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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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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 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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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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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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When a substance—isolated from its environment—is subjected to heat changes, corresponding changes in temperature and phase of the substance is observed; this is graphically represented by heating and cooling curves.
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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Statistical Mechanics

Background:

  • Topological degeneracy in quantum systems is sensitive to perturbations.
  • Understanding quantum phase transitions at finite temperatures is crucial.
  • Non-Hermitian Hamiltonians offer new avenues for exploring quantum phenomena.

Purpose of the Study:

  • To investigate the dynamic response of thermal states in an Ising chain subjected to a nonlocal non-Hermitian perturbation.
  • To determine if the zero-temperature phase diagram is preserved at finite temperatures.
  • To demonstrate the bulk-boundary correspondence at nonzero temperatures.

Main Methods:

  • Analysis of the response of a thermal state in an Ising chain.
  • Introduction of a nonlocal non-Hermitian perturbation.
  • Numerical simulations using Loschmidt echoes for finite-size systems.

Main Results:

  • The perturbation coalesces topological Kramer-like degeneracy in the ferromagnetic phase.
  • Dynamic responses differ for initial thermal states in distinct quantum phases.
  • Final states in the ferromagnetic phase approach a half component with fixed parity, while paramagnetic phase states remain largely unchanged.
  • The zero-temperature phase diagram is preserved at finite temperatures.
  • Bulk-boundary correspondence is manifested at nonzero temperatures.

Conclusions:

  • Quantum phase transitions in Ising chains can be understood through the dynamics of thermal states under non-Hermitian perturbations.
  • The study provides an alternative approach to analyzing quantum phase transitions at nonzero temperatures.
  • Finite temperature effects do not alter the fundamental phase diagram of the Ising chain in this context.