Rajah P. Nutakki, Ludovic D. C. Jaubert, Lode Pollet
SciPost Phys. 15, 040 (2023) ·
published 1 August 2023
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The centred pyrochlore lattice is a novel geometrically frustrated lattice, realized in the metal-organic framework Mn(ta)$_2$ [Phys. Rev. Research 5, L022018 (2023)] where the basic unit of spins is a five site centred tetrahedron. Here, we present an in-depth theoretical study of the $J_1-J_2$ classical Heisenberg model on this lattice, using a combination of mean-field analytical methods and Monte Carlo simulations. We find a rich phase diagram with low temperature states exhibiting ferrimagnetic order, partial ordering, and a highly degenerate spin liquid with distinct regimes of low temperature correlations. We discuss in detail how the regime displaying broadened pinch points in its spin structure factor is consistent with an effective description in terms of a fluid of interacting charges. We also show how this picture holds in two dimensions on the analogous centred kagome lattice and elucidate the connection to the physics of thin films in ($d+1$) dimensions. Furthermore, we show that a Coulomb phase can be stabilized on the centred pyrochlore lattice by the addition of further neighbour couplings. This demonstrates the centred pyrochlore lattice is an experimentally relevant geometry which naturally hosts emergent gauge fields in the presence of charges at low energies.
SciPost Phys. Codebases 9 (2022) ·
published 29 November 2022
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We present a novel and open-source implementation of the worm algorithm, which is an algorithm to simulate Bose-Hubbard and sign-positive spin models using a path-integral representation of the partition function. The code can deal with arbitrary lattice structures and assumes spin-exchange terms, or bosonic hopping amplitudes, between nearest-neighbor sites, and local or nearest-neighbor interactions of the density-density type. We explicitly demonstrate the near-linear scaling of the algorithm with respect to the system volume and the inverse temperature and analyze the autocorrelation times in the vicinity of a $U(1)$ second order phase transition. The code is written in such a way that extensions to other lattice models as well as closely-related sign-positive models can be done straightforwardly on top of the provided framework.
SciPost Phys. Codebases 9-r1.0 (2022) ·
published 29 November 2022
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We present a novel and open-source implementation of the worm algorithm, which is an algorithm to simulate Bose-Hubbard and sign-positive spin models using a path-integral representation of the partition function. The code can deal with arbitrary lattice structures and assumes spin-exchange terms, or bosonic hopping amplitudes, between nearest-neighbor sites, and local or nearest-neighbor interactions of the density-density type. We explicitly demonstrate the near-linear scaling of the algorithm with respect to the system volume and the inverse temperature and analyze the autocorrelation times in the vicinity of a $U(1)$ second order phase transition. The code is written in such a way that extensions to other lattice models as well as closely-related sign-positive models can be done straightforwardly on top of the provided framework.
SciPost Phys. Lect. Notes 2 (2018) ·
published 11 June 2018
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These notes are intended as a detailed discussion on how to implement the diagrammatic Monte Carlo method for a physical system which is technically simple and where it works extremely well, namely the Fröhlich polaron problem. Sampling schemes for the Green function as well as the self-energy in the bare and skeleton (bold) expansion are disclosed in full detail. We discuss the Monte Carlo updates, possible implementations in terms of common data structures, as well as techniques on how to perform the Fourier transforms for functions with discontinuities. Control over the variety of parameters, especially in the bold scheme, is demonstrated. Sample codes are made available online along with extensive documentation. Towards the end, we discuss various extensions of the method and their applications. After working through these notes, the reader will be well equipped to explore the richness of the diagrammatic Monte Carlo method for quantum many-body systems.
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in Submissions | report on Efficient and scalable Path Integral Monte Carlo Simulations with worm-type updates for Bose-Hubbard and XXZ models