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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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Phase Diagram01:24

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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...
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An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
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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 Rule01:20

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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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Berry Phase in Lattice QCD.

Arata Yamamoto1

  • 1Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan.

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|August 13, 2016
PubMed
Summary
This summary is machine-generated.

We present a lattice quantum chromodynamics (QCD) method to calculate the Berry phase for a single fermion. This approach allows for the computation of topological invariants like the Chern number using Monte Carlo simulations.

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Area of Science:

  • Theoretical Physics
  • High Energy Physics
  • Computational Physics

Background:

  • The Berry phase is a fundamental concept in quantum mechanics, crucial for understanding topological properties of quantum systems.
  • Lattice Quantum Chromodynamics (QCD) provides a non-perturbative framework for studying the behavior of quarks and gluons.

Purpose of the Study:

  • To develop and apply a lattice QCD method for calculating the Berry phase of a single fermion.
  • To demonstrate the utility of this method by computing the first Chern number for a (2+1)-dimensional Wilson fermion.

Main Methods:

  • Ground-state projection of a single-fermion propagator.
  • Construction of the Berry link variable in momentum-space lattice.
  • Monte Carlo simulation for calculating the Berry phase and Chern number.

Main Results:

  • Successfully calculated the Berry phase for a single fermion using lattice QCD.
  • Computed the first Chern number of the (2+1)-dimensional Wilson fermion as a demonstration.

Conclusions:

  • The proposed lattice QCD approach is a viable method for calculating the Berry phase.
  • This method offers a pathway to compute topological invariants in quantum field theories.