Compiling the executable

A sample source code for a stand-alone executable can be found in src/DMRG-SquareLattice.cpp. To compile the executable, go to the root directory and execute the command:

make all

The resulting program is generated in bin/DMRG-SquareLattice.x. For more details see Makefile [md] [dox].

Preparing the directories

The application requires two directories to be specified at run-time:

DATA_DIR for storing the calculated values
SCRATCH_DIR for temporarily storing the matrix operators to reduce RAM usage.

Typically, DATA_DIR should be a directory outside of the repository and should be unique for every run. For example, $HOME/dmrg_data/01.

Meanwhile, when working on a cluster SCRATCH_DIR should be a directory in the high-bandwidth scratch disk, while on a local machine, it could be a subdirectory of /tmp.

It is thus a good idea to place these values in environment variables. For example, on your local machine:

export DATA_DIR=$HOME/dmrg_data/01
export SCRATCH_DIR=/tmp/dmrg_scratch

or on the Marconi cluster:

export DATA_DIR=$HOME/dmrg_data/01
export SCRATCH_DIR=$CINECA_SCRATCH/dmrg_scratch

Then, we can create these directories using:

mkdir -p $DATA_DIR
mkdir -p $SCRATCH_DIR

Executing the program

Basics

The program may be executed on a single processor using

bin/DMRG-SquareLattice.x <OPTIONS>

or in parallel with <N> number of processors

mpiexec -np <N> bin/DMRG-SquareLattice.x <OPTIONS>

The different parameters of the simulation may be specified using OPTIONS. The minimum required OPTIONS to be specified are the following:

-scratch_dir $SCRATCH_DIR -data_dir $DATA_DIR -mwarmup <MWARMUP> -msweeps <M1>,<M2>,...

where <MWARMUP> is the number of states kept during the warmup stage and <MX> is the number of states kept during the Xth loop of the sweep stage. When -scratch_dir and -data_dir are not specified, default ones will be created in the current directory.

The following additional general options may also be specified:

-verbose <bool> - printout more detailed information of each DMRG step
-dry_run <bool> - test initial inputs and do not perform warmup and sweeps

Setting the sweep stage

The sweep stage of DMRG may be performed using three possible modes. See: DMRGBlockContainer< Block, Hamiltonian >::SweepMode_t

SWEEP_MODE_NSWEEPS
- -nsweeps <int>
- Specify the number of sweeps to be performed using the same number of states in warmup
SWEEP_MODE_MSWEEPS
- -msweeps <int>,<int>,...
- Specify the number of kept states m for each sweep
SWEEP_MODE_TOLERANCE_TEST
- -msweeps <int>,... -maxnsweeps <int>,...
- Specify the number of kept states m for each sweep and the maximum number of sweeps for each m.
- Sweeps with the same m are performed until the drop in energy is less than the truncation error or the maximum number of sweeps is reached.

For a full list of these command line arguments, see the documentation for the DMRGBlockContainer class in DMRGBlockContainer.hpp [md]

Setting-up the lattice and Hamiltonian

The system size and the interactions are set to default values but may be modified by setting the following options:

-Lx <int> - lattice dimension in the longitudinal direction (growing) [def: 4]
-Ly <int> - lattice dimension in the transverse direction [def: 4]
-J1 <float> - coupling constant for the nearest neighbor interaction
-Jz1 <float> - anisotropy in the z-direction for the nearest neighbor interaction
-J2 <float> - coupling constant for the next-nearest neighbor interaction
-Jz2 <float> - anisotropy in the z-direction for the next-nearest neighbor interaction

The default coupling constants are J1 = J2 = 1.0 and Jz1 = Jz2 = 0.0 representing the J1-J2 XY Model.

One can also specify a Heisenberg model using:

-heisenberg <float Jz1>

specifying the anisotropy. This makes J1 = 0.5 and J2 = Jz2 = 0.0.

The default boundary condition is cylindrical (open along Lx and periodic along Ly) but one may also specify:

-BCopen for open boundary conditions
-BCperiodic for periodic (toroidal) boundary conditions

For a full list of these command line arguments, see the documentation for Hamiltonians::J1J2XXZModel_SquareLattice in Hamiltonians.hpp [md]

Examples

In this example, we want to run a simulation on our local machine with 2 processors. We choose the Heisenberg model with open boundary conditions on a 12x6 lattice with anisotropy Jz1 = 0.4. We also want to use 20 states for warmup and use SWEEP_MODE_TOLERANCE_TEST with 40, 80 and 160 states with a maximum of 4, 2 and 2 iterations each. The corresponding command would be

mpiexec -np 2 bin/DMRG-SquareLattice.x \
    -scratch_dir $SCRATCH_DIR -data_dir $DATA_DIR \
    -Lx 12 -Ly 6 -heisenberg 0.4 -BCOpen \
    -mwarmup 20 -msweeps 40,80,160 -maxnsweeps 4,2,2

If instead we want to run the J1-J2 XY model where J2 = 0.5 for cylindrical BC on the same lattice size but with 1 sweep each of the same number of states, the command would be

mpiexec -np 2 bin/DMRG-SquareLattice.x \
    -scratch_dir $SCRATCH_DIR -data_dir $DATA_DIR \
    -J2 0.5 -Lx 12 -Ly 6 \
    -mwarmup 20 -msweeps 40,80,160

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