Question

I was wondering if there is anywhere a formal proof that shows that the ground state energy of a Heisenberg XXX model with periodic boundary conditions becomes equal to the ground state energy with open boundary conditions.

Basically does the ground state energy that you can analytically compute for the Heisenberg model on a cyclic chain becomes that of the straight chain in the limit to infinity? I'm assuming it does, but can't find a rigorous proof somewhere. Any help would be appreciated!

Answer 1

The ground state energy of a Heisenberg XXX model with periodic boundary conditions becomes equal to the ground state energy with open boundary conditions in the limit to infinity.

Step-by-step explanation:

The ground state energy of a Heisenberg XXX model with periodic boundary conditions becomes equal to the ground state energy with open boundary conditions in the limit to infinity. However, there is no formal proof available for this specific model.

The equality of ground state energies with different boundary conditions can be attributed to the principle of ergodicity, where the system explores all configurations and averages out the effects of the boundary conditions.