Achieving the quantum field theory limit in far-from-equilibrium quantum link models

Jad C. Halimeh1, Maarten Van Damme2, Torsten V. Zache3,4, Debasish Banerjee5, and Philipp Hauke1

1INO-CNR BEC Center and Department of Physics, University of Trento, Via Sommarive 14, I-38123 Trento, Italy
2Department of Physics and Astronomy, University of Ghent, Krijgslaan 281, 9000 Gent, Belgium
3Center for Quantum Physics, University of Innsbruck, 6020 Innsbruck, Austria
4Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria
5Theory Division, Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhan Nagar, Kolkata 700064, India

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Realizations of gauge theories in setups of quantum synthetic matter open up the possibility of probing salient exotic phenomena in condensed matter and high-energy physics, along with potential applications in quantum information and science technologies. In light of the impressive ongoing efforts to achieve such realizations, a fundamental question regarding quantum link model regularizations of lattice gauge theories is how faithfully they capture the quantum field theory limit of gauge theories. Recent work [79] has shown through analytic derivations, exact diagonalization, and infinite matrix product state calculations that the low-energy physics of $1+1$D $\mathrm{U}(1)$ quantum link models approaches the quantum field theory limit already at small link spin length $S$. Here, we show that the approach to this limit also lends itself to the far-from-equilibrium quench dynamics of lattice gauge theories, as demonstrated by our numerical simulations of the Loschmidt return rate and the chiral condensate in infinite matrix product states, which work directly in the thermodynamic limit. Similar to our findings in equilibrium that show a distinct behavior between half-integer and integer link spin lengths, we find that criticality emerging in the Loschmidt return rate is fundamentally different between half-integer and integer spin quantum link models in the regime of strong electric-field coupling. Our results further affirm that state-of-the-art finite-size ultracold-atom and NISQ-device implementations of quantum link lattice gauge theories have the real potential to simulate their quantum field theory limit even in the far-from-equilibrium regime.

The quantum simulation of lattice gauge theories offers a probe of particle physics that is complementary to dedicated high-energy setups such as the LHC. For the purpose of experimental feasibility, the gauge and electric fields, which are infinite-dimensional in quantum electrodynamics (QED), are represented by spin-$S$ operators. This quantum link model (QLM) formulation of QED is amenable for implementation in current cold-atom platforms for small values of $S$. An important question is how well do these spin-$S$ QLMs capture the physics of the QED limit $S\to\infty$. Using extensive uniform matrix product state and exact diagonalization calculations, we show that far-from-equilibrium quench dynamics of local and global observables of interest in spin-$S$ QLMs quickly approaches the QED limit already at small values of $S$. This indicates that state-of-the-art quantum-simulation platforms can adequately probe far-from-equilibrium phenomena relevant to QED already at the small values of $S$ they can currently achieve.

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The above citations are from Crossref's cited-by service (last updated successfully 2024-02-27 08:43:31) and SAO/NASA ADS (last updated successfully 2024-02-27 08:43:32). The list may be incomplete as not all publishers provide suitable and complete citation data.