So for a quantum spin chain, one can easily prove via the partition function that you have a fluctuation-dissipation type relation between the magnetic susceptibility and the variance of the magnetization in cases where the Hamiltonian commutes with the external field.

For example, if I have a Heisenberg Hamiltonian in a transverse field, I can show

$$\frac1\beta\frac{d\langle M\rangle}{dh}=\langle M^2\rangle-\langle M\rangle^2$$

Where $M$ is the magnetization operator, and $\beta$ is the inverse temperature.

My question is whether this relationship should be expected to hold in the thermodynamic limit, i.e. if I let $T\to0$ and the length of the chain go to infinity. The usual derivation would seems to break down.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.