Related Experiment Video
Updated: Jul 25, 2026
05:20
Characterization of Thermal Transport in One-dimensional Solid Materials
Published on: January 26, 2014
Compressibility divergence and the finite temperature Mott transition
G Kotliar1, Sahana Murthy, M J Rozenberg
1Serin Physics Laboratory, Rutgers University, 136 Frelinghuysen Road, Piscataway, New Jersey 08854, USA.
Physical Review Letters
|July 30, 2002
Summary
We investigated compressibility near the Mott transition using dynamical mean-field theory (DMFT) and quantum Monte Carlo simulations. Our findings reveal a divergence, offering insights into materials like cerium.
Area of Science:
- Condensed Matter Physics
- Strongly Correlated Electron Systems
Background:
- The Mott transition is a fundamental phenomenon in condensed matter physics, separating metallic and insulating states in materials.
- Understanding the behavior of electron systems near this transition is crucial for predicting material properties.
- Dynamical mean-field theory (DMFT) is a powerful tool for studying strongly correlated systems.
Purpose of the Study:
- To investigate the behavior of compressibility near the density-driven Mott transition at finite temperatures.
- To explore the applicability of DMFT and quantum Monte Carlo simulations to the Hubbard model.
- To connect these findings to experimental observations, such as the alpha-gamma phase transition in cerium.
Main Methods:
- Application of dynamical mean-field theory (DMFT) to the one-band and two-band Hubbard models.
- Utilizing quantum Monte Carlo (QMC) simulations to corroborate DMFT results.
- Analysis within the framework of Landau theory to interpret the observed phenomena.
Main Results:
- Demonstrated a divergence in compressibility near the Mott transition.
- Confirmed this divergence using both DMFT and QMC simulations across different Hubbard models.
- Established a theoretical link between the Mott transition and the alpha-gamma endpoint in cerium.
Conclusions:
- Compressibility divergence is a key characteristic of the Mott transition at finite temperatures.
- DMFT and QMC provide consistent and reliable predictions for strongly correlated systems.
- The study offers a theoretical framework for understanding phase transitions in materials like cerium.
Related Concept Videos
02:31Phase Transitions
Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to occupy...
02:38Third Law of Thermodynamics
A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
00:59States of Matter and Phase Changes
The internal energy of a substance—the total kinetic energy of all its molecules and the potential energy of their associated forces—depends on the strength of the intermolecular forces in the condensed phases and the pressure exerted on the substance. The internal energy of a substance is the highest in the gaseous state, the lowest in the solid state, and intermediate in the liquid state. Phase transitions are caused by changes in physical conditions, such as temperature and pressure, that...
01:28Magnetostatic Boundary Conditions
An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
01:21Entropy Changes Accompanying Specific Processes
Entropy, a measure of disorder in a system, changes during phase transitions like freezing or boiling. At the transition temperature Ttrs, where two phases are in equilibrium, the phase transition is a reversible process. The entropy change can be calculated from a substance's enthalpy of transition using the equation ΔStrs = ΔtrsH /Ttrs.When a perfect gas expands isothermally from one volume to another, entropy increases logarithmically with volume. Conversely, isothermal compression results...
01:21Phase Transitions
A phase transition is the process in which a substance changes from one state of matter to another, like from a solid to a liquid, liquid to gas, or vice versa, at a specific temperature and under given pressure conditions. This change is spontaneous and is affected by alterations in temperature and pressure. These parameters impact the strength of the forces between molecules (intermolecular forces) in the substance.During a phase transition, both the initial and final phases of the substance...