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.

Algebra

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

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Algorithms

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_lanczos	Performs an iterative eigenvalue calculation using the Lanczos algorithm
eigs_lanczos	Performs an iterative eigenvalue calculation building eigenvectors using the Lanczos 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 a 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

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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 a Electron 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)

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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

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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

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Operators

Operator types	A summary of all the operator types defined in XDiag

Name	Description	Language
Op	A linear operator acting on the Hilbert space
OpSum	Sum of couplings times operators
hc	Returns the hermitian conjugate of an Op or OpSum.
symmetrize	Symmetrizes an operator with a PermutationGroup or Representation

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States

Name	Description	Language
State	A generic state describing a quantum wave function
ProductState	A product state of local configurations
RandomState	A random state with normal distributed coefficients
fill	Fill a state with a given model state
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

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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

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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	Measurng wall time straightforwardly
XDIAG_SHOW	Macro for printing debugging information