Lieb's Theorem and Maximum Entropy Condensates

Joseph Tindall; Frank Schlawin; Michael Sentef; Dieter Jaksch

doi:10.22331/q-2021-12-23-610

Lieb’s Theorem and Maximum Entropy Condensates

Joseph Tindall¹, Frank Schlawin^2,3, Michael Sentef², and Dieter Jaksch^1,3,4

¹Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
²Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany
³The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, Hamburg, Germany
⁴Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany

Published:	2021-12-23, volume 5, page 610
Eprint:	arXiv:2103.04687v3
Doi:	https://doi.org/10.22331/q-2021-12-23-610
Citation:	Quantum 5, 610 (2021).

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Abstract

Coherent driving has established itself as a powerful tool for guiding a many-body quantum system into a desirable, coherent non-equilibrium state. A thermodynamically large system will, however, almost always saturate to a featureless infinite temperature state under continuous driving and so the optical manipulation of many-body systems is considered feasible only if a transient, prethermal regime exists, where heating is suppressed. Here we show that, counterintuitively, in a broad class of lattices Floquet heating can actually be an advantageous effect. Specifically, we prove that the maximum entropy steady states which form upon driving the ground state of the Hubbard model on unbalanced bi-partite lattices possess uniform off-diagonal long-range order which remains finite even in the thermodynamic limit. This creation of a `hot' condensate can occur on $\textit{any}$ driven unbalanced lattice and provides an understanding of how heating can, at the macroscopic level, expose and alter the order in a quantum system. We discuss implications for recent experiments observing emergent superconductivity in photoexcited materials.

Featured image: Off-diagonal order in the steady state of the driven Hubbard model versus the `imbalance' of the underlying bi-partite lattice. Data is for the thermodynamic limit. The steady state is formed by driving the ground-state to infinite temperature whilst preserving SU(2) symmetry. The resulting correlations are always uniform with distance (see inset). Notable lattices are listed on the right.

Popular summary

In general, heat is deleterious towards quantum effects. Under certain symmetry constraints, however, this is not true and heating can be used to re-arrange and expose order in a quantum system.
In this article we show how, in a paradigmatic electronic system, the amount of order which results from this process can be directly related to certain geometrical properties of the underlying lattice. This allows us to identify a range of lattice structures where heating can be used to manipulate and manifest quantum order even at the macroscopic level.
We discuss possible experimental realisations of our work and its potential as a novel method for engineering and controlling superconductivity.

► BibTeX data

@article{Tindall2021liebstheorem,
  doi = {10.22331/q-2021-12-23-610},
  url = {https://doi.org/10.22331/q-2021-12-23-610},
  title = {Lieb's {T}heorem and {M}aximum {E}ntropy {C}ondensates},
  author = {Tindall, Joseph and Schlawin, Frank and Sentef, Michael and Jaksch, Dieter},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {610},
  month = dec,
  year = {2021}
}

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Cited by

[1] Joseph Tindall, Amy Searle, Abdulla Alhajri, and Dieter Jaksch, "Quantum physics in connected worlds", Nature Communications 13 1, 7445 (2022).

[2] Y. B. Shi, K. L. Zhang, and Z. Song, "Dynamic generation of nonequilibrium superconducting states in a Kitaev chain", Physical Review B 106 18, 184505 (2022).

[3] A. M. Marques, J. Mögerle, G. Pelegrí, S. Flannigan, R. G. Dias, and A. J. Daley, "Kaleidoscopes of Hofstadter butterflies and Aharonov-Bohm caging from 2n -root topology in decorated square lattices", Physical Review Research 5 2, 023110 (2023).

[4] A. M. Marques and R. G. Dias, "Generalized Lieb's theorem for noninteracting non-Hermitian n -partite tight-binding lattices", Physical Review B 106 20, 205146 (2022).

[5] Masaya Nakagawa, Naoto Tsuji, Norio Kawakami, and Masahito Ueda, "$\eta$ Pairing of Light-Emitting Fermions: Nonequilibrium Pairing Mechanism at High Temperatures", arXiv:2103.13624, (2021).

The above citations are from Crossref's cited-by service (last updated successfully 2023-05-29 19:10:29) and SAO/NASA ADS (last updated successfully 2023-05-29 19:10:30). The list may be incomplete as not all publishers provide suitable and complete citation data.

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