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
15 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 15:39 | answer | added | eapovo | timeline score: 4 | |
| Dec 11, 2022 at 14:23 | comment | added | PhyDuck | @NorbertSchuch OK, Thanks a lot for the tips!! I'm going to try to solve the 2-site problem to get the form. | |
| Dec 11, 2022 at 14:08 | comment | added | Norbert Schuch | By the way, the true ground state is complicated, so I'm not sure what answer you expect to "Then what is the true ground state of it?" | |
| Dec 11, 2022 at 14:07 | comment | added | Norbert Schuch | So the energy of your proposed state is higher, so it is not the ground state. -- I suggest you solve the problem for 2 sites by hand, to see what you get: You will see that you don't get the classical antiferromagnet which you propose. | |
| Dec 11, 2022 at 14:02 | history | edited | PhyDuck | CC BY-SA 4.0 |
added 1 character in body
|
| Dec 11, 2022 at 14:01 | comment | added | PhyDuck | @NorbertSchuch Thank you for your reply. For the state I'm pointing out, I think the energy is -NJ/4, because from the first expression of the Hamiltonian, if the neighboring lattice has opposite spins, it gives a negative maximum, and that's why I think this is the ground state. By the way, you're right, the energy should be negative, which is -4.5154 | |
| Dec 11, 2022 at 13:57 | history | edited | Norbert Schuch |
edited tags
|
|
| Dec 11, 2022 at 13:55 | comment | added | Norbert Schuch | BTW, the ground state energy should be negative. Did you forget a minus sign? | |
| Dec 11, 2022 at 13:52 | comment | added | Norbert Schuch | Did you compute the energy of the state you propose? What did you get? Did you try to solve the model on 2 or 3 sites, to see how the ground state looks like? And why to you claim "if J is positive, we can get a anti-ferromagnetic state"? | |
| Dec 11, 2022 at 13:40 | history | edited | PhyDuck | CC BY-SA 4.0 |
added 13 characters in body; edited title
|
| Dec 11, 2022 at 13:36 | history | edited | PhyDuck | CC BY-SA 4.0 |
added 44 characters in body
|
| S Dec 11, 2022 at 13:34 | review | First questions | |||
| Dec 11, 2022 at 14:49 | |||||
| S Dec 11, 2022 at 13:34 | history | asked | PhyDuck | CC BY-SA 4.0 |