Universal order parameters and quantum phase transitions: a finite-size approach

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Statistical Mechanics

Background:

• Quantum phase transitions (QPTs) are fundamental phenomena in many-body systems.
• Identifying universal order parameters is crucial for characterizing QPTs.
• Traditional methods face challenges with finite-size systems and numerical limitations.

Purpose of the Study:

• To propose a novel method for constructing universal order parameters in finite-size lattice systems.
• To establish a connection between quantum state properties and QPT characterization.
• To enable robust finite-size scaling analysis for QPTs.

Main Methods:

• Exploiting H-orthogonality of near-degenerate lowest energy states.
• Connecting fidelity per site between H-orthogonal states to the energy gap.
• Utilizing density matrix renormalization group (DMRG) for numerical simulations.

Main Results:

• Demonstrated a procedure for constructing universal order parameters.
• Established an explicit link between fidelity, energy gap, and finite-size fluctuations.
• Successfully applied the method to the 1D q-state Potts model for q=2, 3, 4, 5.

Conclusions:

• The proposed method provides a universal approach to order parameters for QPTs.
• Finite-size fluctuations and energy gaps encode essential physical information for QPTs.
• This technique enhances the capabilities of numerical algorithms in studying QPTs.