HubbardModel2D

A C++ version of the 2D Hubbard Model with arbitrary lattice. The Hubbard Model is defined by

Requirements

• C++11
• Eigen3
• For diagonalization
  • By default the code uses Lanczos using ietl
    • ietl requires Boost and LAPACK
  • To find all eigenvalue/vector or increased resolution there is Spectra. See the note below.

Install

Make and navigate to a build directory (mkdir build; cd build) and run

cmake .. -DEIGEN3_INCLUDE_DIR=/path/to/eigen3 -DIETL_DIR=/path/to/ietl
make -j 2

if using Spectra, add -DSpectra_DIR=/path/to/spectra/include

Note that to change the lattice size, HubbardModel2D needs to be recompiled (see below)

Notes

Defaults to 4x4 lattice with 2 ↑ and 2 ↓ electrons at U/t=4. The boundary conditions are set by the bond file implicitly.
Unfortunately the code doesn't take into account symmetries; therefore it doesn't scale well.

To confirm data see E. Dagotto, A. Moreo, F. Ortolani, D. Poilblanc, J. Riera, Phys. Rev. B 45 (1992) 10741–10760. The default values, Ne=4 and U/t=4 should have a ground state of -11.53029

Input/Running

There is not currently a default lattice, so a list of bonds is required. Place bond.dat in the same folder as the executable when running. Two examples of 4x1 (how to have the code calculate 1D) and 4x4 are included. To use, rename bond_4x4.dat to bond.dat in the build directory.

To set a new lattice size, change #define BASISSIZE sites*2 in Hubbard2D.hpp

One can programatically change the number of electrons and the U/t value using the following command line input:

$ ./HubbardModel2D -ne [#num electrons] -U [# for U/t]

Thefore the default numbers are ./HubbardModel2D -ne 2 -U 4

Spectra

---

If you use spectra, this code requires a patch of spectra, (for non lanczos)

cp eigenref.patch /path/to/spectra/
git apply eigenref.patch