Quantum Monte Carlo Simulations of the 2D Su-Schrieffer-Heeger Model

Area of Science:

• Condensed Matter Physics
• Quantum Simulation
• Materials Science

Background:

• Quantum simulations have advanced the understanding of charge density wave (CDW) phase transitions.
• The Su-Schrieffer-Heeger (SSH) Hamiltonian describes electron-phonon coupling where phonons modulate electron hopping on bonds.
• Previous studies of the SSH model were limited to one dimension using quantum Monte Carlo methods.

Purpose of the Study:

• To investigate the two-dimensional (2D) Su-Schrieffer-Heeger (SSH) model.
• To identify and characterize the ground state phases of the 2D SSH model at half filling.
• To determine the conditions for the onset of a bond ordered wave (BOW) phase and its properties.

Main Methods:

• Numerical simulations of the 2D SSH model.
• Analysis of ground state properties at half filling.
• Investigation of the role of electron-phonon coupling strength.

Main Results:

• A bond ordered wave (BOW) insulator phase is identified in the ground state of the 2D SSH model at half filling.
• A critical electron-phonon coupling strength is required for the onset of the BOW phase in 2D, contrasting with the 1D case.
• The precise nature of the bond ordering pattern was determined, and the critical transition temperature was associated with spontaneous Z_{4} symmetry breaking.

Conclusions:

• The 2D SSH model exhibits a distinct BOW insulating phase.
• The emergence of the BOW phase in 2D is dependent on a critical electron-phonon coupling.
• The study clarifies the nature of bond ordering and identifies symmetry breaking associated with the phase transition.