## Quantum dynamics in transverse-field Ising models from classical networks

Markus Schmitt, Markus Heyl

SciPost Phys. 4, 013 (2018) · published 28 February 2018

- doi: 10.21468/SciPostPhys.4.2.013
- Submissions/Reports

### Abstract

The efficient representation of quantum many-body states with classical resources is a key challenge in quantum many-body theory. In this work we analytically construct classical networks for the description of the quantum dynamics in transverse-field Ising models that can be solved efficiently using Monte Carlo techniques. Our perturbative construction encodes time-evolved quantum states of spin-1/2 systems in a network of classical spins with local couplings and can be directly generalized to other spin systems and higher spins. Using this construction we compute the transient dynamics in one, two, and three dimensions including local observables, entanglement production, and Loschmidt amplitudes using Monte Carlo algorithms and demonstrate the accuracy of this approach by comparisons to exact results. We include a mapping to equivalent artificial neural networks, which were recently introduced to provide a universal structure for classical network wave functions.

### Cited by 16

### Ontology / Topics

See full Ontology or Topics database.### Authors / Affiliations: mappings to Contributors and Organizations

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^{1 }Markus Schmitt, -
^{2 }Markus Heyl

^{1}Georg-August-Universität Göttingen / University of Göttingen [GAU]^{2}Max-Planck-Institut für Physik komplexer Systeme / Max Planck Institute for the Physics of Complex Systems

- Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG]
- Studienstiftung des Deutschen Volkes (through Organization: Studienstiftung des deutschen Volkes / German National Academic Foundation)