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Phase Transitions02:31

Phase Transitions

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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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Phase Transitions: Melting and Freezing02:39

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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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Phase Diagram01:19

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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).
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States of Matter and Phase Changes00:59

States of Matter and Phase Changes

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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...
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Fermi Level01:18

Fermi Level

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The Fermi-Dirac function is represented by an S-shaped curve indicating the probability of an energy state being occupied by an electron at a given temperature. The Fermi level is the energy level at which there is a fifty percent chance of finding an electron, and it is positioned between the lower-energy valence band and the higher-energy conduction band.
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Phase Changes01:19

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Phase transitions play an important theoretical and practical role in the study of heat flow. In melting or fusion, a solid turns into a liquid; the opposite process is freezing. In evaporation, a liquid turns into a gas; the opposite process is condensation.
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Measurement-Induced Phase Transition for Free Fermions above One Dimension.

Igor Poboiko1, Igor V Gornyi1, Alexander D Mirlin1

  • 1Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany and Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany.

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Researchers developed a theory for measurement-induced entanglement phase transitions in free-fermion models. This critical point separates gapless and area-law phases, with implications for quantum information and condensed matter physics.

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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics
  • Statistical Mechanics

Background:

  • Quantum systems can undergo phase transitions driven by measurements.
  • Entanglement properties are crucial for understanding quantum phases.

Purpose of the Study:

  • Develop a theoretical framework for measurement-induced entanglement phase transitions in free-fermion models in d>1 dimensions.
  • Characterize the critical point separating different entanglement phases.

Main Methods:

  • Mapping the problem to an SU(R) replica nonlinear sigma model (R→1).
  • Utilizing renormalization-group analysis for critical index calculation.
  • Performing numerical studies on a 2D square lattice model.

Main Results:

  • Identified a critical point separating a gapless phase (ℓ^{d-1}lnℓ scaling) from an area-law phase (ℓ^{d-1} scaling).
  • Calculated critical indices using one-loop renormalization-group approximation for d=1+ε.
  • Numerically determined the critical point and correlation length critical index (ν≈1.4) for a 2D model.

Conclusions:

  • The developed theory provides a comprehensive understanding of measurement-induced entanglement phase transitions.
  • The findings offer insights into the universal behavior of quantum entanglement under measurement.
  • The study bridges theoretical predictions with numerical validation for quantum phase transitions.