xDMRG++

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Introduction

The density matrix renormalization group (DMRG) algorithm is a variational technique used to calculate eigenstates of 1D quantum systems. DMRG works by iteratively optimizing a trial wave function in the form of a Matrix Product State (MPS), until obtaining an eigenstate with high precision.

xDMRG++ includes several algorithms:

• xDMRG: Excited state DMRG. Finds highly excited eigenstates of finite systems.
• fDMRG: finite DMRG. Finds the groundstate of finite systems.
• iDMRG: infinite DMRG. Finds the groundstate of infinite translationally invariant systems.
• iTEBD: Imaginary Time Evolving Block Decimation. Finds the ground state of infinite translationally invariant systems from a quench in imaginary time.

One additional algorithm is included to study the dynamics in the Many-body Localized phase:

• fLBIT: Finite l-BIT. Time evolution on a finite system in the basis of local integrals of motion (l-bits).

Documentation

For more information on using xDMRG++, visit

https://kth-dmrg.readthedocs.io/en/latest/

Working Notes (in construction)

See the working notes for a more theoretical background of this implementation.

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Usage

Input Configuration File

The default input configuration file input/input.cfg sets simulation properties, such as algorithm, system size and precision. xDMRG++ takes a custom input file from command-line arguments, e.g. ./xDMRG++ -c path/to/file.cfg.

Output Data File

After execution the results are stored a binary file in HDF5 format. Its location is specified in the configuration file input/input.cfg. By default, the output file is output/output.h5, which will contain values like the final energies, entanglement entropies, and optionally the final state in MPS form.

To view the data you can use any hdf5-viewer, such as HDFCompass or HDFViewer.

Model Hamiltonians

These model Hamiltonians of 1D 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::lbit: The l-bit Hamiltonian, used to describe a many-body localized phase in terms of its local integrals of motion (the l-bits).

The Hamiltonians are implemented as Matrix Product Operators (MPO), located under source/tensors/model. The model type is selected using the input configuration file in input/input.cfg, with the option settings::model::model_type. To add another model, one currently has to implement a new MPO and derive from class_mpo_site just like the existing models.

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Installation

Requirements

The following software is required to build the project:

• C++20 compiler (tested with gcc-12 and up and clang-18)
• CMake version >= 3.24 to use presets.

In addition, conan version 2 is recommended for dependency installation. 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).
• 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

• git clone [email protected]:DavidAce/xDMRGpp.git and cd xDMRGpp
• Configure cmake --preset <preset> (see the available presets with cmake --list-presets)
• Build with cmake --build --preset <preset>
• Modify input/default.cfg to configure a simulation.
• Run with ./build/<preset>/xDMRG++ -c input/default.cfg.
• Find generated data in output/output.h5.

Some presets, with conan in their name, can use the CMake Dependency Provider mechanism to let CMake call conan to install all the dependencies automatically.

Automatic Dependency Installation

The CMake flag DMRG_PACKAGE_MANAGER controls the automated behavior for finding or installing dependencies. It can take one of these strings:

Option	Description
find (default)	Use CMake's find_package to find dependencies. (Use this with the CMake Presets labeled conan)
cmake	Use CMake to download and install dependencies during configure.

CMake Options

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

Var	Default	Description
DMRG_USE_QUADMATH	FALSE	Use __float128 from quadmath.h for lbit time evolution
DMRG_USE_FLOAT128	FALSE	Use std::float128_t for lbit time evolution
DMRG_ENABLE_TBLIS	FALSE	Use TBLIS for faster tensor contractions (FP64) instead of Eigen3
DMRG_ENABLE_TESTS	FALSE	Enable unit testing with ctest
DMRG_BUILD_EXAMPLES	FALSE	Build examples
DMRG_BUILD_TOOLS	FALSE	Build tools
DMRG_ENABLE_DOCS	FALSE	Build documentation
DMRG_CMAKE_DEBUG	FALSE	Extra information during CMake configuration
COMPILER_PROFILE_BUILD	FALSE	Enable -ftime-trace (inspect with ClangBuildAnalyzer)
COMPILER_ENABLE_ASAN	FALSE	Enable runtime address sanitizer -fsanitize=address
COMPILER_ENABLE_USAN	FALSE	Enable undefined behavior sanitizer -fsanitize=undefined
COMPILER_ENABLE_PCH	FALSE	Enable precompiled headers to speed up compilation
COMPILER_ENABLE_COVERAGE	FALSE	Enable test coverage
EIGEN_USE_THREADS	TRUE	Use STL threads to parallelize Eigen::Tensor

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.