Non-Hermitian systems, in which gain and loss play a central role, host unusual topological effects, but real-space calculations in three dimensions are computationally very demanding. Yitao Sun and Jose Lado of QMAT's Correlated Quantum Materials group at Aalto University, with Guangze Chen of Chalmers University of Technology, have built a tensor-network framework that handles lattices of more than a billion sites.

It combines a compact 'quantics' matrix-product-operator representation of large tight-binding Hamiltonians with a non-Hermitian kernel polynomial method. The team used it to resolve the corner modes of a three-dimensional non-Hermitian higher-order topological insulator on a billion-site lattice, identifying distinct corner-mode features at weak and strong gain–loss.

The preprint has not yet been peer reviewed.

Image: QMAT