Field Theory vs Lattice: Exploring Differences in Calculations and Results"

In summary, when studying a model in the field theory, there are results that should match up with those found in the lattice. However, when calculations are done in the lattice, results are different. This discrepancy may be due to the size of the system being considered.
  • #1
gonadas91
80
5
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!
 
  • #3
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.
 
  • #4
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.
 
  • #5
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!
 

1. What is the main difference between field theory and lattice calculations?

The main difference between field theory and lattice calculations is the approach used to study and analyze physical systems. Field theory is a theoretical framework that describes the behavior of particles and fields in space and time, while lattice calculations use numerical simulations on a discrete grid to model the behavior of particles in a physical system.

2. Which method is more accurate in predicting results?

Both field theory and lattice calculations have their strengths and limitations, so it is difficult to determine which is more accurate in predicting results. Field theory is more suitable for studying high-energy processes and interactions, while lattice calculations are better for low-energy or strongly interacting systems. It is important to use the appropriate method for the specific physical system being studied.

3. Can field theory and lattice calculations be used together?

Yes, field theory and lattice calculations can be used together to complement each other's strengths. For example, field theory can provide a theoretical framework for interpreting lattice results, while lattice calculations can provide numerical data for testing and refining field theory predictions.

4. How do the computational requirements differ between field theory and lattice calculations?

The computational requirements for field theory and lattice calculations differ significantly. Lattice calculations require a large amount of computing power and resources to simulate physical systems on a discrete grid, while field theory calculations are mostly done analytically and may not require as much computational power. However, as the complexity of the system being studied increases, the computational requirements for both methods also increase.

5. What are the current challenges in using field theory and lattice calculations in research?

Some of the current challenges in using field theory and lattice calculations in research include developing more sophisticated and accurate theoretical models, improving the computational speed and efficiency of simulations, and finding ways to better integrate and combine the results from both methods. Additionally, there is still much to be understood about the limitations and applicability of these methods in different physical systems.

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