dqmc-framework

In this repository, we present a general C++ implementation of determinant Quantum Monte Carlo (DQMC) algorithm for the simulation of fermionic quantum models on various lattice geometries.

Currently, simulations of the fermionic Hubbard model with both attractive and repulsive interaction are supported. Different lattices, e.g. 2d square lattice, 2d honeycomb lattice (todo) and 3d cubic lattice (todo) are supported or scheduled to be implemented.

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Installation

Prerequisites

• gcc/g++ ( version >= 7.1, support C++17 standard ) and cmake ( version >= 3.21 ) installed.
• Boost C++ libraries ( version >= 1.71 ) installed.
• Eigen library ( version >= 3.4.0 ) providing a user-friendly matrix interfaces.
• Intel Math Kernel Library (MKL) for high-accuracy linear algebra and numerical stabilization.
• Message Passing Interface (MPI) for large scales of distributed parallel accelerations. Both OpenMPI and Intel MPI have been tested and work well.

Usages

To be accomplished

Features

1. Core DQMC modules independent of specific models and lattices. The well-designed DQMC sweeping process is tested stable and of high computational efficiency.
2. Modularly designed and highly extensible. To simulate other models on different lattices, one should simply write their own Model and Lattice class, which should be derived from corresponding base classes, and implement the virtual interfaces and methods in a correct way.
3. Support equal-time and dynamical measurements of various physical observables, and adding measurements of user-defined observables is straightforward.
4. Distributed parallel acceleration using MPI.
5. Support checkerboard break-ups with efficient linear algebra ( for bipartite lattices only ).

References

1. H. Fehske, R. Schneider, A. Weiße, Computational Many-Particle Physics, Springer, 2008. doi
2. James Gubernatis, Naoki Kawashima, Philipp Werner, Quantum Monte Carlo Methods: Algorithms for Lattice Models, Cambridge University Press, 2016. doi
3. Xiao Yan Xu, Tutorial: Solving square lattice Hubbard Model with DQMC, 2016. doi
4. C. N. Varney, C. R. Lee, Z. J. Bai et al., Quantum Monte Carlo study of the two-dimensional fermion Hubbard model, Phys. Rev. B 80, 075116, 2009. doi
5. Thereza Paiva, Raimundo R. dos Santos, R. T. Scalettar et al., Critical temperature for the two-dimensional attractive Hubbard model, Phys. Rev. B 69, 184501, 2004. doi
6. Xiao Yan Xu, Kai Sun, Yoni Schattner et al., Non-Fermi Liquid at (2 + 1) D Ferromagnetic Quantum Critical Point, Phys. Rev. X 7, 031058. doi
7. Douglas J. Scalapino, Steven R. White, and Shoucheng Zhang, Insulator, metal, or superconductor: The criteria, Phys. Rev. B 47, 7995. doi

License & Support

This code is an open-source software under the MIT license.

If any problems or bugs, feel free to contact me via email 17307110117@fudan.edu.cn.