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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Abstract
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.
Featured image: Quench dynamics in the spin-$S$ $mathrm{U}(1)$ quantum link model in the weak-coupling regime within the target sector of Gauss’s law. The results are obtained from the infinite matrix product state technique. Time evolution of (a,b) the return rate and (c,d) the chiral condensate both show fast convergence for (a,c) half-integer and (b,d) integer link spin length $S$, although the case of integer $S$ shows overall faster convergence than the case of half-integer $S$. Both the converged return rate and the chiral condensate show good quantitative agreement for half-integer and integer $S$, as evidenced by the dotted black lines for $S=4$ in (a,c) [taken respectively from (b,d)] and for $S=7/2$ in (b,d) [taken respectively from (a,c)]. The approach to the thermodynamic limit in the quench dynamics of the chiral condensate in the weak-coupling regime for link spin lengths (e) $S=7/2$ and (f) $S=4$. The finite-size results are obtained from exact diagonalization, while those in the thermodynamic limit are calculated using the infinite matrix product state technique. In this target sector, we see much faster convergence to the thermodynamic limit for integer than for half-integer $S$.
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Cited by
[1] Jean-Yves Desaules, Debasish Banerjee, Ana Hudomal, Zlatko Papić, Arnab Sen, and Jad C. Halimeh, “Weak Ergodicity Breaking in the Schwinger Model”, arXiv:2203.08830.
[2] Zhao-Yu Zhou, Guo-Xian Su, Jad C. Halimeh, Robert Ott, Hui Sun, Philipp Hauke, Bing Yang, Zhen-Sheng Yuan, Jürgen Berges, and Jian-Wei Pan, “Thermalization dynamics of a gauge theory on a quantum simulator”, Science 377 6603, 311 (2022).
[3] Torsten V. Zache, Maarten Van Damme, Jad C. Halimeh, Philipp Hauke, and Debasish Banerjee, “Toward the continuum limit of a (1 +1 )D quantum link Schwinger model”, Physical Review D 106 9, L091502 (2022).
[4] Jad C. Halimeh, Ian P. McCulloch, Bing Yang, and Philipp Hauke, “Tuning the Topological θ -Angle in Cold-Atom Quantum Simulators of Gauge Theories”, PRX Quantum 3 4, 040316 (2022).
[5] Haifeng Lang, Philipp Hauke, Johannes Knolle, Fabian Grusdt, and Jad C. Halimeh, “Disorder-free localization with Stark gauge protection”, Physical Review B 106 17, 174305 (2022).
[6] Maarten Van Damme, Torsten V. Zache, Debasish Banerjee, Philipp Hauke, and Jad C. Halimeh, “Dynamical quantum phase transitions in spin-S U (1 ) quantum link models”, Physical Review B 106 24, 245110 (2022).
[7] Rasmus Berg Jensen, Simon Panyella Pedersen, and Nikolaj Thomas Zinner, “Dynamical quantum phase transitions in a noisy lattice gauge theory”, Physical Review B 105 22, 224309 (2022).
[8] Jad C. Halimeh and Philipp Hauke, “Stabilizing Gauge Theories in Quantum Simulators: A Brief Review”, arXiv:2204.13709.
The above citations are from SAO/NASA ADS (last updated successfully 2022-12-20 03:48:12). The list may be incomplete as not all publishers provide suitable and complete citation data.
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