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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...
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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...
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The phase rule describes the relationship between the variance (degrees of freedom), the number of components, and the number of phases in a system at equilibrium.Variance is a concept that denotes the number of independent intensive properties (properties are those that do not depend on the amount of material in the system), such as temperature, pressure, and composition, that can be altered without impacting the number of phases in equilibrium.In a single-component system, such as pure water,...
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Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
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The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules...
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Generalized fidelity susceptibility at phase transitions.

Wen-Long You1, Li He

  • 1College of Physics, Optoelectronics and Energy, Soochow University, Suzhou, Jiangsu 215006, People's Republic of China.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|May 8, 2015
PubMed
Summary

We reveal the connection between quantum fidelity susceptibility (QFS) and dynamical structure factor, proving QFS is a moment of the structure factor. Generalized fidelity susceptibility can detect quantum phase transitions missed by QFS.

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Area of Science:

  • Quantum Many-Body Physics
  • Condensed Matter Theory
  • Quantum Information Science

Background:

  • Quantum fidelity susceptibility (QFS) is a crucial measure for detecting quantum phase transitions.
  • Understanding the relationship between QFS and other fundamental quantities is essential for advancing quantum mechanics.
  • Linear response theory provides a framework for analyzing the response of quantum systems to external perturbations.

Purpose of the Study:

  • To establish the intrinsic relationship between quantum fidelity susceptibility and the dynamical structure factor.
  • To provide a non-perturbative proof for QFS.
  • To explore the applicability of generalized fidelity susceptibility (GFS) in identifying quantum phase transitions.

Main Methods:

  • Derivation of QFS beyond perturbation theory using Lehmann representation.
  • Analysis of QFS as a moment of the dynamical structure factor.
  • Investigation of generalized fidelity susceptibility for operators not directly coupled to driving parameters.

Main Results:

  • A concise proof of QFS beyond perturbation theory is presented.
  • Quantum fidelity susceptibility is identified as the negative-two-power moment of the dynamical structure factor.
  • Generalized fidelity susceptibility exhibits similar scaling behaviors and can detect criticalities missed by QFS.

Conclusions:

  • The study elucidates the fundamental connection between QFS and the dynamical structure factor.
  • Generalized fidelity susceptibility offers a more powerful tool for characterizing quantum phase transitions.
  • The findings contribute to a deeper understanding of quantum criticality and linear response theory.