Staircase Prethermalization and Constrained Dynamics in Lattice Gauge Theories

Apr 21, 2021
Leeds-Loughborough-Nottingham Nonequilibrium Seminar


The dynamics of lattice gauge theories is characterized by an abundance of local symmetry constraints. Although errors that break gauge symmetry appear naturally in NISQ-era quantum simulators, their influence on the gauge-theory dynamics is insufficiently investigated. In this talk, we show that a small gauge breaking of strength $\lambda$ induces a staircase of long-lived prethermal plateaus. The number of prethermal plateaus increases with the number of matter fields $L$, with the last plateau being reached at a timescale $\lambda^{−L/2}$, showing an intimate relation of the concomitant slowing down of dynamics with the number of local gauge constraints. By means of a Magnus expansion, we demonstrate how exact resonances between different gauge-invariant supersectors are the main reason behind the emergence of staircase prethermalization. Our results bode well for NISQ quantum devices, as they indicate that the proliferation timescale of gauge-invariance violation is counterintuitively delayed exponentially in system size. From a phenomenological perspective, our work shows how prethermal behavior is significantly enriched in models with slight breaking of local gauge invariance relative to their counterparts where a global symmetry is broken.

[1] J. C. Halimeh, P. Hauke, Staircase Prethermalization and Constrained Dynamics in Lattice Gauge Theories, arXiv:2004.07248 [cond-mat.quant-gas] (2020).

[2] J. C. Halimeh, P. Hauke, Origin of staircase prethermalization in lattice gauge theories, arXiv:2004.07254 [cond-mat.str-el] (2020).

[3] J. C. Halimeh, P. Hauke, Reliability of lattice gauge theories, Phys. Rev. Lett.125, 030503 (2020).

[4] J. C. Halimeh, H. Lang, J. Mildenberger, Z. Jiang, P. Hauke, Gauge-Symmetry Protection Using Single-Body Terms, arXiv:2007.00668 [quant-ph] (2020).

[5] M. van Damme, H. Lang, P. Hauke, J. C. Halimeh, Reliability of lattice gauge theories in the thermodynamic limit, arXiv:2104.07040 [cond-mat.quant-gas] (2021).

Jad C. Halimeh
Postdoc (2019 – 2021)
Now Senior Postdoc at LMU München