Quantum Monte Carlo Study Reveals Instability of Two-Dimensional Dipolar Fermi Fluids at All Densities

Fermionic cold atoms offer a powerful means to model the complex behaviour of electrons in materials, and recent advances allow scientists to precisely control interactions between these atoms. Clio Johnson, Neil D. Drummond, James P. Hague, and Calum MacCormick investigate the properties of these atoms when arranged in two dimensions and subjected to dipolar interactions, where each atom acts like a tiny magnet. Their work demonstrates that ferromagnetism, a state where atoms align their magnetic moments, proves unstable under the conditions they explore, revealing a surprising sensitivity to interaction parameters. This research provides a crucial benchmark for developing theoretical models, specifically density functional theory, and will ultimately help scientists interpret experimental observations of these fascinating quantum systems and better understand the behaviour of interacting electrons in real materials.

Dipolar Fermi Gases and Quantum Monte Carlo

Scientists employ quantum Monte Carlo methods to investigate the behavior of ultracold dipolar Fermi gases, systems composed of fermionic atoms possessing magnetic dipole moments. These interactions, extending over long ranges, create complex many-body problems requiring sophisticated computational techniques. The research focuses on accurately calculating the ground state properties of these gases, a challenging task in quantum mechanics due to the intricate interactions between numerous particles. The team utilizes Variational Monte Carlo and Diffusion Monte Carlo, employing random sampling to solve the quantum mechanical equations.

Variational Monte Carlo optimizes an approximate solution to the Schrödinger equation, a trial wave function, by minimizing its energy. The accuracy of this method relies heavily on the form of the trial wave function, which is constructed using a Jastrow-Slater approach. This combines a Slater determinant, representing the antisymmetric nature of fermions, with a Jastrow factor, explicitly accounting for atomic interactions and improving calculation accuracy. A backflow transformation further refines the Jastrow factor by incorporating the effects of interactions on individual atomic wave functions.

Diffusion Monte Carlo then projects out the ground state wave function from the initial trial wave function, simulating the time evolution of the wave function in imaginary time. To simplify calculations, pseudopotentials replace the complex short-range interactions between atoms with effective potentials. Calculations are performed on finite-sized systems, requiring finite-size scaling techniques to extrapolate results to the infinite system limit. The research carefully addresses various sources of error, including statistical and systematic errors, and employs optimization techniques to refine the trial wave function and backflow parameters. The ultimate goal is to accurately determine the equation of state, identify different phases, and calculate the magnetic properties of these gases. The study focused on accurately modeling pairwise interactions between atoms trapped in two dimensions, utilizing a softened dipolar interaction potential to represent realistic atomic behavior. To achieve precise calculations, researchers implemented this interaction within the casino quantum Monte Carlo code, enabling both variational Monte Carlo and diffusion Monte Carlo simulations. The core of the methodology involved constructing trial wave functions with adjustable parameters, optimized by minimizing the energy expectation value to accurately represent the ground state of the atomic system.

Diffusion Monte Carlo then projected out the ground state component of this trial wave function by simulating processes governed by the Schrödinger equation in imaginary time, while maintaining fermionic antisymmetry through careful phase control. Calculations were performed for both one-component ferromagnetic and two-component paramagnetic systems, allowing investigation of itinerant ferromagnetism and its stability. To manage computational complexity, the team implemented a truncated summation of interaction energies, evaluating explicit sums up to a radius and approximating the long-range tail with an integral. This approximation, accurate to a high degree, ensured reasonable computational cost while maintaining precision.

Specifically, calculations utilized a large number of lattice vectors within the explicit sum, and the radius scaled with system size to minimize errors. Two distinct systems of natural units were employed, facilitating comparison with previous work and parameterization of energies. These methodological innovations enabled precise determination of the energy as a function of density, paving the way for density functional theory to support experimental studies of inhomogeneous fermionic cold atom systems.

Fermionic Gases Show Unstable Itinerant Ferromagnetism

This research delivers a robust parameterization of energy data for two-dimensional fermionic atomic gases, crucial for simulating correlated electronic systems using cold atoms. Scientists performed extensive diffusion Monte Carlo calculations to model the behavior of these gases, considering both ferromagnetic and paramagnetic states with interacting dipolar atoms. The study focuses on accurately describing the interactions between atoms, employing a softened dipolar potential relevant to specific atomic species, and also exploring the behavior of bare dipolar interactions. Measurements confirm that itinerant ferromagnetism is unstable within the explored parameter spaces, both with and without the softening of dipolar interactions.

The team parameterized the energy as a function of atomic density, expressed using a dimensionless radius, which defines the average space occupied by each atom. For softened interactions, the calculations utilized a specific softening parameter. The energy is then expressed in terms of this radius, allowing for precise modeling of the system’s behavior at different densities. For bare dipolar interactions, the team fixed the radius as the unit of length, enabling direct comparison with previous research. Calculations were performed using the casino QMC code, implementing variational Monte Carlo and diffusion Monte Carlo methods to accurately determine ground state energies. The results demonstrate a pathway to accurately model complex quantum systems using tunable cold atom simulations, providing a valuable tool for exploring strongly correlated electron behavior in materials science and condensed matter physics. The team successfully modelled systems relevant to specific atomic species, exploring a range of interaction strengths and incorporating a softening parameter consistent with experimental observations. This detailed energy parameterization, expressed as an interpolation formula, will facilitate future density functional theory calculations applied to inhomogeneous cold atom systems, bridging the gap between theoretical modelling and experimental investigation. The calculations demonstrate that itinerant ferromagnetism is unstable within the explored parameter spaces, for both softened and bare dipolar interactions.

Corrections to account for finite system size were carefully considered, and the use of a Jastrow factor effectively mitigated short-range divergences, improving the precision of the results. While these calculations focused on a two-component system, future work will extend the modelling to four-state systems and investigate the crystallization of these cold atom systems, building upon existing research in the field. This work establishes a valuable resource for exploring the behaviour of strongly interacting fermionic cold atoms and advancing the development of quantum simulators.