Research

Long-range interacting quantum systems

In recent years, there has been growing attention towards the study of the quantum dynamics of long-range (LR) interacting particles, motivated by the fact that they effectively describe most atomic molecular and optical systems, such as Bose-Einstein condensates, cavity QED and trapped ions. The prominent collective character of these systems gives rise to novel dynamical phenomena, metastable phases of matter, and forms of dynamical criticality, which do not have a counterpart in traditional quantum systems with local interactions. 

We are interested in the effects of LRI  on the standard paradigm of quantum thermalization, with a quantum information perspective.
For instance, we have illustrated how the standard quasi-particle contribution to the EE dynamics gets suppressed, leading to a time-dependent logarithmic scaling of the EE that is governed instead by a collective (semi-classical) contribution 2.. This provides a very transparent and quantitative relationship between entanglement propagation measures (such as entropy, quantum Fisher information, spin squeezing) and chaos quantifiers (such as Lyapunov exponents and out-of-time-order correlations) in the semiclassical regime 2.. This phenomenology is consistent with a many-body spectrum characterised by athermal scarred eigenstates...

Selected publications:

1. entanglement entropy in for ground states of the Dyson LRI model           
   S. Pappalardi, P. Calabrese and G. Parisi - J. Stat. Mech. (2019)

2. the origin of the slow entanglement dynamics in LRI spin systems

A. Lerose and S.Pappalardi - Phys. Rev. Research (R) (2020)

A. Lerose and S. Pappalardi - Phys. Rev. A, (2020)

3. Many-body quantum scars in long-range interacting quantum systems.

A. Lerose, T. Parolini, R. Fazio, D A Abanin, S Pappalardi - Phys. Rev. X,  (2025).

4. Review on out-of-equilibrium dynamics

N. Defenu, A. Lerose and S.Pappalardi - Physics Reports 1074 (2023).

Multipartite entanglement in many-body systems

There are many facets to entanglement theory and, in particular, many-body systems offer the perfect playground to explore multipartite entanglement. In our group, we are interested in the Quantum Fisher Information (QFI), which characterizes the usefulness of quantum states for phase-estimation purposes. It is also a witness of multipartite entanglement: it gives the size of the biggest entangled block of a composite system.  This quantity has recently attracted growing attention in the community of many-body systems, mostly due to its remarkable relation to thermal susceptibilities, which makes the QFI experimental accessible in condensed matter physics. 

We are interested in establishing the QFI as a complementary quantity to characterise quantum many-body states, thus identifying their usefulness for metrological purposes.
So far, besides their connection in the semi-classical limit with the entanglement entropy and chaos quantifiers 1., we have shown that the QFI allows distinguishing thermal density matrices from ETH eigenstates at the corresponding energy 2.. Another convincing example is the one of many-body quantum scars (athermal eigenstates in the middle of the spectrum) which possesses a QFI that scales extensively with system size, in contrast to generic thermal states, hence signalling their significance as a resource in quantum-enhanced metrology 3.

Selected publications

1. QFI in semi-classical dynamics where QFI=EE (entanglement entropy)
   A. Lerose and S. Pappalardi - Phys. Rev. A (2020).

2. QFI for ETH eigenstates
   M. Brenes, S. Pappalardi,  J. Goold and A. Silva - Phys. Rev. Lett. (2019). 

3.  QFI for many-body quantum scars
   J.Y. Desaules, F. Pietracaprina, Z. Papić, J. Goold and S. Pappalardi - Phys. Rev. Lett. (2022)
   S. Dooley, S. Pappalardi and J. Goold - Phys.Rev.B. (2023). 

4. QFI in monitored systems
   A Lira-Solanilla, X Turkeshi, S Pappalardi - Arxiv 2412.16062 (2024). 

The eigenstate thermalization hypothesis

Understanding how isolated quantum systems thermalise under unitary evolution is a theme as old as quantum mechanics itself. In isolated classical systems, thermalisation relies on the emergence of chaos and ergodicity, which together lead phase-space trajectories starting from the same energy to become indistinguishable when averaged over time. In the quantum domain, relaxation to thermal equilibrium is nowadays well understood by the Eigenstate Thermalization Hypothesis (ETH). According to ETH, local observables in the energy eigenbasis are pseudorandom matrices, whose statistical properties are smooth thermodynamic functions. This simple assumption on the structure of matrix elements has proved to be extremely successful in describing the dynamical properties of physical Hamiltonian systems: from their thermalization to the entanglement of chaotic eigenstates and to two-point dynamical correlations at equilibrium.

We are interested in understanding the universal aspects of the eigenstate thermalisation hypothesis using, in particular, multi­time correlation functions.

The latter are the relevant quantities beyond linear response to characterize higher-order hydrodynamics, quantum chaos, and scrambling. For instance, recently we have shown that general ETH, which accounts for higher-order correlations among matrix elements, can be rationalized theoretically using the language of Free Probability. Free Probability is a branch of math that generalizes probability to non-commuting variables. (Check out the Free probability blog here.) This mathematical framework seems to be very promising in describing higher-order correlations in physical lattice systems and beyond...

Selected publications:

1. ETH and multipartite entanglement:
   M. Brenes, S. Pappalardi, J. Goold, A. Silva - Phys.Rev.Lett. (2020).

2. ETH and Free Probability: 

S. Pappalardi, L.Foini and J.Kurchan - Phys.Rev.Lett. (2022).

S. Pappalardi, F Fritzsch, T. Prosen - Phys. Rev. Lett (2025).

M. Fava, J. Kurchan and S. Pappalardi - Phys. Rev. X (2025).

E. Vallini and S. Pappalardi - Arxiv 2411.12050.

Hydrodynamics in many-body dynamics

A distinctive universal feature of classical dynamics is given by hydrodynamics, which describes the late­time behaviour of thermalizing systems in terms of the fluctuations of conserved densities. While it is well established that classical hydrodynamics captures the universal longtime behaviour of many­body systems, it is still unclear for which observables and in what way quantum effects become important for late­time dynamics. 

We are interested in understanding the constraints imposed by hydrodynamics on generic quantum many­body dynamics and, in particular, on the eigenstate thermalisation hypothesis.

For instance, we studied time-­ordered correlation functions, showing that, while free cumulants naturally appear within the ETH, it is the classical cumulants that have a hierarchical structure in a hydrodynamic regime, implying that free cumulants factorize into products of two (or three)­point functions.

Selected publications:

1. Hydrodynamics in Floquet local circuits:
   A. Matthies, N. Dannenfeld, S. Pappalardi, and A. Rosch, Arxiv 2410.16182.

2. Hydrodynamics and ETH 

J. Wang, R. Mishra, T.H. Yang, L.V. Delacrétaz, and S. Pappalardi, Arxiv 2505.06869.