Competing Nodal d-Wave Superconductivity and Antiferromagnetism.

Area of Science:

• Condensed Matter Physics
• Quantum Materials Science
• Computational Physics

Background:

• Competing unconventional superconductivity and antiferromagnetism are prevalent in strongly correlated quantum materials.
• Direct simulation of these phenomena is often hindered by the fermion sign problem.

Purpose of the Study:

• To investigate a sign-problem-free repulsive toy model with symmetries analogous to the Hubbard model.
• To map out the distinct phases and transitions in this model using unbiased quantum Monte Carlo simulations.

Main Methods:

• Unbiased quantum Monte Carlo (QMC) simulations on a 2D square lattice.
• Supplementation with mean-field and continuum field-theory arguments.
• Analysis of a sign-problem-free repulsive toy model.

Main Results:

• Identification of three distinct phases: nodal d-wave superconductivity, antiferromagnetism, and a coexisting phase of antiferromagnetism with nodeless d-wave superconductivity.
• Characterization of phase transitions: 2+1-D XY universality class for the transition to antiferromagnetism, and Heisenberg-Gross-Neveu theory for the transition to nodal d-wave superconductivity.
• The phase diagram topology mirrors that of layered organic materials.

Conclusions:

• The sign-problem-free model provides a tractable platform for studying competing orders in quantum materials.
• The findings offer insights into the mechanisms driving transitions between magnetic and superconducting states.
• The resemblance to layered organic materials suggests potential experimental relevance and avenues for further research.