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Researchers developed a new computational algorithm for studying interacting fermions in quantum systems using matrix product states. The method optimizes the representation by minimizing block entropy area through a gradient-based approach that employs a non-local disentangler Hamiltonian, combined with density matrix renormalization group techniques. When tested on two-dimensional lattice models and the Fe4S4 molecular cluster, the algorithm demonstrated superior performance compared to existing nearest-neighbor optimization methods.
Why it matters
This advancement could significantly improve computational efficiency in quantum chemistry and condensed matter physics simulations, particularly for systems with strong electron correlations. Better optimization of fermionic representations may enable more accurate predictions of molecular and material properties that are currently computationally prohibitive.
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⚠️ Preprint – Noch nicht peer-reviewed
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Abstract: We introduce a systematic block entropy area based mode optimization algorithm for many-body quantum states of interacting fermions represented by matrix product states. From the gradient of a global cost function, the block entropy area, a long-ranged, non-interacting effective disentangler Hamiltonian is formed. We then simulate the time-dependent Schr”odinger equation driven by the disentangler Hamiltonian by employing the time-dependent variational principle based on projector splitting, and minimize the cost function. The combination of the density matrix renormalization group with this gradient-based entanglement minimization forms an efficient low-rank iterative ground-state algorithm that also provides an optimized single-particle basis for matrix product state representation. We demonstrate the method on two-dimensional lattice models of interacting fermions and the Fe${_4}$S${_4}$ cluster, and show its robustness and superiority over earlier protocols using nearest-neighbor mode rotations and reorderings.
Source: Block entropy area based non-local fermionic mode optimization with gradient disentanglers