Postdoc @ Royal Holloway University of London 

Thursday June 30 – 15.15 BST

Work statistics and entanglement across the superfluid-insulator transition 

Out-of-equilibrium strongly correlated systems have been shown to display interesting work fluctuations across a phase transition [1,2]. The work distribution at criticality has been investigated recently in a few models, most of which are exactly solvable, with a focus on the first and second moments after a sudden quench. Very recently, results for inhomogeneous Hubbard chains driven for a finite time indicated that the skewness of the work distribution, besides being a measure of non-Gaussianity, also captures transitions between different correlated phases [3]. Here, we explore the first three moments of the work distribution across the superfluid-insulator transition (SIT), which is well described by the attractive Fermionic Hubbard model in the presence of randomly distributed impurities [4]. The SIT can be triggered by changing either (i) the concentration of impurities or (ii) the disorder strength. We study two quench protocols implementing these two paths and discuss the impact of the entanglement and of the temperature for maximal work extraction. Our results indicate that for disorder strengths sufficiently large to overcome the Coulomb attraction, all three moments of the work distribution show a kink at the critical concentration $C_C=N/2$. This is the same point in which the entanglement is minimal or vanishes. All the effects of the transition are suppressed at high temperatures, with work being absorbed by the system and very large fluctuations. The protocol in which the SIT is triggered by route (i) is more efficient for the average work extraction and its variance is minimized at $C_C$. 

[1] “Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter” 
A. Silva 
Phys. Rev. Lett. 101, 120603,  2008 
[2] “Work statistics and symmetry breaking in an excited-state quantum phase transition” 
Z. Mzaouali, R. Puebla, J. Goold, M. El Baz, and S. Campbell 
Phys. Rev. E 103, 032145, 2021 
[3] “Work-distribution quantumness 
and irreversibility when crossing a quantum phase transition in finite time.” 
K. Zawadzki, R. M. Serra, and I. D’Amico. 
Phys. Rev. Research, 2(3) 033167, 2020 
[4] “Superfluid-insulator transition unambiguously detected by 
entanglement in one-dimensional disordered superfluids.” 
G.A. Canella and V. V. França. Scientific reports, 9(1)1–6, 2019.