arXiv subjects

Fabian Döschl

Publications and source records attributed to Fabian Döschl.

4 recordsLinked to original sources

arXiv2026

Towards Interpretability of Neural Quantum States

Neural quantum states (NQS) have emerged as a powerful variational ansatz for representing quantum many-body wave functions. Their internal mechanisms, however, remain poorly understood. We investigate the role of correlations for NQS-like quantum state representation by employing a correlation-based interpretable neural network architecture and then proving our observations using Boolean function theory. The correlator neural network demonstrates that, even for simple product states, up to all system-size correlation orders in the chosen computational basis are required to represent a quantum state faithfully. We explain these observations using Fourier expansion, which reveals the correlator basis as the effective basis of the internal NQS structure, the resulting necessity for high-order correlations that is supported by an entanglement bound that scales with the correlation order, consequences of linear dependencies in constrained Hilbert spaces for correlation requirements, and connections between spin basis rotations and the correlator basis. Furthermore, we analyze how neural networks achieve high correlation orders by increasing the magnitude of the network weights, which can be compensated by increasing the network depth. Lastly, we discuss how activation functions, network architectures, and choice of reference basis influence correlation requirements. Our results provide new insights and a better understanding of the internal structure and requirements of NQS, enabling a more systematic use of NQS in future research.

quant-ph↗

arXiv2026

Matter-induced plaquette terms in a $\mathbb{Z}_2$ lattice gauge theory

Lattice gauge theories (LGTs) provide a powerful framework for studying confinement, topological order, and exotic quantum matter. In particular, the paradigmatic phenomenon of confinement, where dynamical matter is coupled to gauge fields and forms bound states, remains an open problem. In addition, LGTs can provide low-energy descriptions of quantum spin liquids, which is the focus of ongoing experimental research. However, the study of LGTs is often limited theoretically by their numerical complexity and experimentally in implementing challenging multi-body interactions, such as the plaquette terms crucial for the realization of many exotic phases of matter. Here we investigate a $(2+1)$D $\mathbb{Z}_2$ LGT coupled to hard-core bosonic matter featuring a global U(1) symmetry, and show that dynamical matter naturally induces sizable plaquette interactions even in the absence of explicit plaquette terms in the Hamiltonian. Using a combination of density matrix renormalization group simulations and neural quantum state calculations up to a system size of $20 \times 20$, we analyze the model across different fillings and electric field strengths. At small coupling strength, we find a large plaquette expectation value, independent of system size, for a wide range of fillings, which decreases in the presence of stronger electric fields. Furthermore, we observe signatures of a confinement-deconfinement transition at weak coupling strengths. Our results demonstrate that dynamical U(1) matter can induce complex multi-body interactions, suggesting a natural route to the realization of strong plaquette terms and paving the way for realizing a topological quantum spin liquid protected by a large gap.

cond-mat.quant-gas↗

arXiv2024

Neural Network Quantum States for the Interacting Hofstadter Model with Higher Local Occupations and Long-Range Interactions

Due to their immense representative power, neural network quantum states (NQS) have gained significant interest in current research. In recent advances in the field of NQS, it has been demonstrated that this approach can compete with state-of-the-art numerical techniques, making NQS a compelling alternative, in particular for the simulation of large, two-dimensional quantum systems. In this study, we show that recurrent neural network (RNN) wave functions can be employed to study systems relevant to current research in quantum many-body physics. Specifically, we employ a 2D tensorized gated RNN to explore the bosonic Hofstadter model with a variable local Hilbert space cut-off and long-range interactions. At first, we benchmark the RNN-NQS for the Hofstadter-Bose-Hubbard (HBH) Hamiltonian on a square lattice. We find that this method is, despite the complexity of the wave function, capable of efficiently identifying and representing most ground state properties. Afterwards, we apply the method to an even more challenging model for current methods, namely the Hofstadter model with long-range interactions. This model describes Rydberg-dressed atoms on a lattice subject to a synthetic magnetic field. We study systems of size up to $12 \times 12$ sites and identify three different regimes by tuning the interaction range and the filling fraction $ν$. In addition to phases known from the HBH model at short-ranged interaction, we observe bubble crystals and Wigner crystals for long-ranged interactions. Especially interesting is the evidence of a bubble crystal phase on a lattice, as this gives experiments a starting point for the search of clustered liquid phases, possibly hosting non-Abelian anyon excitations. In our work we show that NQS are an efficient and reliable simulation method for quantum systems, which are the subject of current research.

cond-mat.dis-nn↗

arXiv2023

Neural network approach to quasiparticle dispersions in doped antiferromagnets

Numerically simulating spinful, fermionic systems is of great interest from the perspective of condensed matter physics. However, the exponential growth of the Hilbert space dimension with system size renders an exact parameterization of large quantum systems prohibitively demanding. This is a perfect playground for neural networks, owing to their immense representative power that often allows to use only a fraction of the parameters that are needed in exact methods. Here, we investigate the ability of neural quantum states (NQS) to represent the bosonic and fermionic $t-J$ model - the high interaction limit of the Fermi-Hubbard model - on different 1D and 2D lattices. Using autoregressive recurrent neural networks (RNNs) with 2D tensorized gated recurrent units, we study the ground state representations upon doping the half-filled system with holes. Moreover, we present a method to calculate dispersion relations from the neural network state representation, applicable to any neural network architecture and any lattice geometry, that allows to infer the low-energy physics from the NQS. To demonstrate our approach, we calculate the dispersion of a single hole in the $t-J$ model on different 1D and 2D square and triangular lattices. Furthermore, we analyze the strengths and weaknesses of the RNN approach for fermionic systems, pointing the way for an accurate and efficient parameterization of fermionic quantum systems using neural quantum states.

cond-mat.str-el↗