function at long imaginary time.

Mitchel D. Kovarik, Ted Barnes

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.

Fabian Grusdt, Márton Kanász-Nagy, Annabelle Bohrdt +1 more