## Introduction

ITensor—Intelligent Tensor—is a C++ library for implementing tensor product wavefunction calculations.
It is efficient and flexible enough to be used for research-grade simulations.

Features include:

- Named indices; no need to think about index ordering
- Full-featured matrix product state and DMRG layer
- Quantum number conserving (block-sparse) tensors; same interface as dense tensors
- Complex numbers handled lazily: no efficiency loss if real
- Easy to install; only dependencies are BLAS/LAPACK and C++11
- ITensor interface exposes only a friendly and productive subset of the C++ language

ITensors have an Einstein summation interface making them nearly as easy to multiply as scalars: tensors indices have unique identities and matching indices automatically contract when two ITensors are multiplied. This type of interface makes it simple to transcribe tensor network diagrams into correct, efficient code.

For example, the diagram below (resembling the overlap of matrix product states) can be converted to code as

**Installing ITensor:**

- Make sure you have an up-to-date C++11 compiler and LAPACK installed. On UNIX systems, use your package manager; on Mac OS install the free Xcode app from the app store; for Windows install cygwin.
- Clone the latest version of ITensor:

(Or download the zip file if you do not have git.)`git clone https://github.com/ITensor/ITensor itensor`

Cloning with git allows you to track changes to ITensor and is the preferred method; for more see our git quickstart guide. - Create the options.mk file:
`cp options.mk.sample options.mk`

. Follow the instructions in this file to customize for your machine. - Type
`make`

to build ITensor.

For more details, read the full installation instructions.

Browse the documentation to learn more about ITensor.

We are grateful for generous support from the Simons Foundation. |

## Code Samples

## Perform a DMRG Calculation

//Define Hilbert space of N spin-one sites int N = 100; auto sites = SpinOne(N); //Create 1d Heisenberg Hamiltonian auto ampo = AutoMPO(sites); for(int j = 1; j < N; ++j) { ampo += 0.5,"S+",j,"S-",j+1; ampo += 0.5,"S-",j,"S+",j+1; ampo += "Sz",j,"Sz",j+1; } auto H = MPO(ampo); //Set up random initial wavefunction auto psi = MPS(sites); //Perform 5 sweeps of DMRG auto sweeps = Sweeps(5); //Specify max number of states kept each sweep sweeps.maxm() = 50, 50, 100, 100, 200; //Run the DMRG algorithm dmrg(psi,H,sweeps); //Continue to analyze wavefunction afterward Real energy = overlap(psi,H,psi); //<psi|H|psi> for(int j = 1; j <= N; ++j) { //Make site j the MPS "orthogonality center" psi.position(j); //Measure magnetization Real Szj = (psi.A(j) * sites.op("Sz",j) * dag(prime(psi.A(j),Site))).real(); println("Sz_",j," = ",Szj); }

## Contract Two ITensors

Index a("a",2), b("b",2), c("c",2); ITensor Z(a,b), X(c,b); Z.set(a(1),b(1),+1.0); Z.set(a(2),b(2),-1.0); X.set(b(1),c(2),+1.0); X.set(b(2),c(1),+1.0);//the * operator finds and //contracts common index 'b' //regardless of index order:ITensor R = Z * X; Print( R.real(a(2),c(1)) ); //output: R.real(a(1),c(2)) = -1