# Quantum Monte Carlo Calculations Applied to Magnetic Molecules

## Abstract

We have calculated the equilibrium thermodynamic properties of Heisenberg spin systems using a quantum Monte Carlo (QMC) method. We have used some of these systems as models to describe recently synthesized magnetic molecules, and-upon comparing the results of these calculations with experimental data-have obtained accurate estimates for the basic parameters of these models. We have also performed calculations for other systems that are of more general interest, being relevant both for existing experimental data and for future experiments. Utilizing the concept of importance sampling, these calculations can be carried out in an arbitrarily large quantum Hilbert space, while still avoiding any approximations that would introduce systematic errors. The only errors are statistical in nature, and as such, their magnitudes are accurately estimated during the course of a simulation. Frustrated spin systems present a major challenge to the QMC method, nevertheless, in many instances progress can be made. In this chapter, the field of magnetic molecules is introduced, paying particular attention to the characteristics that distinguish magnetic molecules from other systems that are studied in condensed matter physics. We briefly outline the typical path by which we learn about magnetic molecules, which requires a close relationship between experiments and theoretical calculations.more »

- Authors:

- Iowa State Univ., Ames, IA (United States)

- Publication Date:

- Research Org.:
- Ames Lab., Ames, IA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 892729

- Report Number(s):
- IS-T 2543

TRN: US0605860

- DOE Contract Number:
- W-7405-Eng-82

- Resource Type:
- Thesis/Dissertation

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; HILBERT SPACE; MONTE CARLO METHOD; PHYSICS; SAMPLING; SIMULATION; SPIN; THERMODYNAMIC PROPERTIES

### Citation Formats

```
Engelhardt, Larry.
```*Quantum Monte Carlo Calculations Applied to Magnetic Molecules*. United States: N. p., 2006.
Web. doi:10.2172/892729.

```
Engelhardt, Larry.
```*Quantum Monte Carlo Calculations Applied to Magnetic Molecules*. United States. doi:10.2172/892729.

```
Engelhardt, Larry. Sun .
"Quantum Monte Carlo Calculations Applied to Magnetic Molecules". United States.
doi:10.2172/892729. https://www.osti.gov/servlets/purl/892729.
```

```
@article{osti_892729,
```

title = {Quantum Monte Carlo Calculations Applied to Magnetic Molecules},

author = {Engelhardt, Larry},

abstractNote = {We have calculated the equilibrium thermodynamic properties of Heisenberg spin systems using a quantum Monte Carlo (QMC) method. We have used some of these systems as models to describe recently synthesized magnetic molecules, and-upon comparing the results of these calculations with experimental data-have obtained accurate estimates for the basic parameters of these models. We have also performed calculations for other systems that are of more general interest, being relevant both for existing experimental data and for future experiments. Utilizing the concept of importance sampling, these calculations can be carried out in an arbitrarily large quantum Hilbert space, while still avoiding any approximations that would introduce systematic errors. The only errors are statistical in nature, and as such, their magnitudes are accurately estimated during the course of a simulation. Frustrated spin systems present a major challenge to the QMC method, nevertheless, in many instances progress can be made. In this chapter, the field of magnetic molecules is introduced, paying particular attention to the characteristics that distinguish magnetic molecules from other systems that are studied in condensed matter physics. We briefly outline the typical path by which we learn about magnetic molecules, which requires a close relationship between experiments and theoretical calculations. The typical experiments are introduced here, while the theoretical methods are discussed in the next chapter. Each of these theoretical methods has a considerable limitation, also described in Chapter 2, which together serve to motivate the present work. As is shown throughout the later chapters, the present QMC method is often able to provide useful information where other methods fail. In Chapter 3, the use of Monte Carlo methods in statistical physics is reviewed, building up the fundamental ideas that are necessary in order to understand the method that has been used in this work. With these ideas in hand, we then provide a detailed explanation of the current QMC method in Chapter 4. The remainder of the thesis is devoted to presenting specific results: Chapters 5 and 6 contain articles in which this method has been used to answer general questions that are relevant to broad classes of systems. Then, in Chapter 7, we provide an analysis of four different species of magnetic molecules that have recently been synthesized and studied. In all cases, comparisons between QMC calculations and experimental data allow us to distinguish a viable microscopic model and make predictions for future experiments. In Chapter 8, the infamous ''negative sign problem'' is described in detail, and we clearly indicate the limitations on QMC that are imposed by this obstacle. Finally, Chapter 9 contains a summary of the present work and the expected directions for future research.},

doi = {10.2172/892729},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Sun Jan 01 00:00:00 EST 2006},

month = {Sun Jan 01 00:00:00 EST 2006}

}