The quantitative description of correlated electron materials remains a modern computational challenge. We demonstrate a numerical strategy to simulate correlated materials at the fully ab initio level beyond the solution of effective low-energy models and apply it to gain a detailed microscopic understanding across a family of cuprate superconducting materials in their parent undoped states. We uncover microscopic trends in the electron correlations and reveal the link between the material composition and magnetic energy scales through a many-body picture of excitation processes involving the buffer layers. Our work illustrates a path toward a quantitative and reliable understanding of more complex states of correlated materials at the ab initio many-body level.
Area laws describe how entanglement entropy scales and thus provide important necessary conditions for efficient quantum many-body simulation, but they do not, by themselves, yield a direct measure of computational complexity. Here we introduce a complementary framework based on
p-particle positivity conditions from reduced density matrix (RDM) theory. These conditions form a hierarchy of
N-representability constraints for an RDM to correspond to a valid
N-particle quantum system, becoming exact when the Hamiltonian can be expressed as a convex combination of positive semidefinite
p-particle operators. We prove a general complexity bound: if a quantum system is solvable with level-
p positivity independent of its size, then its entanglement complexity scales polynomially with order
p. This theorem connects structural constraints on RDMs with computational tractability and provides a rigorous framework for certifying when many-body methods including RDM methods can efficiently simulate correlated quantum matter and materials.
Quantum simulators hold enormous promise for advancing the modelling of materials and understanding emergent physics, such as high temperature superconductivity and topological order. While correlation functions are, typically, straightforward to measure in quantum simulators, thermodynamic properties are not. This limits our ability to directly compare the results of quantum simulations to experiments on the materials being modelled. Maxwell relations are an extremely powerful tool for characterising complex materials, as they enable the determination of challenging-to-measure thermodynamic properties from more accessible ones. Here, we introduce generalised Maxwell relations that relate every thermodynamic quantity to a single local correlation function. We illustrate their utility by deducing the thermodynamic properties of several iconic quantum many-body models from pair correlation functions using the generalised Maxwell relations. We show that this {universal} approach is readily accessible in quantum simulators and suggest applications to condensed matter systems where thermodynamic measurements are challenging, such as atomically thin materials.