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Trimer states with ℤ₃ topological order in Rydberg atom arrays

Giudice, Giacomo and Surace, Federica Maria and Pichler, Hannes and Giudici, Giuliano (2022) Trimer states with ℤ₃ topological order in Rydberg atom arrays. Physical Review B, 106 (19). Art. No. 195155. ISSN 2469-9950. doi:10.1103/physrevb.106.195155.

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Trimers are defined as two adjacent edges on a graph. We study the quantum states obtained as equal-weight superpositions of all trimer coverings of a lattice, with the constraint of having a trimer on each vertex: the so-called trimer resonating-valence-bond (tRVB) states. Exploiting their tensor network representation, we show that these states can host ℤ₃ topological order or can be gapless liquids with U(1) × U(1) local symmetry. We prove that this continuous symmetry emerges whenever the lattice can be tripartite such that each trimer covers all the three sublattices. In the gapped case, we demonstrate the stability of topological order against dilution of maximal trimer coverings, which is relevant for realistic models where the density of trimers can fluctuate. Furthermore, we clarify the connection between gapped tRVB states and ℤ₃ lattice gauge theories by smoothly connecting the former to the ℤ₃ toric code, and discuss the nonlocal excitations on top of tRVB states. Finally, we analyze via exact diagonalization the zero-temperature phase diagram of a diluted trimer model on the square lattice and demonstrate that the ground state exhibits topological properties in a narrow region in parameter space. We show that a similar model can be implemented in Rydberg atom arrays exploiting the blockade effect. We investigate dynamical preparation schemes in this setup and provide a viable route for probing experimentally ℤ₃ quantum spin liquids.

Item Type:Article
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URLURL TypeDescription
Giudice, Giacomo0000-0001-7141-2553
Surace, Federica Maria0000-0002-1545-5230
Pichler, Hannes0000-0003-2144-536X
Giudici, Giuliano0000-0003-4742-978X
Additional Information:We acknowledge inspiring discussions with Norbert Schuch, Juraj Hasik, Andrej Gendiar, and Olexei Motrunich. TN calculations were performed by resolving symmetries at the tensor level with the TensorKit.jl package [56]. This work has been supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme through the ERC-CoG SEQUAM (Grant No. 863476), the ERC-CoG QSIMCORR (Grant No. 771891), and ERC-StG QARA (Grant No. 101041435), as well as the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy (Grant No. EXC-2111–390814868).
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
European Research Council (ERC)863476
European Research Council (ERC)771891
European Research Council (ERC)101041435
Deutsche Forschungsgemeinschaft (DFG)EXC-2111–390814868
Issue or Number:19
Record Number:CaltechAUTHORS:20230105-911538600.5
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:118742
Deposited By: Research Services Depository
Deposited On:08 Feb 2023 02:06
Last Modified:08 Feb 2023 02:06

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