SmoQyDQMC

Documentation for SmoQyDQMC.jl. This package implements the determinant quantum Monte Carlo (DQMC) method for Hubbard, and electron-phonon interactions, including both Holstein and Su-Schrieffer-Heeger (SSH) style electron-phonon coupling.

Funding

Initial development of the v1.0 version of this package was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Award Number DE-SC0022311. Further development of the v2.0 version of this package was supported by the National Science Foundation under grant No. OAC-2410280 and the Simons Foundation under a Scientific Software Research Faculty award.

Installation

To install the SmoQyDQMC.jl, simply open the Julia REPL and run the commands

julia> ]
pkg> add SmoQyDQMC

or equivalently via Pkg do

julia> using Pkg; Pkg.add("SmoQyDQMC")

Updating

To update SmoQyDQMC.jl try the following:

julia> ]
pkg> update SmoQyDQMC

However, sometimes this fails to update required dependencies. If issues arise, we recommend first removing and then reinstalling SmoQyDQMC.jl:

julia> ]
pkg> remove SmoQyDQMC
pkg> add SmoQyDQMC

Publication List

This sections lists of some of the publications that report results generated using the SmoQyDQMC.jl package.

[1]: C. McCabe, J. Boyd, K. Wang, M. Lebrat, C. Regal, A. Kaufman, A. M. Rey and L. Homeier. Realizing multi-orbital Emery models with ultracold atoms, arXiv preprint arXiv:2604.22955 (2026).
[2]: F. Correia, K. Corbett and E. Khatami. Finite-Temperature Ferromagnetic Correlations of the Kagome Lattice Hubbard Model, arXiv preprint arXiv:2604.26827 (2026).
[3]: C. Jordan, G. Issa, E. Khatami, R. Scalettar, B. Cohen-Stead and S. Johnston. Charge order in the half-filled bond-Holstein model. Phys. Rev. B 113, 235101 (2026).
[4]: H. Liu, L. Zhang and T. Ma. Tuning superconductivity and charge density wave order by next-nearest-neighbor hopping integral in honeycomb Holstein model. Phys. Rev. B 113, 205153 (2026).
[5]: S. Malkaruge Costa, B. Cohen-Stead and S. Johnston. Antiferromagnetism and Kekulé valence bond order in the honeycomb optical Su-Schrieffer-Heeger-Hubbard model. Phys. Rev. B 113, 115138 (2026).
[6]: J. Nys and J. Carrasquilla. Fermionic neural Gibbs states, arXiv preprint arXiv:2512.04663 (2025).
[7]: Q. Li, D.-W. Qu, B.-B. Chen, T. Shi and W. Li. Thermal tensor network simulations of lattice fermions with fixed filling. Phys. Rev. B 113, 085150 (2026).
[8]: M. Naamneh, E. C. O'Quinn, E. Paris, D. McNally, Y. Tseng, W. R. Pudełko, D. J. Gawryluk, J. Shamblin, B. Cohen-Stead, M. Shi, M. Radovic, M. K. Lang, T. Schmitt, S. Johnston and N. C. Plumb. Persistence of small polarons into the superconducting doping range of $\text{Ba}_{1\text{-}x}\text{K}_{x}\text{BiO}_{3}$. Phys. Rev. Res. 7, 043082 (2025).
[9]: A. Al-Eryani, S. Andergassen and M. M. Scherer. Intertwined fluctuations and isotope effects in the Hubbard-Holstein model on the square lattice from functional renormalization. Phys. Rev. Res. 7, 043052 (2025).
[10]: J. Xiong, H. Li, Y. Su and D. Li. Application of many-body nonperturbative theories to the three-dimensional attractive Hubbard model. Phys. Rev. B 112, 064509 (2025).
[11]: Y. Su, R. Xiao, J. Xiong, H. Li, H. Huang and D. Li. Nonpertubative Many-Body Theory for the Two-Dimensional Hubbard Model at Low Temperature: From Weak to Strong Coupling Regimes, arXiv preprint arXiv:2503.12468 (2025).
[12]: Y. Zhang, P. M. Dee, B. Cohen-Stead, T. A. Maier, S. Johnston and R. Scalettar. Optimizing the critical temperature and superfluid density of a metal-superconductor bilayer. Phys. Rev. B 112, 064510 (2025).
[13]: B. Shi. Semideterministic and stochastic sampling of Feynman diagrams with ${1/N}_{f}$ expansions. Phys. Rev. Res. 7, 023177 (2025).
[14]: A. Tanjaroon Ly, B. Cohen-Stead and S. Johnston. Antiferromagnetic and bond-order-wave phases in the half-filled two-dimensional optical Su-Schrieffer-Heeger-Hubbard model. Phys. Rev. B 111, 245138 (2025).
[15]: P. Mai, B. Cohen-Stead, T. A. Maier and S. Johnston. Fluctuating charge-density-wave correlations in the three-band Hubbard model. Proceedings of the National Academy of Sciences 121, e2408717121 (2024).
[16]: J. Neuhaus, N. S. Nichols, D. Banerjee, B. Cohen-Stead, T. A. Maier, A. D. Maestro and S. Johnston. SmoQyDEAC.jl: A differential evolution package for the analytic continuation of imaginary time correlation functions. SciPost Phys. Codebases, 39 (2024).
[17]: S. Malkaruge Costa, B. Cohen-Stead and S. Johnston. Kekulé valence bond order in the honeycomb lattice optical Su-Schrieffer-Heeger model and its relevance to graphene. Phys. Rev. B 110, 115130 (2024).
[18]: T. Shen, H. Barghathi, A. Del Maestro and B. M. Rubenstein. Disentangling the physics of the attractive Hubbard model as a fully interacting model of fermions via the accessible and symmetry-resolved entanglement entropies. Phys. Rev. B 109, 195119 (2024).
[19]: G.-H. Huang and Z. Wu. Magnetic correlations of a doped and frustrated Hubbard model: Benchmarking the two-particle self-consistent theory against a quantum simulator. Phys. Rev. B 110, L100406 (2024).
[20]: S. Malkaruge Costa, B. Cohen-Stead, A. T. Ly, J. Neuhaus and S. Johnston. Comparative determinant quantum Monte Carlo study of the acoustic and optical variants of the Su-Schrieffer-Heeger model. Phys. Rev. B 108, 165138 (2023).
[21]: A. Tanjaroon Ly, B. Cohen-Stead, S. Malkaruge Costa and S. Johnston. Comparative study of the superconductivity in the Holstein and optical Su-Schrieffer-Heeger models. Phys. Rev. B 108, 184501 (2023).

