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Complexity and information geometry in the transverse XY model.

Nitesh Jaiswal1, Mamta Gautam1, Tapobrata Sarkar1

  • 1Department of Physics, Indian Institute of Technology, Kanpur-208016, India.

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Summary
This summary is machine-generated.

We investigated Nielsen complexity and Fubini-Study complexity in the transverse XY spin chain, finding nonanalyticity at critical lines. Our study reveals their distinct scaling behaviors near quantum phase transitions.

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Area of Science:

  • Quantum information theory
  • Condensed matter physics
  • Statistical mechanics

Background:

  • Quantum complexity is crucial for understanding quantum systems.
  • Nielsen and Fubini-Study complexities offer different perspectives on quantum states.
  • The transverse XY spin chain is a key model for studying quantum phase transitions.

Purpose of the Study:

  • To analyze Nielsen and Fubini-Study complexities in the transverse XY spin chain.
  • To identify nonanalytic behavior of these complexities at critical lines.
  • To determine the scaling of complexities near quantum phase transitions.

Main Methods:

  • Analytical calculations for Nielsen and Fubini-Study complexities.
  • Investigation of scaling behavior near quantum criticality.
  • Numerical analysis for generic cases of Fubini-Study complexity.

Main Results:

  • Established nonanalyticity of both complexities at critical lines.
  • Derived scaling behaviors near quantum phase transitions in the thermodynamic limit.
  • Obtained analytic expressions for Fubini-Study complexity in special cases.
  • Demonstrated distinct characteristics of Nielsen and Fubini-Study complexities.

Conclusions:

  • Nielsen and Fubini-Study complexities exhibit different behaviors in the transverse XY model.
  • Complexity measures provide insights into quantum phase transitions.
  • The study highlights the importance of choosing appropriate complexity measures for specific physical systems.