Related Experiment Video
Updated: May 18, 2026
05:39
Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
Published on: August 2, 2019
Information geometry and quantum phase transitions in the Dicke model.
Anshuman Dey1, Subhash Mahapatra, Pratim Roy
1Department of Physics, Indian Institute of Technology, Kanpur 208016, India. deyanshu@iitk.ac.in
Summary
We explored the information geometry of the Dicke model, finding its parameter manifold remains smooth and scalar curvature continuous through phase transitions, even without the rotating wave approximation.
Area of Science:
- Quantum optics
- Statistical mechanics
- Information geometry
Background:
- The Dicke model describes light-matter interactions.
- Understanding its thermodynamic limit is crucial.
- Information geometry offers tools to analyze model parameters.
Purpose of the Study:
- To investigate the information geometry of the Dicke model in the thermodynamic limit.
- To calculate the scalar curvature of its parameter space.
- To analyze the model's behavior with and without the rotating wave approximation.
Main Methods:
- Calculation of the Riemannian metric tensor for the Dicke model.
- Computation of the scalar curvature (R).
- Analysis across the phase transition, with and without the rotating wave approximation.
Main Results:
- The parameter manifold of the Dicke model is shown to be smooth.
- The scalar curvature (R) is continuous across the phase boundary.
- The analysis holds true both with and without the rotating wave approximation.
Conclusions:
- The Dicke model's parameter space exhibits smooth information geometric properties.
- Scalar curvature continuity suggests robust behavior at phase transitions.
- The rotating wave approximation does not alter the fundamental smoothness and continuity of the scalar curvature.
Related Concept Videos
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...
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...
02:32The de Broglie Wavelength
In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
01:19Phase Diagram
The phase of a given substance depends on the pressure and temperature. Thus, plots of pressure versus temperature showing the phase in each region provide considerable insights into the thermal properties of substances. Such plots are known as phase diagrams. For instance, in the phase diagram for water (Figure 1), the solid curve boundaries between the phases indicate phase transitions (i.e., temperatures and pressures at which the phases coexist).
01:24Phase Diagram
A phase diagram is a graphical representation of the physical states of a substance under different conditions of temperature and pressure. It shows the boundaries between solid, liquid, and gas phases and the conditions at which these phases coexist in equilibrium. An area in a phase diagram represents a single phase, whereas lines or phase boundaries represent the equilibrium between two phases.In the phase diagram of water, the boundary line between the solid and liquid states illustrates...
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...