Field Theory vs Lattice: Why Do Calculations Yield Different Results?

[gonadas91]

Hello guys! I just just wondering a general thing about calculations done in the field theory and those made in the lattice. In the field theory we have some results that in principle should match with the lattice ones in the thermodynamic limit. However, when we tried to solve the same problem in the lattice, calculations provide a different answer. Maths are checked to be correct

Is there any case when this can happen? That some model can be studied using the field theory but when you go into the lattice, the model provides different answers¿ Thanks!

 

[The_Duck]

Maybe you can be more specific. What field theory are you studying? What quantity disagrees between the lattice and the continuum?

If there is disagreement between lattice and continuum results, that just means you have failed to construct a lattice version of your field theory.

 

[atyy]

One place where it is still not known how to construct lattice versions of a field theory is non-abelian chiral fermions interacting with a gauge field.

 

[gonadas91]

Thanks for the replies, we are studying a many body system, so we work with fermionic operators and we make use of bosonization to obtain the scaling of the renormalized parameter of our model. Bosonization should provide exact results for low energy physics and ground state properties. When we treat the same model in the lattice version, there must be something we are missing out, and maybe it has to be with the size of the system. In the lattice version, we just isolate a specific part of the system, we treat it separatelly with the many body hamiltonian, and later we couple it to a bath, projecting in the low energy subspace. (which is specified by the lowest energy states of the many body hamiltonian)

When we do that, and for the same limit of the interaction parameter we are considering, bosonization gives a result that should be recovered with the lattice version. However, when we project into the low energy subspace, no projection is found, and the renormalized parameter vanishes, contrary to bosonization. We have started to think about the influence of the size of the system, but any ideas for this? Thanks!