ELFT HÍRADÓ

[Kormos Márton <kormos.marton AT ttk.bme.hu>]

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