Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions

Area of Science:

• Condensed matter physics
• Quantum optics

Background:

• Long-range interactions are crucial in quantum systems, influencing quantum optics and condensed matter physics.
• Understanding quantum-critical properties in systems with long-range interactions is challenging theoretically.

Purpose of the Study:

• To provide an overview of recent advancements in investigating quantum magnets with long-range interactions.
• To summarize quantum-critical properties and phase transitions in various 1D and 2D quantum magnets.

Main Methods:

• Utilizing two Monte Carlo integration techniques: perturbative continuous unitary transformations (PCUT) and stochastic series expansion (SSE).
• PCUT with white graph embedding for high-order series expansions in the thermodynamic limit.
• SSE for calculations on large finite systems, employing finite-size scaling for infinite system properties.

Main Results:

• Successful application of PCUT and SSE to 1D and 2D quantum magnets with Ising, XY, and Heisenberg interactions.
• Determination of quantum-critical properties, including critical exponents, for diverse lattice structures.
• Exploration of quantum phase transitions above the upper critical dimension.

Conclusions:

• Monte Carlo methods offer powerful tools for studying complex quantum magnetic systems.
• These techniques enable accurate determination of quantum-critical properties and scaling behaviors.
• Advancements provide deeper insights into the role of long-range interactions in quantum phenomena.