Second Rényi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries

@article{Estienne2022SecondRE,
  title={Second R{\'e}nyi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries},
  author={Benoit Estienne and Yacine Ikhlef and Andrei Rotaru},
  journal={SciPost Physics},
  year={2022}
}
We consider the entanglement entropy in critical one-dimensional quantum systems with open boundary conditions. We show that the second Rényi entropy of an interval away from the boundary can be computed exactly, provided the same conformal boundary condition is applied on both sides. The result involves the annulus partition function. We compare our exact result with numerical computations for the critical quantum Ising chain with open boundary conditions. We find excellent agreement, and we… 

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References

SHOWING 1-10 OF 114 REFERENCES

Universal parity effects in the entanglement entropy of XX chains with open boundary conditions

We consider the Rényi entanglement entropies in the one-dimensional XX spin-chains with open boundary conditions in the presence of a magnetic field. In the case of a semi-infinite system and a block

Entanglement entropy of two disjoint blocks in critical Ising models

TLDR
Analysis of the scaling of the Renyi and entanglement entropy of two disjoint blocks of critical Ising models as function of their sizes and separations and analytic results based on conformal field theory are presented.

Boundary effects in the critical scaling of entanglement entropy in 1D systems.

TLDR
It is found that open boundary conditions induce an alternating term in both the energy density and the entanglement entropy which are approximately proportional, decaying away from the boundary with a power law.

Entanglement entropy of two disjoint intervals in c = 1 theories

TLDR
The analytic conformal field theory result for the second order Rényi entropy for a free boson compactified on an orbifold describing the scaling limit of the Ashkin–Teller (AT) model on the self-dual line is provided.

Entanglement entropies in conformal systems with boundaries

We study the entanglement entropies in one-dimensional open critical systems, whose effective description is given by a conformal field theory with boundaries. We show that for pure-state systems

Renyi entanglement entropies of descendant states in critical systems with boundaries: conformal field theory and spin chains

We discuss the Renyi entanglement entropies of descendant states in critical one-dimensional systems with boundaries, that map to boundary conformal field theories in the scaling limit. We unify the

Entanglement and boundary critical phenomena

We investigate boundary critical phenomena from a quantum-information perspective. Bipartite entanglement in the ground state of one-dimensional quantum systems is quantified using the Renyi entropy

Entanglement entropy of two disjoint blocks in XY chains

TLDR
The Rényi entanglement entropies of two disjoint intervals in XY chains are studied and it is shown that the asymptotic results for large blocks agree with recent conformal field theory predictions if corrections to the scaling are included in the analysis correctly.

Entanglement entropy of two disjoint intervals in conformal field theory

We study the entanglement of two disjoint intervals in the conformal field theory of the Luttinger liquid (free compactified boson). Tr ρAn for any integer n is calculated as the four-point function

Entanglement entropy in critical quantum spin chains with boundaries and defects

Entanglement entropy (EE) in critical quantum spin chains described by 1+1D conformal field theories contains signatures of the universal characteristics of the field theory. Boundaries and defects in
...