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Entanglement in a valence-bond solid state.

Heng Fan1, Vladimir Korepin, Vwani Roychowdhury

  • 1Electrical Engineering Department, University of California at Los Angeles, Los Angeles, California 90095, USA.

Physical Review Letters
|December 17, 2004
PubMed
Summary
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We investigated quantum entanglement in a valence-bond solid state. Entanglement properties of subsystems were found to be independent of chain size and location, approaching a constant value as subsystem size increases.

Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Quantum information theory

Background:

  • The valence-bond solid state is a key model for understanding quantum magnetism.
  • Entanglement is a fundamental resource in quantum mechanics, crucial for quantum information processing.

Purpose of the Study:

  • To characterize entanglement in the Affleck-Kennedy-Lieb-Tasaki (AKLT) quantum spin chain ground state.
  • To investigate how entanglement scales with subsystem size and its independence from system parameters.

Main Methods:

  • Calculation of subsystem entanglement entropy.
  • Evaluation of concurrence for specific subsystems.
  • Analysis of the reduced density matrix for blocks of spins.

Main Results:

Related Experiment Videos

  • The reduced density matrix of a continuous block of bulk spins is independent of chain size and block location.
  • Entanglement of a block with the rest of the system saturates exponentially with increasing block size.
  • Entanglement of end spin-1/2 qubits and pairs of bulk spins with the remainder of the system was quantified.

Conclusions:

  • The AKLT spin chain exhibits robust and predictable entanglement properties.
  • Entanglement in this system shows characteristics of topological order.
  • The findings provide insights into the nature of entanglement in one-dimensional quantum many-body systems.