
Giacomo Giudice, F. M. Surace, Hannes Pichler, G. Giudici Trimer states with Z3 topological order in Rydberg atom arrays,
Phys. Rev. B 106 195155 (20221128),
http://dx.doi.org/10.1103/PhysRevB.106.195155 doi:10.1103/PhysRevB.106.195155 (ID: 720842)
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Trimers are defined as two adjacent edges on a graph. We study the quantum states obtained as equalweight superpositions of all trimer coverings of a lattice, with the constraint of having a trimer on each vertex: the socalled trimer resonatingvalencebond (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 zerotemperature 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.

G. Giudici, M. Lukin, H. Pichler Dynamical preparation of quantum spin liquids in Rydberg atom arrays,
Phys. Rev. Lett. 129 90401 (20220826),
http://dx.doi.org/10.1103/PhysRevLett.129.090401 doi:10.1103/PhysRevLett.129.090401 (ID: 720742)
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We theoretically analyze recent experiments [G. Semeghini et al., Science 374, 1242 (2021)] demonstrating the onset of a topological spin liquid using a programmable quantum simulator based on Rydberg atom arrays. In the experiment, robust signatures of topological order emerge in outofequilibrium states that are prepared using a quasiadiabatic state preparation protocol. We show theoretically that the state preparation protocol can be optimized to target the fixed point of the topological phase  the resonating valence bond (RVB) state of hard dimers  in a time that scales linearly with the number of atoms. Moreover, we provide a twoparameter variational manifold of tensor network (TN) states that accurately describe the manybody dynamics of the preparation process. Using this approach we analyze the nature of the nonequilibrium state, establishing the emergence of topological order.

G. Giudice, G. Giudici, M. Sonner, J. Thoenniss, A. Lerose, D. A. Abanin, L. Piroli Temporal Entanglement, Quasiparticles, and the Role of Interactions,
Phys. Rev. Lett. 128 (20220602),
http://dx.doi.org/10.1103/PhysRevLett.128.220401 doi:10.1103/PhysRevLett.128.220401 (ID: 721051)
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In quantum manybody dynamics admitting a description in terms of noninteracting quasiparticles, the FeynmanVernon influence matrix (IM), encoding the effect of the system on the evolution of its local subsystems, can be analyzed exactly. For discrete dynamics, the temporal entanglement (TE) of the corresponding IM satisfies an area law, suggesting the possibility of an efficient representation of the IM in terms of matrixproduct states. A natural question is whether integrable interactions, preserving stable quasiparticles, affect the behavior of the TE. While a simple semiclassical picture suggests a sublinear growth in time, one can wonder whether interactions may lead to violations of the area law. We address this problem by analyzing quantum quenches in a family of discrete integrable dynamics corresponding to the realtime Trotterization of the interacting XXZ Heisenberg model. By means of an analytical solution at the dualunitary point and numerical calculations for generic values of the system parameters, we provide evidence that, away from the noninteracting limit, the TE displays a logarithmic growth in time, thus violating the area law. Our findings highlight the nontrivial role of interactions, and raise interesting questions on the possibility to efficiently simulate the local dynamics of interacting integrable systems.