On the continuum limit of the entanglement Hamiltonian

@article{Eisler2019OnTC,
  title={On the continuum limit of the entanglement Hamiltonian},
  author={Viktor Eisler and Erik Tonni and Ingo Peschel},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2019}
}
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… 

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References

SHOWING 1-10 OF 128 REFERENCES
Analytical results for the entanglement Hamiltonian of a free-fermion chain
We study the ground-state entanglement Hamiltonian for an interval of $N$ sites in a free-fermion chain with arbitrary filling. By relating it to a commuting operator, we find explicit expressions
Properties of the entanglement Hamiltonian for finite free-fermion chains
We study the entanglement Hamiltonian for fermionic hopping models on rings and open chains and determine single-particle spectra, eigenfunctions and the form in real space. For the chain, we find a
On entanglement Hamiltonians of an interval in massless harmonic chains
  • G. Giulio, E. Tonni
  • Physics
    Journal of Statistical Mechanics: Theory and Experiment
  • 2020
We study the continuum limit of the entanglement Hamiltonians of a block of consecutive sites in massless harmonic chains. This block is either in the chain on the infinite line or at the beginning
Entanglement Hamiltonians for non-critical quantum chains
We study the entanglement Hamiltonian for finite intervals in infinite quantum chains for two different free-particle systems: coupled harmonic oscillators and fermionic hopping models with
Entanglement Spectrum of Chiral Fermions on the Torus.
TLDR
The modular Hamiltonian of chiral fermions on the torus is determined, finding that, in addition to a local Unruh-like term, each point is nonlocally coupled to an infinite but discrete set of other points, even for a single interval.
Entanglement Hamiltonian of Interacting Fermionic Models.
TLDR
This work introduces a technique to directly determine the entanglement Hamiltonian of interacting fermionic models by means of auxiliary field quantum Monte Carlo simulations and studies the evolution of the entangling Hamiltonian as a function of the physical temperature.
Free-fermion entanglement and spheroidal functions
We consider the entanglement properties of free fermions in one dimension and review an approach which relates the problem to the solution of a certain differential equation. The single-particle
Entanglement Hamiltonians for Chiral Fermions with Zero Modes.
TLDR
It is shown how Riemann-Hilbert solutions combined with finite rank perturbation theory allow us to obtain exact expressions for entanglement Hamiltonians.
Entanglement properties of the harmonic chain
We study the entanglement properties of a closed chain of harmonic oscillators that are coupled via a translationally invariant Hamiltonian, where the coupling acts only on the position operators. We
Entanglement Hamiltonians in 1D free lattice models after a global quantum quench
We study the temporal evolution of the entanglement hamiltonian of an interval after a global quantum quenchin free lattice models in one spatial dimension. In a harmonic chain we explore a quench of
...
...