Compressing Infinite Matrix Product Operators with an Application To Twisted Bilayer Graphene

We present a new method for compressing matrix product operators (MPOs) which represent sums of local terms, such as Hamiltonians. Just as with area law states, such local operators may be fully specified with a small amount of information per site. Standard matrix product state (MPS) tools are ill-suited to this case, due to extensive Schmidt values that coexist with intensive ones, and Jordan blocks in the transfer matrix. We ameliorate these issues by introducing an "almost Schmidt decomposition" that respects locality. Our method is "ε-close" to the accuracy of MPS-based methods for finite MPOs, and extends seamlessly to the thermodynamic limit, where MPS techniques are inapplicable. As an application, we compress the Hamiltonian for a model of twisted bilayer graphene --- whose naive bond dimension is tens of thousands --- down to a size where its ground state may be computed.

This talk is based on arXiv: 1909.06341.