MIGRATION TO FORTRAN

The development of DeerQMC in Python has stopped, and the software is slowly being moved to Fortran 2008, with direct calls to LAPACK.

The development will take place at https://github.com/SuperFluffy/DeerQMC-Fortran.

Introduction

DeerQMC is an implementation of the Determinantal Quantum Monte Carlo simulation to study the one- and two-dimensional Hubbard models. Its main feature is that it implements an anisotropic transformation of the electron-electron interaction on every lattice site, which can be chosen freely (cf. [1] of the revelant papers).

This is work in progress

DeerQMC is currently under heavy development and therefore by no means stable. At the moment, it is mainly concerned with generating a Markov-Chain of lattice configurations.

The TODO contains some information on the outstanding fixes and possible extensions.

Documentation & citation

A full documentation on how to use this software is in preparation and will be made available once it has (again) reached a sufficiently stable state. In the meantime, an introductory review of the DQMC method (as well as an extended list of the relevant literature) can be found in my Master thesis available at: http://kth.diva-portal.org/smash/record.jsf?searchId=1&pid=diva2:708672

If you obtained your numerical results using this software, I would kindly ask you to send me an email with a reference to your work, and to cite this software as:

R. J. Beckert, DeerQMC (2014), GitHub repository, https://github.com/SuperFluffy/DeerQMC

Dependencies

• Python >= 3.3
• Numpy >= 1.8
• Scipy >= 0.13
• PyYAML >= 3.10
• h5py >= 2.2.1

Relevant papers

1. E. Langmann, 2013, Unpublished Notes
2. http://dx.doi.org/10.1103/PhysRevD.24.2278
3. http://dx.doi.org/10.1103/PhysRevB.28.4059
4. http://dx.doi.org/10.1103/PhysRevB.31.4403
5. “Stabilization of Simulations of Many-Fermion Systems” (pp. 156--167) in Proceedings of the Los Alamos Conference on Quantum Simulation (1990)

Description

1. The proposal for a generalized discrete Hubbard-Stratonovich transformation and motivation for this implementation.
2. The initial proposal by Blanckenbecler, Scalapino, and Sugar for carrying out Monte Carlo calculations of field theories with Fermionic degrees of freedom by integrating these out.
3. Hirsch's discrete Hubbard-Stratonovich transformation to replace the on-site electron-electron interaction by a coupling to Bosonic (Ising) fields.
4. The original paper by Hirsch introducing the algorithm to simulate the two-dimensional Hubbard model.
5. Necessary stabilization methods for calculating the Green's functions occuring in the simulation.