Confinement and Kink Entanglement Asymmetry on a Quantum Ising Chain

Brian J. J. Khor; D. M. Kürkçüoglu; T. J. Hobbs; G. N. Perdue; Israel Klich

doi:10.22331/q-2024-09-06-1462

Confinement and Kink Entanglement Asymmetry on a Quantum Ising Chain

Brian J. J. Khor^1,2, D. M. Kürkçüoglu^2,3, T. J. Hobbs⁴, G. N. Perdue², and Israel Klich¹

¹Department of Physics, University of Virginia, Charlottesville, VA, USA
²Fermi National Accelerator Laboratory, Batavia, IL 60510, USA
³Superconducting Quantum Materials and Systems Center (SQMS), Fermi National Accelerator Laboratory, Batavia, IL 60510, USA
⁴High Energy Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA

Published:	2024-09-06, volume 8, page 1462
Eprint:	arXiv:2312.08601v3
Doi:	https://doi.org/10.22331/q-2024-09-06-1462
Citation:	Quantum 8, 1462 (2024).

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Abstract

In this work, we explore the interplay of confinement, string breaking and entanglement asymmetry on a 1D quantum Ising chain. We consider the evolution of an initial domain wall and show that, surprisingly, while the introduction of confinement through a longitudinal field typically suppresses entanglement, it can also serve to increase it beyond a bound set for free particles. Our model can be tuned to conserve the number of domain walls, which gives an opportunity to explore entanglement asymmetry associated with link variables. We study two approaches to deal with the non-locality of the link variables, either directly or following a Kramers-Wannier transformation that maps bond variables (kinks) to site variables (spins). We develop a numerical procedure for computing the asymmetry using tensor network methods and use it to demonstrate the different types of entanglement and entanglement asymmetry.

Featured image: Integrable entanglement dynamics and domain wall profile (top) and Non-integrable entanglement dynamics and domain wall profile upon the introduction of confining field (bottom). Confinement breaks integrability, enhances entanglement entropy and causes the domain wall collision to become non-ballistic.

Popular summary

Confinement is the physical phenomenon in which elementary particles in the nucleus stay bound together despite the fact that these particles have the same charge should have repel each other owing to similar charges. In general, the presence of confinement will reduce the amount of quantum entanglement for well known physical systems such as the one dimensional Ising spin chain. However, we present a situation in which the presence of confinement enhances the amount of quantum entanglement in one dimensional Ising chain. This is possible when we impose a mathematical condition on our spin chain called integrability, and in this case we show that confinement increases entanglement production. Our result will be of interest to the quantum simulation, high energy physics, and condensed matter physics community.

► BibTeX data

@article{Khor2024confinementkink,
  doi = {10.22331/q-2024-09-06-1462},
  url = {https://doi.org/10.22331/q-2024-09-06-1462},
  title = {Confinement and {K}ink {E}ntanglement {A}symmetry on a {Q}uantum {I}sing {C}hain},
  author = {Khor, Brian J. J. and K{\"{u}}rk{\c{c}}{\"{u}}oglu, D. M. and Hobbs, T. J. and Perdue, G. N. and Klich, Israel},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1462},
  month = sep,
  year = {2024}
}

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[2] Shuo Liu, Hao-Kai Zhang, Shuai Yin, and Shi-Xin Zhang, "Symmetry restoration and quantum Mpemba effect in symmetric random circuits", arXiv:2403.08459, (2024).

[3] Fabio Caceffo, Sara Murciano, and Vincenzo Alba, "Entangled multiplets, asymmetry, and quantum Mpemba effect in dissipative systems", Journal of Statistical Mechanics: Theory and Experiment 2024 6, 063103 (2024).

[4] Konstantinos Chalas, Filiberto Ares, Colin Rylands, and Pasquale Calabrese, "Multiple crossing during dynamical symmetry restoration and implications for the quantum Mpemba effect", arXiv:2405.04436, (2024).

[5] Lata Kh. Joshi, Johannes Franke, Aniket Rath, Filiberto Ares, Sara Murciano, Florian Kranzl, Rainer Blatt, Peter Zoller, Benoît Vermersch, Pasquale Calabrese, Christian F. Roos, and Manoj K. Joshi, "Observing the Quantum Mpemba Effect in Quantum Simulations", Physical Review Letters 133 1, 010402 (2024).

[6] Marco Lastres, Sara Murciano, Filiberto Ares, and Pasquale Calabrese, "Entanglement asymmetry in the critical XXZ spin chain", arXiv:2407.06427, (2024).

[7] Shion Yamashika, Filiberto Ares, and Pasquale Calabrese, "Entanglement asymmetry and quantum Mpemba effect in two-dimensional free-fermion systems", Physical Review B 110 8, 085126 (2024).

[8] Filiberto Ares, Vittorio Vitale, and Sara Murciano, "The quantum Mpemba effect in free-fermionic mixed states", arXiv:2405.08913, (2024).

[9] Jack Y. Araz, Siddhanth Bhowmick, Matt Grau, Thomas J. McEntire, and Felix Ringer, "State preparation of lattice field theories using quantum optimal control", arXiv:2407.17556, (2024).

[10] Katja Klobas, Colin Rylands, and Bruno Bertini, "Translation symmetry restoration under random unitary dynamics", arXiv:2406.04296, (2024).

[11] Jack Y. Araz, Raghav G. Jha, Felix Ringer, and Bharath Sambasivam, "Thermal state preparation of the SYK model using a variational quantum algorithm", arXiv:2406.15545, (2024).

[12] Xhek Turkeshi, Pasquale Calabrese, and Andrea De Luca, "Quantum Mpemba Effect in Random Circuits", arXiv:2405.14514, (2024).

[13] Johannes Knaute, Matan Feuerstein, and Erez Zohar, "Entanglement and confinement in lattice gauge theory tensor networks", Journal of High Energy Physics 2024 2, 174 (2024).

[14] Alessandro Foligno, Pasquale Calabrese, and Bruno Bertini, "Non-equilibrium dynamics of charged dual-unitary circuits", arXiv:2407.21786, (2024).

[15] Shuo Liu, Hao-Kai Zhang, Shuai Yin, Shi-Xin Zhang, and Hong Yao, "Quantum Mpemba effects in many-body localization systems", arXiv:2408.07750, (2024).

[16] Katja Klobas, "Non-equilibrium dynamics of symmetry-resolved entanglement and entanglement asymmetry: Exact asymptotics in Rule 54", arXiv:2407.21793, (2024).

The above citations are from SAO/NASA ADS (last updated successfully 2024-09-09 10:08:55). The list may be incomplete as not all publishers provide suitable and complete citation data.

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