Cold-Atom Simulations Reveal New Insights Into Material Specific Heat

The thermal characteristics of materials underpin numerous technologies and provide insights into fundamental physical phenomena. Recent advances in experimental techniques, particularly those involving cold-atom measurements, now permit the precise simulation of complex theoretical models, such as the Fermi-Hubbard model, a cornerstone of condensed matter physics. A new study by M. A. Habitzreuter, Willdauany C. de Freitas Silva, et al., details an investigation into the specific heat and density anomalies within this model. Published research reveals a three-peak structure in the specific heat as a function of filling, interaction strength, and temperature, attributable to the interplay between kinetic and potential energy contributions. The team’s simulations also demonstrate a corresponding density anomaly, detectable through the thermal expansion coefficient, and connect this behaviour to the well-known change of sign in the Seebeck coefficient, offering a novel analytical perspective on this established phenomenon.

Anomalous thermal properties manifest across diverse materials, impacting both fundamental science and life itself. The study of these anomalies represents a significant area of contemporary physics, extending across systems from complex fluids to solid-state compounds. Water, with its unusual density anomaly and high specific heat, exemplifies this phenomenon and is crucial for sustaining life, while materials like Fe–Ni Invar demonstrate unexpected thermal behaviour driven by the interplay between atomic vibrations, known as phonons, and the intrinsic magnetic moments of electrons, termed spins.

Heavy fermion compounds, such as cerium ruthenium disilicide, exhibit negative thermal expansion and a large Grüneiser parameter, indicating a strong coupling between thermal expansion and specific heat. Organic charge-transfer salts, including candidates for spin liquid states, display directional-dependent thermal expansion anomalies linked to low-temperature behaviour, often arising from the electronic structure of the material and modelled using the Hubbard model, a theoretical framework describing interacting electrons in a lattice. Recent research extends the investigation of these anomalies to systems more readily controlled, such as those created with cold atoms, allowing precise manipulation of interactions and enabling the study of density anomalies near Mott transitions, where materials undergo changes in their electronic properties.

The behaviour of materials under varying temperatures is central to both technological innovation and fundamental scientific discovery. Recent advances in experimental techniques, particularly those employing cold-atom measurements, now allow physicists to simulate complex theoretical models, such as the Fermi-Hubbard model, with unprecedented control over key parameters. This research focuses on a detailed investigation of the thermal properties of the Hubbard model, specifically the specific heat, as a function of electron filling, interaction strength, and temperature, utilising the model as a cornerstone of condensed matter physics which describes interacting electrons within a lattice and provides a simplified, yet powerful, framework for understanding the behaviour of strongly correlated electron systems.

To explore these properties, researchers employed Determinant Quantum Monte Carlo (DQMC) simulations, a computationally intensive technique used to solve the many-body Schrödinger equation for interacting electron systems, allowing for accurate calculations of ground-state properties crucial for understanding the thermodynamic behaviour of the model. The simulations were conducted across a range of parameters, systematically varying the electron filling, the strength of the on-site Coulomb repulsion between electrons, and the temperature of the system, revealing a three-maxima structure in the specific heat as a function of electron filling, particularly in strongly correlated regimes. This unusual specific heat profile is explained by a decomposition of the total specific heat into kinetic and potential contributions, where the kinetic contribution arises from the movement of electrons and the potential contribution stems from the interactions between them.

Further analysis of the kinetic contribution in momentum space revealed a density anomaly, a change in the material’s density with temperature, detectable through the thermal expansion coefficient, establishing a connection between the specific heat behaviour and the thermal expansion coefficient, providing a pathway for experimental verification using cold-atom experiments. Importantly, researchers demonstrate a link between this thermal expansion anomaly and the well-known change of sign in the Seebeck coefficient, a measure of a material’s thermoelectric properties, providing a new perspective on understanding the origin of the Seebeck coefficient change and potentially leading to improved thermoelectric materials.

The resulting data generates a detailed phase diagram, delineating regions exhibiting metallic, insulating, and other behaviours, extending beyond the commonly studied half-filling regime and offering a new perspective on the behaviour of correlated electron systems. Heat maps effectively visualise the behaviour of the derivative of specific heat with respect to density across varying densities and interaction strengths, providing a comprehensive overview of the system’s phase space and pinpointing potential phase boundaries.

This study contributes to a more nuanced understanding of strongly correlated electron systems and their potential for novel applications, bridging the gap between theoretical modelling, computational simulation, and experimental observation. By focusing on quantities accessible in cold atom experiments, the study provides a direct link between theoretical predictions and real-world measurements, facilitating the validation of theoretical models and guiding future experimental investigations into the behaviour of strongly correlated materials. The detailed analysis of the kinetic contribution to the specific heat in momentum space offers a new perspective on the density anomaly and its connection to the Seebeck coefficient, expanding the understanding of thermoelectric properties in strongly correlated systems and opening avenues for exploring new materials with enhanced thermoelectric performance.

This research paves the way for the design of novel materials with tailored properties and enhances our fundamental understanding of the complex behaviour of matter under extreme conditions.