Timeline for Why the ground-state energy of S-1/2 Anti-Ferromagnetic Heisenberg Chain is not$-\frac{N}{4}J$
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 24, 2022 at 6:00 | vote | accept | PhyDuck | ||
| Dec 24, 2022 at 6:00 | vote | accept | PhyDuck | ||
| Dec 24, 2022 at 6:00 | |||||
| Dec 11, 2022 at 17:53 | comment | added | Norbert Schuch | That's true, it gives an intuition where the deviation comes from. -- But that it is lower is not surprising: After all, the ground state energy can never be above any variational state you write down (I mean, it is the smallest of all possible variational energies.) | |
| Dec 11, 2022 at 17:48 | comment | added | eapovo | Haha, no I am not. It does still provide for an explanation for why the ground state differs from the Néel state and why its energy is lower. | |
| Dec 11, 2022 at 17:42 | comment | added | Norbert Schuch | Are you saying that 6.5 is a better approximation to 4.5 than 2.5 is? | |
| Dec 11, 2022 at 17:07 | comment | added | eapovo | The authors of [1] actually show that the quantum correction to the order parameter diverge so you are right about that. One can, however, calculate the energy with OP's parameters and obtain around -6.5, which seems like a reasonable approximation. | |
| Dec 11, 2022 at 16:45 | comment | added | Norbert Schuch | Because AFAIR, spin wave theory is a basically perturbation theory on top of a mean-field state, here an AFM. But the Heisenberg chain is gapless, so I'm not sure how well a perturbative approach will work (as perturbation theory typically requires a gap). -- In fact, I would not be surprised if there is some kind of divergence here: E.g., the intuitive reasoning behind the Mermin-Wagner Theorem (absence of symmetry breaking in certain models at finite temperature) is that if there were symmetry breaking, one could do spin-wave theory, which in turn would lead to a divergent correction. | |
| Dec 11, 2022 at 16:11 | comment | added | eapovo | I am not sure about the implications of an energy gap here. Why do you think it affects the applicability of spin-wave theory? | |
| Dec 11, 2022 at 15:49 | comment | added | Norbert Schuch | Isn't spin wave theory more suitable for gapped Hamiltonians? | |
| Dec 11, 2022 at 15:39 | history | answered | eapovo | CC BY-SA 4.0 |