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Lifshitz phase transitions in a one-dimensional Gamma model.

Zi-An Liu1,2, Tian-Cheng Yi1,2, Jin-Hua Sun3

  • 1College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China.

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Summary

This study explores quantum phase transitions in a spin-1/2 Gamma model. Competing interactions lead to Lifshitz transitions and topological changes in the Fermi surface, signaled by entanglement measures.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Magnetism
  • Materials Science

Background:

  • The Gamma model describes off-diagonal exchange interactions in one-dimensional systems.
  • Strong spin-orbit couplings are crucial for understanding magnetic properties.

Purpose of the Study:

  • Investigate quantum phase transitions and magnetic properties of the spin-1/2 Gamma model.
  • Analyze the role of competing exchange interactions on the ground state.
  • Characterize the rich phase diagram and Lifshitz transitions.

Main Methods:

  • Theoretical study of a one-dimensional spin-1/2 Gamma model.
  • Analysis of competing nearest-neighbor and second-neighbor interactions.
  • Investigation of spinless fermion semimetallic ground states.
  • Topological characterization of Fermi surface using Weyl nodes.

Main Results:

  • Identified a rich phase diagram with three gapless phases.
  • Observed Lifshitz transitions characterized by changes in Weyl node types (I and II).
  • Found a coexistence of type-I and type-II Weyl nodes in phase II.
  • Demonstrated that entanglement measures (concurrence, entropy) signal second-order transitions.

Conclusions:

  • The Gamma model provides an exactly solvable platform for studying Lifshitz transitions.
  • Topological changes in the Fermi surface occur without symmetry breaking.
  • Entanglement measures are effective indicators of quantum phase transitions in correlated electron systems.