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Two-site entropy and quantum phase transitions in low-dimensional models.

O Legeza1, J Sólyom

  • 1Research Institute for Solid State Physics and Optics, H-1525 Budapest, P.O. Box 49, Hungary.

Physical Review Letters
|April 12, 2006
PubMed
Summary

We introduce a novel method using two-site von Neumann entropy to detect quantum phase transitions in lattice models. This approach proves more effective than traditional indicators for both fermionic and spin systems.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Information Theory

Background:

  • Quantum phase transitions (QPTs) are fundamental phenomena in low-dimensional systems.
  • Traditional methods for detecting QPTs include analyzing energy gaps and order parameters, which can be challenging in complex models.

Purpose of the Study:

  • To propose and validate a new, more sensitive method for identifying quantum phase transitions.
  • To demonstrate the efficacy of using two-site von Neumann entropy for QPT detection.

Main Methods:

  • Developing a novel approach based on calculating the von Neumann entropy of two adjacent central sites in a long lattice chain.
  • Applying the method to both fermionic and spin lattice models.
  • Comparing the results with traditional indicators like energy gaps, order parameters, and single-site entropy.

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Main Results:

  • The two-site von Neumann entropy effectively indicates quantum phase transitions in low-dimensional lattice models.
  • This method shows superior performance compared to energy gaps, order parameters, and single-site entropy.
  • The approach is versatile, working equally well for both fermionic and spin models.

Conclusions:

  • Two-site von Neumann entropy provides a robust and sensitive measure for detecting quantum phase transitions.
  • The proposed method offers a convenient and powerful tool, particularly when combined with the density-matrix renormalization-group algorithm.