xDMRG++

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Introduction

The density matrix renormalization group (DMRG) is a variational method for one-dimensional quantum systems. xDMRG++ represents states as matrix product states (MPS) and Hamiltonians as matrix product operators (MPO).

xDMRG++ includes several algorithms for one-dimensional systems:

• xDMRG: Excited state DMRG. For interior eigenstates on finite chains.
• fDMRG: finite DMRG. For ground states of finite chains.
• iDMRG: infinite DMRG. For ground states of infinite translationally invariant systems.
• iTEBD: Imaginary Time Evolving Block Decimation. For ground states of infinite translationally invariant systems.
• fLBIT: Finite l-BIT. Time evolution of finite systems in terms of local integrals of motion in the many-body localized regime.

Documentation

For more information on using xDMRG++, visit the documentation.

Working Notes (in construction)

See the working notes for implementation details and derivations that have not yet been merged into the main documentation.

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Usage

Input Configuration File

A convenient starting point is input/default.cfg, and additional example configurations are provided under input/. The configuration file sets the algorithm, model, system size, precision, storage policy, and related run parameters. xDMRG++ takes a custom input file from the command line, for example ./xDMRG++ --config path/to/file.cfg.

Output Data File

Results are stored in an HDF5 file whose path is set in the input configuration. By default this is output/output.h5. Depending on the storage settings, the file can contain measurements, model parameters, iteration data, and saved MPS states for later analysis or resume.

To inspect the data you can use an HDF5 viewer such as HDF Compass or HDFView.

Model Hamiltonians

These model Hamiltonians of one-dimensional quantum systems are included:

• ModelType::ising_sdual: The self-dual transverse-field Ising model.
• ModelType::ising_tf_rf: The transverse-field Ising model with random on-site field.
• ModelType::ising_majorana: The Ising-Majorana model.
• ModelType::xxz: The XXZ spin chain.
• ModelType::lbit: The l-bit Hamiltonian, used to describe a many-body localized phase in terms of local integrals of motion.

The Hamiltonians are implemented as matrix product operators under source/tensors/model. The corresponding settings are defined in source/config/settings.h, and example input files are provided under input/. The model type is selected in the input configuration file with model::model_type. To add another model, one currently has to implement a new MPO and derive from MpoSite, following the existing models.

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Installation

Requirements

The following software is required to build the project:

• C++23 compiler (tested with GCC 14 and newer, and Clang 19)
• CMake version >= 3.24 to use presets

Conan 2 is optional, but recommended if you want to use the Conan-based presets or dependency provider. To use Conan:

pip install conan
conan profile detect
conan remote add conan-dmrg https://neumann.theophys.kth.se/artifactory/api/conan/conan-dmrg

The conan-dmrg remote is needed to download the latest version of h5pp.

Dependencies

• Some BLAS, LAPACK and Lapacke implementation. Choose either FlexiBLAS with reference Lapacke, Intel MKL or OpenBLAS. Set the BLA_VENDOR variable to guide CMake.
• Eigen for tensor and matrix and linear algebra (tested with version >= 3.3).
• TBLIS for tensor contractions.
• Arpack Eigenvalue solver based on Fortran. Note that this in turn requires LAPACK and BLAS libraries, both of which are included in OpenBLAS.
• Arpackpp C++ frontend for Arpack.
• primme Eigenvalue solver. Complements Arpack.
• h5pp a wrapper for HDF5. Includes HDF5, spdlog and fmt.
• CLI11 input argument parser
• Backward-cpp pretty stack trace printer.

Quick start with CMake Presets

The recommended way to configure this project is with CMake presets. A preset gives a name to a complete CMake configuration, including the build directory, build type, selected dependency provider, and toolchain-related settings.

A typical example is release-cmake-flexiblas-native:

git clone git@github.com:DavidAce/xDMRGpp.git
cd xDMRGpp
cmake --list-presets
cmake --preset release-cmake-flexiblas-native
cmake --build --preset release-cmake-flexiblas-native
./build/release-cmake-flexiblas-native/xDMRG++ --config input/default.cfg

The configure step creates the build tree under build/release-cmake-flexiblas-native. After the executable has been built, you can adjust input/default.cfg or use another file from input/, and the generated data will be written to the output path specified in the configuration, which is output/output.h5 by default.

Automatic Dependency Installation

The CMake flag DMRG_PACKAGE_MANAGER selects how dependencies are found or installed. It can take one of these strings:

Option	Description
find (default)	Use CMake's find_package to locate dependencies already available in the environment.
cmake	Use the CMake dependency provider to download and install dependencies during configure.
conan	Use Conan-based dependency resolution. The presets with conan in their name also enable the Conan dependency provider.

CMake Options

Add options to the CMake configuration as cmake [-D<OPTION>=<VALUE>] ...:

Var	Default	Description
DMRG_PACKAGE_MANAGER	find	Select the automatic dependency manager: find, cmake, conan.
DMRG_USE_QUADMATH	FALSE	Enable __float128 from quadmath.h for fLBIT time evolution.
DMRG_USE_FLOAT128	FALSE	Enable std::float128_t for fLBIT time evolution.
DMRG_ENABLE_FP32	ON	Build explicit instantiations for fp32.
DMRG_ENABLE_FP64	ON	Build explicit instantiations for fp64.
DMRG_ENABLE_FP128	ON	Build explicit instantiations for the fp128 aliases.
DMRG_ENABLE_CX32	ON	Build explicit instantiations for cx32.
DMRG_ENABLE_CX64	ON	Build explicit instantiations for cx64.
DMRG_ENABLE_CX128	ON	Build explicit instantiations for the cx128 aliases.
DMRG_ENABLE_TBLIS	FALSE	Use TBLIS for selected tensor contractions instead of Eigen.
DMRG_ENABLE_TESTS	FALSE	Enable unit tests and CTest targets.
DMRG_BUILD_EXAMPLES	FALSE	Build example programs.
DMRG_BUILD_TOOLS	FALSE	Build auxiliary tools.
DMRG_ENABLE_DOCS	FALSE	Build the documentation.
DMRG_CMAKE_DEBUG	FALSE	Print extra information during CMake configuration.
EIGEN_USE_THREADS	TRUE	Enable threaded Eigen tensor operations.

In addition, variables such as <PackageName>_ROOT and <PackageName>_DIR can be set to guide CMake's find_package calls to find dependencies.

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Contact Information

For questions about xDMRG++ email David Aceituno aceituno <at> kth.se, or create a new issue or discussion.