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Entanglement Entropy in the Ising Model with Topological Defects.

Ananda Roy1, Hubert Saleur2,3

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|March 18, 2022
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Summary
This summary is machine-generated.

We present the first lattice computation of entanglement entropy (EE) in conformal field theories (CFTs) with topological defects. Zero-energy modes significantly impact EE, leading to finite-size corrections and altering universal terms, contrary to field-theory predictions.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Field Theory
  • Statistical Mechanics

Background:

  • Entanglement entropy (EE) reveals universal properties of conformal field theories (CFTs), particularly with boundaries or defects.
  • Topological defects in CFTs reflect internal symmetries and have theoretical predictions, but lack lattice computations.

Purpose of the Study:

  • To perform the first ab initio lattice computation of entanglement entropy (EE) for the Ising model with a topological defect.
  • To investigate the impact of topological defects on EE and compare lattice results with field-theory predictions.

Main Methods:

  • Ab initio lattice computation of entanglement entropy.
  • Analysis of the Ising model in the presence of a topological defect.

Main Results:

  • Entanglement entropy depends on the subsystem's geometry relative to the defect.
  • Zero-energy modes introduce significant finite-size corrections to EE.
  • The universal subleading term in EE near the defect differs from field-theory predictions and is linked to zero-energy modes, not the modular S matrix.

Conclusions:

  • Lattice computations are crucial for understanding entanglement entropy in CFTs with topological defects.
  • Zero-energy modes play a vital role in EE, necessitating their inclusion in theoretical models.
  • This study highlights discrepancies between field-theory and lattice results for EE in the presence of topological defects.