Fig. 4: Averaged late-time participation entropy. | npj Quantum Information

Fig. 4: Averaged late-time participation entropy.

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

Fig. 4

a Averaged late-time participation entropy \(\overline{{S}_{2}^{{{{\rm{PE}}}}}}\) as a function of μ and V. The stripes I, II and III show the experimentally measured averaged late-time participation entropy, and the underlying phase diagram shows the numerically calculated averaged late-time participation entropy using the Hamiltonian (1). The white dashed line shows theoretical phase boundaries as a guide to eye. Comparisons between experimental data and numerical simulation along (b) the path I with fixed μ = 0.5, (c) II with fixed V = 1, and (d) III with fixed V = 3. Points with statistical error bars are experimental data, and solid lines are numerical simulation using the Hamiltonian (1). Dashed lines exhibit the numerically calculated averaged late-time participation entropy rescaled as \(\widetilde{\overline{{S}_{2}^{{{{\rm{PE}}}}}}}(L)=\frac{\log {{{{\mathcal{N}}}}}_{10}}{\log {{{{\mathcal{N}}}}}_{L}}\cdot \overline{{S}_{2}^{{{{\rm{PE}}}}}}(L)\) for larger system sizes. Error bars represent the standard deviation.

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