Observation of critical phase transition in a generalized Aubry-André-Harper model with superconducting circuits

Abstract

Quantum simulation enables study of many-body systems in non-equilibrium by mapping to a controllable quantum system, providing a powerful tool for computational intractable problems. Here, using a programmable quantum processor with a chain of 10 superconducting qubits interacted through tunable couplers, we simulate the one-dimensional generalized Aubry-André-Harper model for three different phases, i.e., extended, localized and critical phases. The properties of phase transitions and many-body dynamics are studied in the presence of quasi-periodic modulations for both off-diagonal hopping coefficients and on-site potentials of the model controlled respectively by adjusting strength of couplings and qubit frequencies. We observe the spin transport for initial single- and multi-excitation states in different phases, and characterize phase transitions by experimentally measuring dynamics of participation entropies. Our experimental results demonstrate that the recently developed tunable coupling architecture of superconducting processor extends greatly the simulation realms for a wide variety of Hamiltonians, and can be used to study various quantum and topological phenomena.

Topological pumping induced by spatiotemporal modulation of interaction

“…Apart from topological perspective, many studies have already shown rich nonequilibrium properties in the quasi-periodic AAH models, such as Anderson localization [52,58], mobility edge [59][60][61], multi-fractal states [62,63]. Up to now, the AAH model has been realized in various experiment platforms, such as ultracold atoms [58,64], photonic waveguides [4,18,65] and superconducting circuits [63].…”

Many-body Hilbert space scarring on a superconducting processor

“…Dynamical signature of HSF via participation entropy.-As discussed above, the Hilbert space tends to fragment into many disconnected Krylov subspaces with different dimensions in Stark systems. A direct quantity reflecting the extent to which a time-evolved state |ψ(t)⟩ spreads over the Hilbert space [34,49] is the dynamical PE, defined as…”