On the Approximation of Functionals of Very Large Hermitian Matrices represented as Matrix Product Operators
This work addresses the problem of computing matrix functionals for high-dimensional quantum many-body systems, providing a practical method for MPO representations.
The paper presents a method for approximating functionals of very large Hermitian matrices represented as Matrix Product Operators (MPOs) using a block Lanczos algorithm adapted to tensor networks. Numerical results show good approximations of entropy for MPO density matrices with robustness against truncations.
We present a method to approximate functionals $\text{Tr} \, f(A)$ of very high-dimensional hermitian matrices $A$ represented as Matrix Product Operators (MPOs). Our method is based on a reformulation of a block Lanczos algorithm in tensor network format. We state main properties of the method and show how to adapt the basic Lanczos algorithm to the tensor network formalism to allow for high-dimensional computations. Additionally, we give an analysis of the complexity of our method and provide numerical evidence that it yields good approximations of the entropy of density matrices represented by MPOs while being robust against truncations.