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18
votes
3answers
1k views

Prove that negative absolute temperatures are actually hotter than positive absolute temperatures

Could someone provide me with a mathematical proof of why, a system with an absolute negative Kelvin temperature (such that of a spin system) is hotter than any system with a positive temperature (in ...
9
votes
3answers
993 views

To calculate the correlation functions of an XX spin chain, Wick's theorem is used. But is it valid for a chain of any size?

The correlation functions found in Barouch and McCoy's paper (PRA 3, 2137 (1971)) for the XX spin chain use a method which uses Wick's theorem. For the zz correlation function, this gives $\langle ...
8
votes
1answer
745 views

Dual conformal symmetry and spin networks in ABJM

In this question, I would love to hear some independent opinions on an issue I asked Juan Maldacena, Nathan Berkovits, Dan Jafferis, and others, but all the physicists may be missing something. The ...
8
votes
0answers
268 views

Lower bounds on spectral gaps of ferromagnetic spin-1/2 XXX Hamiltonians?

Question. Are there any references or techniques which can be applied to obtain energy gaps for ferromagnetic XXX spin-1/2 Hamitlonians, on general interaction graphs, or tree-graphs? I'm interested ...
5
votes
1answer
188 views

Interpretation of the 1D transverve field Ising model vacuum state in a spin-language

The 1D transverse field Ising model, \begin{equation} H=-J\sum_{i}\sigma_i^z\sigma_{i+1}^z-h\sum_{i}\sigma^x_i, \end{equation} can be solved via the Jordan-Wigner (JW) transformation (for further ...
4
votes
1answer
255 views

Have the correlation functions of the XY spin chain model been calculated using a functional partition function with source terms?

Have the correlation functions of the XY spin chain model, \begin{equation} H=-\sum_l (J_x \sigma_l^x \sigma_{l+1}^x+J_x \sigma_l^y \sigma_{l+1}^y)-B\sum_l \sigma_l^z \end{equation} been calculated ...
3
votes
1answer
72 views

How do we determine the statistics and spin of quasi-particles?

I am considering the Heisenberg XXZ model at the moment. In the literature it says that (in the $J\Delta\rightarrow\infty$ limit, i.e. the ferromagnetic Ising regime) one can either view low-energy ...
3
votes
1answer
184 views

Undefined amplitudes in the Coordinate Bethe Ansatz for the XXX model?

Rather specific question for someone familiar with the Coordinate Bethe Ansatz... I am considering the Heisenberg XXX-model, consisting of a one-dimensional chain of L sites with a spin-1/2 particle ...
3
votes
1answer
569 views

What is a free fermion model?

Title says it all really.. Why is the XX spin chain a free fermion (non-interacting) model, and the XXZ chain not? Is it right that $\sum_l a_l^\dagger a_{l+1}$ isn't an interaction between fermions ...
3
votes
1answer
727 views

Some limiting cases of the Heisenberg XXZ model (2/2)

NOTE: Because this was a long question I have split it up in two different questions! For a course on quantum integrability I am reading these notes. (Franchini: Notes on Bethe Ansatz Techniques. ...
2
votes
0answers
140 views

Spontaneous symmetry breaking in the quantum 1D XX model?

The ground states of the quantum 1D Ising and Heisenberg models exhibit spontaneous magnetization. Is this also true for the 1D XX model?
1
vote
1answer
1k views

Simularity transformation of Heisenberg XXZ Hamiltonian

I am considering the Heisenberg XXZ Hamiltonian: $$ H(\Delta, J) = J\sum_{i=1}^L\left(\sigma^x_i\sigma^x_{i+1} + \sigma^y_i\sigma^y_{i+1} + \Delta \sigma^z_i\sigma^z_{i+1} \right) $$ Apparently, one ...
1
vote
0answers
132 views

What does it mean for a quantum spin chain to be “low energy”?

Is it another way of saying the ground state?
0
votes
1answer
263 views

Seeking a specific quantum spin system of interacting spin 1/2 particles

Is there a system of interacting quantum spin 1/2 particles (of any topology) whose the states where all spins are up or down are eigenstates of its Hamiltonian and yet does not conserve the total ...