Hilbert space fragmentation in open quantum systems
- Creators
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Li, Yahui
- Sala, Pablo
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Pollmann, Frank
Abstract
We investigate the phenomenon of Hilbert space fragmentation (HSF) in open quantum systems and find that it can stabilize highly entangled steady states. For concreteness, we consider the Temperley-Lieb model, which exhibits quantum HSF in an entangled basis, and investigate the Lindblad dynamics under two different couplings. First, we couple the system to a dephasing bath that reduces quantum fragmentation to a classical one with the resulting stationary state being separable. We observe that despite vanishing quantum correlations, classical correlations develop due to fluctuations of the remaining conserved quantities, which we show can be captured by a classical stochastic circuit evolution. Second, we use a coupling that preserves the quantum fragmentation structure. We derive a general expression for the steady state, which has a strong coherent memory of the initial state due to the extensive number of noncommuting conserved quantities. We then show that it is highly entangled as quantified by logarithmic negativity.
Copyright and License
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Acknowledgement
The tensor-network calculations in this work were performed using the TeNPy Library [100]. The authors thank Oliver Hart, Barbara Kraus, Olexei Motrunich, and Sanjay Moudgalya for valuable advice. Y.L. thanks Fabian Essler, Zongping Gong, Johannes Hauschild, Dieter Jaksch, Yujie Liu, Hannes Pichler, Elisabeth Wybo, and Zhongda Zeng for helpful discussions. P.S. acknowledges support by the Walter Burke Institute for Theoretical Physics at Caltech and the Institute for Quantum Information and Matter. This research was financially supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program under Grant Agreement No. 771537. F.P. acknowledges the support of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy EXC-2111-390814868. F.P.'s research is part of the Munich Quantum Valley, which is supported by the Bavarian state government with funds from the Hightech Agenda Bayern Plus.
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Additional details
- Walter Burke Institute for Theoretical Physics
- California Institute of Technology
- Institute for Quantum Information and Matter
- European Research Council
- 771537
- Deutsche Forschungsgemeinschaft
- EXC-2111-390814868
- Caltech groups
- Walter Burke Institute for Theoretical Physics, Institute for Quantum Information and Matter