# On the continuum limit of the entanglement Hamiltonian

## TL;DR

This paper demonstrates that the lattice entanglement Hamiltonian for free fermions converges to the conformal form in the continuum limit when including long-range hopping, supported by analytical and numerical evidence.

## Contribution

It shows how the lattice entanglement Hamiltonian approaches the conformal form by incorporating distant neighbor hoppings, clarifying the continuum limit behavior.

## Key findings

- Lattice entanglement Hamiltonian converges to conformal form with long-range hopping.
- Analytical derivation for infinite chains at arbitrary fillings.
- Numerical confirmation for finite rings and finite temperatures.

## Abstract

We consider the entanglement Hamiltonian for an interval in a chain of free fermions in its ground state and show that the lattice expression goes over into the conformal one if one includes the hopping to distant neighbours in the continuum limit. For an infinite chain, this can be done analytically for arbitrary fillings and is shown to be the consequence of the particular structure of the entanglement Hamiltonian, while for finite rings or temperatures the result is based on numerical calculations.