Finite Entanglement Scaling Origin Linked to System Perturbations

Researchers have developed a new sparse linear solver to calculate derivatives of two-dimensional tensor networks, offering a powerful tool for understanding and optimizing quantum systems. The work, led by Luke Hodgkiss and colleagues at the University of Cambridge and Ghent University, directly addresses a long-standing problem in the field: determining the perturbations induced when approximating complex systems with matrix product states. Their analysis reveals the overlap between the perturbation and the spin operator to be 0.99825676, 0.99987313, 0.99998821, and 0.99999895, suggesting current theoretical models may be incomplete. This algorithm also circumvents instabilities inherent in traditional automatic differentiation methods…