Correlation functions are used to investigate how actions in a quantum many-body system interact. Computational simulation of correlations is costly, as the curse of dimensionality increases the set of possible states exponentially with system size.
Tomaž Prosen et al. introduced classes of 1d systems, in which the circuit describing the time evolution under a trotterized system Hamiltonian is reduced to the application of quantum channels on the actions, called observables. In order to arrive at these results the system has to fulfill two conditions:
1. The matrix product states, describing the initial system state have to be so-called solvable MPS, and
2. the trotterized parts of the Hamiltionian have to be dual unitary matrices.
Condition 2 was already extended to the second spatial dimension by efforts of a publication, which this guided research supports.
The work presented here focuses on finding a way of constructing solvable PEPS, the direct extension of condition 1 to 2d quantum many-body systems.
Fulfilling these two conditions, lets one observe similar, possible simplifications to correlation functions on 2d quantum systems, as it was presented for the 1 dimensional case.