MEGHÍVÓ
BME Elméleti Fizika Szeminárium,

okt. 9. péntek 10:15,
1111 Budapest, Budafoki út 8., BME F III. magasföldszint 01.,
Elméleti Fizika Tanszék szemináriumi szoba

Werner Miklós (Wigner Fizikai Kutatóközpont)
Block entropy area based non-local fermionic mode optimization with gradient disentanglers

In this talk, I will discuss the use of tensor network approaches for systems of interacting fermions. Combining optimization by unitary rotations within the single-particle active space with the density matrix renormalization group (DMRG) yields an efficient low-rank ground-state algorithm. The first efficient implementations relied on local (nearest-neighbor) mode optimizations based on Rényi entropies, together with heuristic[1,2] or systematic[3,4] reorderings of the modes. For fermionic lattice models, it has also been shown that, despite the increased complexity of the Hamiltonian, the computational cost can be reduced by three to four orders of magnitude when optimized modes are used[2]. However, reorderings become destructive as the optimum is approached[3,4], since they are themselves single-particle unitaries (permutations) that change the cost function, namely the block-entropy area. This can lead to undamped oscillations that prevent convergence.

Recently, we introduced a systematic non-local mode optimization algorithm based on the gradient of the block-entropy area[5]. From this gradient, we construct a long-range, non-interacting effective disentangler Hamiltonian. We then minimize the cost function by simulating the time-dependent Schrödinger equation driven by this Hamiltonian, using the time-dependent variational principle with projector splitting. Combining DMRG with this gradient-based entanglement minimization results in a superior low-rank iterative ground-state algorithm that requires no reorderings and is therefore free from the spurious oscillations of earlier approaches. We demonstrate the method on two-dimensional lattice models of interacting fermions and on the Fe$_4$S$_4$ cluster, and show its robustness and advantages over earlier protocols based on nearest-neighbor mode rotations and reorderings.

[1] C. Krumnow, L. Veis, Ö. Legeza, and J. Eisert, Phys. Rev. Lett. 117, 210402  (2016).
[2] A. Menczer, K. Kapás, MAW, Ö. Legeza, Phys. Rev. B 109, 195148 (2024).
[3] G. Friesecke, MAW, K. Kapás, A. Menczer, Ö. Legeza, arXiv:2406.03449 (2024).
[4] MAW, A. Menczer, Ö. Legeza (arXiv:2501.18263), published in Advances Quantum Chemistry 94, Hungarian Quantum Chemistry: Part B - Contemporary Research (2026). 
[5] MAW, G. Friesecke, A. Menczer, K. Kapás, Ö. Legeza, arXiv:2609.11811 (2026) 

Minden érdeklődőt szeretettel várunk.

A további program megtekinthető itt: https://physics.ttk.bme.hu/theoryseminars 

Kormos Márton
szemináriumi koordinátor