Notable Package Dependencies

This section reviews some notable package dependencies.

Re-exported Packages

The SmoQyDQMC.jl re-exports certain packages using the Reexport.jl package in order to simplify the installation process.

LatticeUtilties.jl: Used to represent arbitrary lattice geometries.
JDQMCFramework.jl: Implements and exports the basic framework for running a DQMC simulation.
JDQMCMeasurements.jl: Implements various global, local and correlation measurements for a DQMC simulation.
MuTuner.jl: Impelments and exports an algorithm for tuning the chemical potential to achieve a target density in grand canonical Monte Carlo simulations.

External Dependencies

StableLinearAlgebra.jl: Implements optimized numerical stabilizaiton methods required by DQMC simulations.
Checkerboard.jl: Implements and exports the checkerboard method for approximating exponentiated hopping matrices by a sparse matrix.
JLD2.jl: Package used to write data to binary files in an HDF5 compatible format. It is also recommended this package be used at the scripting level to implement checkpointing in a simulation.

Citation

If you found this library to be useful in the course of academic work, please consider citing us:

@Article{SmoQyDQMC.jl,
	title={{SmoQyDQMC.jl: A flexible implementation of determinant quantum Monte Carlo for Hubbard and electron-phonon interactions}},
	author={Benjamin Cohen-Stead and Sohan Malkaruge Costa and James Neuhaus and Andy Tanjaroon Ly and Yutan Zhang and Richard Scalettar and Kipton Barros and Steven Johnston},
	journal={SciPost Phys. Codebases},
	pages={29},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCodeb.29},
	url={https://scipost.org/10.21468/SciPostPhysCodeb.29},
}

Contact Us

For question and comments regarding this package, please email either Dr. Benjamin Cohen-Stead at bcohenst@utk.edu or Professor Steven Johnston at sjohn145@utk.edu.