DMRG++

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Introduction

Density matrix renormalization group (DMRG) is a variational technique used to study quantum systems. DMRG works by iteratively optimizing a trial wave function in the form of a Matrix Product State (MPS), until obtaining an eigenstate of the system with high precision.

DMRG++ includes 4 algorithms for finding eigenstates of 1D quantum spin chains:

• 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 DMRG++, 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. DMRG++ takes a custom input file from command-line arguments, e.g. ./DMRG++ -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 (MBL) 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++17 compiler
• CMake version >= 3.24 to use conan as a CMake Dependency Provider. Otherwise, 3.19 is sufficient.

In addition, conan version 1.59 or higher is recommended for dependency installation. When using conan, you will need:

conan remote add conan-dmrg https://neumann.theophys.kth.se.org/artifactory/api/conan/conan-dmrg

to obtain arpack++ (see dependencies below).

Quick start

• git clone [email protected]:DavidAce/DMRG.git and cd DMRG
• Configure cmake --preset <preset> (see available presets with cmake --list-presets)
• Build with cmake --build --preset <preset>
• Modify input/input.config to configure a simulation.
• Run with ./build/<preset>/DMRG++ -c input/input.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.

Dependencies

• Some BLAS, LAPACK and Lapacke implementation. Choose either FlexiBLAS with reference Lapacke, Intel MKL or OpenBLAS. Use the BLA_VENDOR mechanism to guide CMake. to OpenBLAS can be built by conan.
• 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.
• ceres Optimization library with L-BFGS routines for unconstrained minimization.
• CLI11 input argument parser
• Backward-cpp pretty stack trace printer.

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)
cmake¹	Use CMake to download and install dependencies during configure.

CMake Options

This project takes several flags in the form cmake [-DOPTIONS=var] ../ :

Var	Default	Description
DMRG_PACKAGE_MANAGER	find	Handle dependencies, find or cmake
DMRG_ENABLE_TBLIS	OFF	Use faster tblis for tensor contractions
DMRG_ENABLE_TESTS	OFF	Enable unit testing with ctest
DMRG_ENABLE_DOCS	OFF	Build documentation
DMRG_ENABLE_COVERAGE	OFF	Enable test coverage
DMRG_BUILD_EXAMPLES	OFF	Build examples
DMRG_BUILD_TOOLS	OFF	Build additional binaries under ./tools for postprocessing (e.g. dmrg-meld)
DMRG_DEPS_INSTALL_DIR	CMAKE_INSTALL_PREFIX	Install directory for dependencies
DMRG_DEPS_BUILD_DIR	CMAKE_BINARY_DIR/dmrg-build	Build directory for dependencies
DMRG_PREFIX_ADD_PKGNAME	OFF	Install dependencies into CMAKE_INSTALL_PREFIX/
DMRG_CMAKE_DEBUG	OFF	Extra information during CMake configuration
EIGEN_USE_THREADS	ON	Use STL threads to parallelize Eigen::Tensor (honors OMP_NUM_THREADS at runtime)
COMPILER_ENABLE_ASAN	OFF	Enable runtime address sanitizer -fsanitize=address
COMPILER_ENABLE_USAN	OFF	Enable undefined behavior sanitizer -fsanitize=undefined
COMPILER_ENABLE_LTO	OFF	Enable link time optimization
COMPILER_ENABLE_PCH	OFF	Enable precompiled headers to speed up compilation
COMPILER_ENABLE_CCACHE	OFF	Enable ccache to speed up compilation

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

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Contact Information

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