I Understanding Ground State Degeneracy in the Transverse Ising Model

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The discussion focuses on finding a comprehensive reference or textbook that thoroughly explains the degenerate perturbation theory in the context of the Transverse Ising model. It specifically addresses how the ground state degeneracy is affected in the weak magnetic field limit, noting that it only lifts at the N'th order in perturbation theory for a lattice of N spins. Participants are seeking detailed explanations and examples that clarify this concept. The inquiry highlights the importance of understanding the perturbative effects on ground state properties in quantum systems. Overall, the thread emphasizes the need for accessible educational resources on this advanced topic.
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).
 

Thread 'Angular Momentum Vector and Its Magnitude'

For the quantum state ##|l,m\rangle= |2,0\rangle## the z-component of angular momentum is zero and ##|L^2|=6 \hbar^2##. According to uncertainty it is impossible to determine the values of ##L_x, L_y, L_z## simultaneously. However, we know that ##L_x## and ## L_y##, like ##L_z##, get the values ##(-2,-1,0,1,2) \hbar##. In other words, for the state ##|2,0\rangle## we have ##\vec{L}=(L_x, L_y,0)## with ##L_x## and ## L_y## one of the values ##(-2,-1,0,1,2) \hbar##. But none of these...
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