Is it possible to have a spin chain with both bosons and fermions interacting?

[gonadas91]

Hello, just as a thought, we are used to describe spin systems of either fermions or bosons (for example, the Ising or Heisenber models, where spins are considered to be all of the same type, in both cases fermions).

However, I was wondering if it makes some sense to have a system where, for example, a chain of spins is created with either bosons (integer spin) or fermions (fractional spins), and where they can interact with each other, that is, considering interaction between fermions and bosons as well.

Thanks!

 

[king vitamin]

When you map the 1D Heisenberg model to bosons or fermions, the resulting theory IS interacting. For the Ising or XY spin chains, the mapping to fermions results in a free theory, but the Heisenberg chain can't be mapped to a free system.

 

[gonadas91]

Thanks for the reply but the question is simpler. Imagine we have a one d chain alternating bosons and fermions: does this make sense to be described in a hamiltoniand where the bosons interact with the fermions? In one d, fermions are equivalent to bosons!

 

[king vitamin]

Oh ok, it sounded like you meant a 1D spin chain, which has bosonic or fermionic representations.

I don't see any issue with writing down a Hamiltonian with bosons and fermions interacting in 1D. Of course, there would exist some transformation which maps the bosonic particles into fermions and fermionic particles into bosons, but the two types of particles should remain distinguishable from each other under this transformation.