Work statistics and Entanglement across the fermionic superfluid-insulator transition

Abstract

Entanglement in many-body systems may display interesting signatures of quantum phase transitions and similar properties are starting to be encountered in the analysis of work fluctuations. Here, we consider the fermionic superfluid-to-insulator transition (SIT) and relate its entanglement properties with its work distribution statistics. The SIT is modeled by the attractive fermionic Hubbard model in the presence of randomly distributed impurities. The work distribution is calculated across two quench protocols, both triggering the SIT. In the first, the concentration of impurities is increased; in the second, the impurities' disorder strength is varied. Our results indicate that, the critical state that induces minimization of the entanglement also maximizes the average work. We demonstrate that, for this state, density fluctuations vanish at all orders, hence all central moments of the work probability distribution are exactly zero at criticality. For systems undergoing a precursor to the transition (short chains with finite impurity potential) numerical results confirm these predictions, with higher moments further from the ideal result. For both protocols, at criticality, the system absorbs the most energy with almost no penalty in terms of fluctuations: ultimately this feature could be used to implement a quantum critical battery. The effects of temperature on these signatures of critical behaviour are also investigated and shown to favor work extraction for high enough temperatures.

References in corpus (17)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Fluctuation theorems: Work is not an observable
• Evidence for Superfluidity of Ultracold Fermions in an Optical Lattice
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons
• Metastable superfluidity of repulsive fermionic atoms in optical lattices
• Quantum Otto heat engine based on a multiferroic chain working substance
• Criticality revealed through quench dynamics the Lipkin-Meshkov-Glick model
• The Ising critical quantum Otto engine
• Entanglement entropy and entanglement witnesses in models of strongly interacting low-dimensional fermions
• Interacting fermions in 1D disordered lattices: Exploring localization and transport properties with lattice density-functional theories
• Work statistics and symmetry breaking in an excited state quantum phase transition
• Entanglement and exotic superfluidity in spin-imbalanced lattices
• Non-Gaussian work statistics at finite-time driving
• Correlation-boosted quantum engine: A proof-of-principle demonstration
• Entanglement enhancement in spatially inhomogeneous many-body systems
• Effects of Temperature and Magnetization on the Mott-Anderson Physics in one-dimensional Disordered Systems