Level degeneracy of the transverse ising model

In summary, the level degeneracy of the transverse Ising model refers to the number of energy levels with the same energy value and can be calculated by finding the number of eigenstates with the same energy value. This can be affected by factors such as the strength of the transverse magnetic field and the number of spins, and it is important in understanding the system's properties and behavior. The level degeneracy is also closely related to quantum entanglement and has been shown to be a measure of its amount in the system.
  • #1
wdlang
307
0
the hamiltonian is

H=-J \sum_{l=1}^N \sigma_l^z \sigma_{l+1}^z+ g \sigma_l^x

here we assume periodic boundary condition

my problem is, what is the highest possible degeneracy of the levels?

initially i expected 2

but numerically i find that it is 4

i cannot understand it
 
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  • #2
it is not even 4

it can be higher

i just noticed that since the single particle excitation spectrum is symmetric, the multiple excitation spectrum can be highly degenerate

but i cannot see the symmetry behind
 

Related to Level degeneracy of the transverse ising model

1. What is the level degeneracy of the transverse Ising model?

The level degeneracy of the transverse Ising model refers to the number of energy levels that have the same energy value. In other words, it is the number of distinct states at a particular energy level.

2. How is the level degeneracy of the transverse Ising model calculated?

The level degeneracy of the transverse Ising model can be calculated by finding the number of eigenstates that have the same energy value. This can be done using mathematical techniques such as diagonalization or perturbation theory.

3. What factors affect the level degeneracy of the transverse Ising model?

The level degeneracy of the transverse Ising model can be affected by various factors such as the strength of the transverse magnetic field, the number of spins in the system, and the boundary conditions. Changes in these factors can alter the energy levels and therefore affect the level degeneracy.

4. Why is the level degeneracy of the transverse Ising model important?

The level degeneracy of the transverse Ising model is important because it provides information about the properties and behavior of the system. It can also help in understanding phase transitions and critical points in the system.

5. How does the level degeneracy of the transverse Ising model relate to quantum entanglement?

The level degeneracy of the transverse Ising model is closely related to quantum entanglement. In fact, it has been shown that the level degeneracy is a measure of the amount of entanglement in the system. As the level degeneracy increases, so does the amount of entanglement between the spins in the system.

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