Version 1
: Received: 5 March 2024 / Approved: 5 March 2024 / Online: 6 March 2024 (11:45:13 CET)
How to cite:
Adelhardt, P.; Koziol, J.A.; Langheld, A.; Schmidt, K.P. Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions. Preprints2024, 2024030325. https://doi.org/10.20944/preprints202403.0325.v1
Adelhardt, P.; Koziol, J.A.; Langheld, A.; Schmidt, K.P. Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions. Preprints 2024, 2024030325. https://doi.org/10.20944/preprints202403.0325.v1
Adelhardt, P.; Koziol, J.A.; Langheld, A.; Schmidt, K.P. Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions. Preprints2024, 2024030325. https://doi.org/10.20944/preprints202403.0325.v1
APA Style
Adelhardt, P., Koziol, J.A., Langheld, A., & Schmidt, K.P. (2024). Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions. Preprints. https://doi.org/10.20944/preprints202403.0325.v1
Chicago/Turabian Style
Adelhardt, P., Anja Langheld and Kai Phillip Schmidt. 2024 "Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions" Preprints. https://doi.org/10.20944/preprints202403.0325.v1
Abstract
Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum-optical platforms promises to gain deep insights in quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows to extract high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo which enables calculations on large finite systems. Finite-size scaling can then be used to determine physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations.
Keywords
quantum spin systems; long-range interactions; Ising interactions; XY interactions; Heisenberg interactions; Monte Carlo; series expansion; perturbative continuous unitary transformation; stochastic series expansion; quantum phase transitions; critical exponents; quantum simulation
Subject
Physical Sciences, Theoretical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
