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This summary is machine-generated.

This study reveals the microscopic origins of quantum phase transitions (QPT) using collective patterns in the transverse Ising model (TIM). It demonstrates how spin interactions drive systems through distinct phases, offering insights into QPT mechanisms.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Statistical Mechanics

Background:

  • Renormalization-group theory provides a theoretical framework for critical phenomena but lacks microscopic detail.
  • Understanding the microscopic drivers and spin responses during phase transitions remains a challenge.

Purpose of the Study:

  • To investigate the microscopic nature of quantum phase transitions (QPT).
  • To analyze the role of collective structures (patterns) in driving phase transitions.
  • To explore QPT in the one-dimensional transverse Ising model (TIM).

Main Methods:

  • Introduction of 2L collective structures (patterns) for the TIM with L spins.
  • Analysis of pattern contributions to system states (ground, excited states).
  • Systematic exploration for small lattice sizes (L=6-12) and comparison with exact diagonalization.
  • Approximation of the thermodynamic limit (L=128).

Main Results:

  • A clear identification of the quantum phase transition analog at interaction strength Jc=1.
  • Ground-state energies match exact diagonalization for small system sizes.
  • The actual QPT point at Jc=1 is approached as system size increases.
  • The pattern picture provides a microscopic view of phase transitions.

Conclusions:

  • The pattern picture offers a microscopic understanding of phase transitions in the TIM.
  • This approach is valuable for analyzing QPT analogs in quantum simulation platforms.
  • Collective patterns are key to understanding the dynamics of phase transitions.