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Jiaju Zhang1, Paola Ruggiero1, Pasquale Calabrese1,2

  • 1SISSA and INFN, Via Bonomea 265, 34136 Trieste, Italy.

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This summary is machine-generated.

We developed a new method to calculate quantum entanglement using trace distance in 1+1 dimensional quantum field theories. This approach provides universal results for short intervals in conformal field theories, matching numerical simulations.

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Area of Science:

  • Quantum Field Theory
  • Condensed Matter Physics

Background:

  • Calculating quantum entanglement is crucial for understanding complex quantum systems.
  • Reduced density matrices quantify entanglement in subsystems.
  • Existing methods for trace distance calculation can be computationally intensive.

Purpose of the Study:

  • To develop a systematic and efficient method for calculating the trace distance between reduced density matrices.
  • To apply this method to conformal field theories (CFTs) in 1+1 dimensions.
  • To derive universal formulas for trace distance in specific regimes.

Main Methods:

  • Utilizing path integral representations of reduced density matrices.
  • Employing an ad hoc replica trick for calculations.
  • Applying operator product expansion (OPE) of twist operators for short intervals.

Main Results:

  • A systematic method for trace distance calculation in 1+1D QFTs.
  • A universal formula for the leading order of trace distance in short intervals of CFTs.
  • Exact calculations for free massless boson and fermion theories.
  • Agreement between analytical CFT results and numerical simulations of spin chains.

Conclusions:

  • The developed method is effective for calculating quantum entanglement measures.
  • The findings offer insights into the structure of entanglement in CFTs.
  • The results are validated by numerical computations, confirming the analytical predictions.