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Simulations on infinite-size lattices.

H G Evertz¹, W von der Linden

¹Institut für Theoretische Physik, Technische Universität Graz, 8010 Graz, Austria.

Physical Review Letters

|June 1, 2001

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We developed a new Monte Carlo method for simulating infinite-sized quantum systems. This approach enables direct calculation of dynamical properties and correlation functions, advancing computational physics research.

Area of Science:

Computational Physics
Statistical Mechanics
Quantum Many-Body Systems

Background:

Existing cluster algorithms have limitations in simulating infinite systems.
Simulating quantum models at high temperatures (beta = infinity) is computationally challenging.

Purpose of the Study:

To introduce a modified Monte Carlo method for direct simulation of infinite-sized systems.
To enable the calculation of dynamical information and two-point functions.
To extend simulations to quantum models at beta = infinity.

Main Methods:

Modification of existing cluster algorithms.
Application of Monte Carlo simulations.
Direct calculation of two-point functions, including dynamical information.

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Main Results:

The method allows direct simulations on systems of infinite size.
Dynamical information and correlation functions at larger distances are obtainable.
The method successfully calculates spectra for the 2D Ising model and Heisenberg quantum spin ladders.

Conclusions:

The developed Monte Carlo method offers a powerful tool for simulating infinite quantum systems.
It provides direct access to dynamical properties and correlation functions.
The method is applicable to various quantum models, demonstrating its versatility.