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On Magnetic Models in Wavefunction Ensembles.

Leonardo De Carlo1,2, William D Wick3

  • 1Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56126 Pisa, Italy.

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Summary
This summary is machine-generated.

Thermodynamics in a wavefunction-only view requires ensembles of wavefunctions. We found finite-temperature phase transitions in quantum spin models only occur with indistinguishable particles and blocked macroscopic superpositions.

Keywords:
large deviationsquantum magnetismwavefunction ensembles

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Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Thermodynamics

Background:

  • Thermodynamics traditionally relies on ensembles of states.
  • A wavefunction-only philosophy necessitates recasting thermodynamics using ensembles of wavefunctions.

Purpose of the Study:

  • To construct Gibbs ensembles for magnetic quantum spin models.
  • To investigate the possibility of finite-temperature phase transitions in these models.

Main Methods:

  • Constructing Gibbs ensembles for quantum spin models.
  • Analyzing the mean-field (Curie-Weiss) model.
  • Applying probability theory and large deviation results (Gärtner-Ellis Theorem).
  • Utilizing computer analysis for complex cases.

Main Results:

  • No finite-temperature phase transitions observed in models with free boundary conditions and distinguishable spins due to high phase space dimensionality.
  • No phase transitions found in the mean-field model with standard quantum mechanical energy, even with exchange symmetry.
  • A variant model with "wavefunction energy" exhibits a phase transition to a magnetized state.

Conclusions:

  • Magnetization in large wavefunction spin chains emerges only with indistinguishable particles and energy conservation blocking macroscopic superpositions.
  • The choice between Gibbs and Boltzmann/Einstein entropy is crucial for quantum thermodynamic ensembles.