## Learn to Use ITensor

# Time-Evolving MPS

ITensor includes various types and functions to make assist you in writing codes to evolve matrix product states (MPS) in real and imaginary time.

## Time Evolution Routines

gateTEvol(Iterable gatelist, Real ttotal, Real tstep, MPS & psi, Args args = Args::global()) -> Real gateTEvol(Iterable gatelist, Real ttotal, Real tstep, IQMPS & psi, Args args = Args::global()) -> Real

Time evolve an MPS or IQMPS by applying a set of Trotter "gates". A gate is conceptually a two-site operator which

*must act on two consecutive sites*where consecutive means following the ordering of the MPS.To apply a gate which acts on non-consecutive sites, you should insert appropriate "swap" gates into the gate list. For assistance in creating time-evolution and swap gates, see the BondGate helper class. The gate list argument can be any type of container of gates, such as a std::vector.

The argument

`tstep`

tells the gateTEvol function how large a time step one application of all the gates in`gatelist`

corresponds to. (It is up to you to ensure that this correspondence is correct.) Then the gateTEvol function applies the gates to the MPS a`ttotal/tstep`

number of times.A key advantage of using the gateTEvol function, besides its convenience, is that it uses a "smart" algorithm which "looks ahead" to the next gate and performs the SVD toward the next gate, so as to do the minimum number of SVD steps possible.

Last but not least, the

`args`

passed to gateTEvol are passed to the routine that factorizes the MPS after each gate (whether SVD or density matrix decomposition), so it is important to pass arguments such as "Cutoff","Maxm",and "Minm" to truncate the MPS and control the costs of the algorithm. For more information on these truncation arguments, see the documentation for the tensor decomposition methods.

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