Spin-S Designer Hamiltonians and the Square Lattice S=1 Haldane Nematic

Area of Science:

• Condensed Matter Physics
• Quantum Magnetism
• Computational Physics

Background:

• Developing quantum spin models with specific symmetries is crucial for understanding exotic phases of matter.
• Marshall positivity and efficient simulation methods like world-line Monte Carlo are key for theoretical and numerical studies.

Purpose of the Study:

• To introduce a general strategy for constructing Marshall-positive lattice spin models with arbitrary spin S.
• To apply this strategy to an S=1 square lattice model and investigate its emergent phases and phase transitions.

Main Methods:

• Formulation of spin rotational symmetric Hamiltonians that are Marshall positive.
• Efficient simulation using world-line Monte Carlo methods.
• Design of a (3x3)-spin plaquette interaction for an S=1 square lattice model.

Main Results:

• The S=1 model exhibits a novel "Haldane nematic" phase characterized by spontaneous Haldane chain formation.
• This phase breaks lattice rotational symmetry but preserves spin rotations, time reversal, and lattice translations.
• The transition between the Néel and Haldane nematic phases is identified as first-order.

Conclusions:

• The proposed strategy enables the creation of novel quantum spin models for simulation.
• The discovered Haldane nematic phase offers new insights into symmetry breaking in quantum magnets.
• The first-order nature of the Néel-Haldane nematic transition provides a benchmark for theoretical models.