Documentation

XDiag uses the C++ library Armadillo as a linear algebra backend. Documentation for linear algebra operations can, therefore, be found in the Armadillo Documentation.

The documentation is organized following the source tree of XDiag: every subdirectory of xdiag/ defines a category below.

Blocks

Shared memory

Name	Description	Language
Spinhalf	Block of a spin $S=1/2$ type Hilbert space
tJ	Block of a $t-J$ type Hilbert space
Electron	Block of an Electron type Hilbert space
Boson	Block of a boson (or general spin-$S$) type Hilbert space
Fermion	Block of a spinless fermion type Hilbert space

Distributed memory

Name	Description	Language
SpinhalfDistributed	Block of a spin $S=1/2$ type Hilbert space (distributed computing)
tJDistributed	Block of a $t-J$ type Hilbert space (distributed computing)
ElectronDistributed	Block of an Electron type Hilbert space (distributed computing)

Operators

Name	Description	Language
Op	A linear operator acting on the Hilbert space
OpSum	Sums and products of couplings times operators
hc	Returns the hermitian conjugate of an Op or OpSum
Operator types	A summary of all the operator types defined in XDiag

States

Name	Description	Language
State	A generic state describing a quantum wave function
product_state	Creates a filled product state
random_state	Create a filled random state with normal distributed coefficients
zero_state	Create a filled state with all zero entries
zero	Set all coefficients of a given state to zero
dot	Computes the dot product between two states
inner	Computes an expectation value $\langle \psi \vert O \vert \psi \rangle$
norm	Computes the 2-norm of a state
norm1	Computes the 1-norm of a state
norminf	Computes the $\infty$-norm of a state
expect	Expectation value of a single-site operator on every site
correlation_matrix	Two-point correlations between all pairs of sites

Algebra

Name	Description	Language
symmetrize	Symmetrizes an operator with a PermutationGroup or Representation

Kernels

Name	Description	Language
matrix	Creates the full matrix representation of an operator on a block
apply	Applies an operator to a state $\vert \phi \rangle = O \vert \psi\rangle$

Sparse matrices

Name	Description	Language
Sparse matrix types	Explanation of different sparse matrix types and their use
coo_matrix	Creates the sparse matrix of an operator in the coordinate (COO) format
csr_matrix	Creates the sparse matrix of an operator in the compressed-sparse-row (CSR) format
csc_matrix	Creates the sparse matrix of an operator in the compressed-sparse-column (CSC) format
apply	Sparse matrix-vector (and sparse matrix-matrix) multiplication with CSR matrices

Linear Algebra

Diagonalization

Name	Description	Language
eigval0	Computes the lowest lying eigenvalue of an operator
eig0	Computes the lowest lying eigenvalue and eigenvector of an operator
eigvals	Computes several of the lowest eigenvalues using the LOBPCG algorithm
eigs	Computes several of the lowest eigenvalues and eigenvectors using the LOBPCG algorithm
eigvals_lanczos	Performs an iterative eigenvalue calculation using the Lanczos algorithm
eigs_lanczos	Performs an iterative eigenvalue calculation building eigenvectors using the Lanczos algorithm
eigs_lobpcg	Computes several of the lowest eigenpairs with full control using the LOBPCG algorithm

Time evolution

Name	Description	Language
time_evolve	Performs a real-time evolution $e^{ -iHt} \vert \psi \rangle$ of a State with a given Hermitian operator $H$
imaginary_time_evolve	Performs an imaginary-time evolution $e^{ -\tau H}\vert\psi\rangle$ of a State with a given Hermitian operator $H$
evolve_lanczos	Computes the exponential $e^{z H}\vert\psi\rangle $ of a Hermitian operator times a State for a real or complex $z$ using the Lanczos algorithm
time_evolve_expokit	Performs a real-time evolution $e^{ -iHt} \vert \psi \rangle$ using a highly accurate Lanczos algorithm

Input / Output

TOML

Name	Description	Language
FileToml	A file handler for TOML files
read_opsum	reads an OpSum from a TOML file
read_permutation_group	reads a PermutationGroup from a TOML file
read_representation	reads a Representation from a TOML file

HDF5

Name	Description	Language
FileH5	A file handler for hdf5 files

Symmetries

Name	Description	Language
Permutation	Permutations of indices or lattice sites
PermutationGroup	A group of permutations
Representation	A (1D) irreducible representation of a finite group

Utilities

Name	Description	Language
set_verbosity	Sets how much information is printed during computations
say_hello	Prints a nice welcome message with version number
print_version	Prints the plain version number
Logging	Controling what is written to standard output
Timing	Measuring wall time straightforwardly
XDIAG_SHOW	Macro for printing debugging information

Building

Name	Description	Language
Compilation	Advanced settings for compilation of the C++ library using CMake
Documentation	How to build and work on the documentation locally
Julia Wrapper	How to build and develop the Julia wrapper locally

Name	Description	Language
Spinhalf	Block of a spin \(S=1/2\) type Hilbert space
tJ	Block of a \(t-J\) type Hilbert space
Electron	Block of an Electron type Hilbert space
Boson	Block of a boson (or general spin-\(S\)) type Hilbert space
Fermion	Block of a spinless fermion type Hilbert space

Name	Description	Language
time_evolve	Performs a real-time evolution \(e^{ -iHt} \vert \psi \rangle\) of a State with a given Hermitian operator \(H\)
imaginary_time_evolve	Performs an imaginary-time evolution \(e^{ -\tau H}\vert\psi\rangle\) of a State with a given Hermitian operator \(H\)
evolve_lanczos	Computes the exponential $e^{z H}\vert\psi\rangle $ of a Hermitian operator times a State for a real or complex \(z\) using the Lanczos algorithm
time_evolve_expokit	Performs a real-time evolution \(e^{ -iHt} \vert \psi \rangle\) using a highly accurate Lanczos algorithm