Understanding Ground State Degeneracy in the Transverse Ising Model

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SUMMARY

The discussion focuses on the ground state degeneracy in the Transverse Ising Model, specifically addressing how perturbation theory reveals that degeneracy is lifted only at N'th order in a weak magnetic field limit for a lattice of N spins. Participants seek comprehensive references or textbooks that thoroughly cover degenerate perturbation calculations within this context. The Transverse Ising Model serves as a critical framework for understanding quantum phase transitions and magnetic properties in condensed matter physics.

PREREQUISITES
  • Understanding of quantum mechanics and perturbation theory
  • Familiarity with the Transverse Ising Model
  • Knowledge of ground state properties in quantum systems
  • Basic concepts of lattice models in statistical mechanics
NEXT STEPS
  • Research degenerate perturbation theory in quantum mechanics
  • Explore advanced textbooks on the Transverse Ising Model, such as "Quantum Phase Transitions" by Subir Sachdev
  • Study the implications of magnetic fields on quantum systems
  • Investigate numerical methods for analyzing ground state properties in lattice models
USEFUL FOR

Physicists, graduate students in condensed matter physics, and researchers interested in quantum phase transitions and the mathematical treatment of ground state degeneracy.

thatboi
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Hi all,
I was wondering if there was a reference/textbook where the degenerate perturbation calculation for the Transverse Ising model was treated fully. I want to better understand how in the weak magnetic field limit, the ground state degeneracy only lifts at N'th order in perturbation theory (for a lattice of N spins).
 

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