Publications Giuliano GIUDICI

2024

Article

• Z. J. Li, G. Giudici, H. Pichler Variational manifolds for ground states and scarred dynamics of blockade-constrained spin models on two and three dimensional lattices, Phys. Rev. Research 6 23146 (2024-05-09), http://dx.doi.org/10.1103/PhysRevResearch.6.023146 doi:10.1103/PhysRevResearch.6.023146 (ID: 721240) Toggle Abstract
  We introduce a variational manifold of simple tensor network states for the study of a family of constrained models that describe spin-1/2 systems as realized by Rydberg atom arrays. Our manifold permits analytical calculation via perturbative expansion of one- and two-point functions in arbitrary spatial dimensions and allows for efficient computation of the matrix elements required for variational energy minimization and variational time evolution in up to three dimensions. We apply this framework to the PXP model on the hypercubic lattice in 1D, 2D, and 3D, and show that, in each case, it exhibits quantum phase transitions breaking the sub-lattice symmetry in equilibrium, and hosts quantum many body scars out of equilibrium. We demonstrate that our variational ansatz qualitatively captures all these phenomena and predicts key quantities with an accuracy that increases with the dimensionality of the lattice, and conclude that our method can be interpreted as a generalization of mean-field theory to constrained spin models.

Preprint

• Z. Zeng, G. Giudici, H. Pichler Quantum dimer models with Rydberg gadgets, (2024-02-16), arXiv:2402.10651 arXiv:2402.10651 (ID: 721245) Toggle Abstract
  The Rydberg blockade mechanism is an important ingredient in quantum simulators based on neutral atom arrays. It enables the emergence of a rich variety of quantum phases of matter, such as topological spin liquids. The typically isotropic nature of the blockade effect, however, restricts the range of natively accessible models and quantum states. In this work, we propose a method to systematically overcome this limitation, by developing gadgets, i.e., specific arrangements of atoms, that transform the underlying Rydberg blockade into more general constraints. We apply this technique to realize dimer models on square and triangular geometries. In these setups, we study the role of the quantum fluctuations induced by a coherent drive of the atoms and find signatures of U(1) and Z2 quantum spin liquid states in the respective ground states. Finally, we show that these states can be dynamically prepared with high fidelity, paving the way for the quantum simulation of a broader class of constrained models and topological matter in experiments with Rydberg atom arrays.

2023

Preprint

• G. Giudici, F. M. Surace, H. Pichler Unraveling PXP Many-Body Scars through Floquet Dynamics, (2023-12-26), arXiv:2312.16288 arXiv:2312.16288 (ID: 721171) Toggle Abstract
  Quantum scars are special eigenstates of many-body systems that evade thermalization. They were first discovered in the PXP model, a well-known effective description of Rydberg atom arrays. Despite significant theoretical efforts, the fundamental origin of PXP scars remains elusive. By investigating the discretized dynamics of the PXP model as a function of the Trotter step τ, we uncover a remarkable correspondence between the zero- and two-particle eigenstates of the integrable Floquet-PXP cellular automaton at τ=π/2 and the PXP many-body scars of the time-continuous limit. Specifically, we demonstrate that PXP scars are adiabatically connected to the eigenstates of the τ=π/2 Floquet operator. Building on this result, we propose a protocol for achieving high-fidelity preparation of PXP scars in Rydberg atom experiments.

2022

Articles

• Giacomo Giudice, F. M. Surace, Hannes Pichler, G. Giudici Trimer states with Z3 topological order in Rydberg atom arrays, Phys. Rev. B 106 195155 (2022-11-28), http://dx.doi.org/10.1103/PhysRevB.106.195155 doi:10.1103/PhysRevB.106.195155 (ID: 720842) Toggle Abstract
  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 non-local 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.
• G. Giudici, M. Lukin, H. Pichler Dynamical preparation of quantum spin liquids in Rydberg atom arrays, Phys. Rev. Lett. 129 90401 (2022-08-26), http://dx.doi.org/10.1103/PhysRevLett.129.090401 doi:10.1103/PhysRevLett.129.090401 (ID: 720742) Toggle Abstract
  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 out-of-equilibrium states that are prepared using a quasi-adiabatic 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 two-parameter variational manifold of tensor network (TN) states that accurately describe the many-body dynamics of the preparation process. Using this approach we analyze the nature of the non-equilibrium 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 (2022-06-02), http://dx.doi.org/10.1103/PhysRevLett.128.220401 doi:10.1103/PhysRevLett.128.220401 (ID: 721051) Toggle Abstract
  In quantum many-body dynamics admitting a description in terms of noninteracting quasiparticles, the Feynman-Vernon 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 matrix-product 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 real-time Trotterization of the interacting XXZ Heisenberg model. By means of an analytical solution at the dual-unitary 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.