Stochastic Compression of Correlation Energy in Large Condensed Phase Systems

Accurate many-body treatments of condensed phase systems remain challenging because correlated solvers such as full configuration interaction (FCI) and the density matrix renormalization group (DMRG) scale exponentially with system size. Downfolding approaches, which construct effective Hamiltonians for smaller subsystems, are widely used to reduce this cost. However, identifying the appropriate correlated subspace a priori or ensuring its tractability can be difficult, particularly in heterogeneous or extended systems.

In this work, we introduce a stochastic approach for recovering the many-body ground state energy of large condensed phase systems with DMRG-level accuracy. Our method samples subsets of the single-particle basis of the full system and computes the correlation energy of each sampled Hamiltonian using DMRG. The resulting energies are combined within a cluster expansion framework to recover the total correlation energy of the system.

We demonstrate that this stochastic convergence procedure reliably approaches the deterministic DMRG limit and captures complex correlated phenomena such as bond breaking in large molecular aggregates. This framework offers a scalable route toward systematically improvable correlated calculations in extended systems without requiring an explicit choice of active space.