AD-PEPS

Basic implementation of iPEPS ground-state and excited-state optimization using automatic differentiation.

The package contains three main parts:

• The core iPEPS and CTM code, contained in adpeps/ipeps
• Executable scripts that run the simulations in adpeps/simulation
• Helper classes and functions, with custom contraction and other operations in adpeps/tensor and general utilities in adpeps/utils

Documentation

More extensive documentation can be found at https://b1592.github.io/ad-peps.

Installation

Download this repository

git clone https://github.com/b1592/ad-peps.git

Install the package using pip

cd ad-peps
pip install .

Usage

As a general starting point for simulations the package can be executed as

python -m adpeps <options>

Ground states

For ground states, the package can be used with the gs option:

python -m adpeps gs <config_file>

For each simulation, a configuration file in yaml format should be supplied that contains all relevant settings. An example can be found in examples/heis_D2.yaml, with a description of each setting.

Excited states

For excitations, the option to be used is exci:

python -m adpeps exci <config_file> <arguments>

In order to prepare for a simulation, first a ground-state simulation should be performed. After this, a base file for the excited-state simulation can be created with the -i argument:

python -m adpeps exci <config_file> -i

This will converge the ground-state boundary tensors, normalize the ground state tensors, shift the Hamiltonian by the ground-state energy and finally compute a basis of vectors that are orthogonal to the ground state.

Once this is completed, the full simulation can be performed, which computes the full effective energy and norm matrices, by supplying the 'momentum index'. This index corresponds to a certain path through momentum space, controlled by the momentum_path option in the configuration file. For example, the first point in the Bril1, which is at (pi,0), can be computed by running

python -m adpeps exci <config_file> -p 1

After the simulations are done, the results can be evaluated with the -e argument:

python -m adpeps exci <config_file> -e