11th Trieste–Ljubljana-Zagreb meeting @ Ljubljana

When: Tuesday, 31th Jan, 2024
Where: Faculty of Mathematics and Physics, University of Ljubljana.
Jadranska ulica 19, 1000 Ljubljana, Slovenia
Auditorium F1, ground floor

Program
9:55–10:00 Welcome remarks
10:00–10:30 Cheryne Dea Jonay (FMF)
10:30–11:00 Federico Rottoli (SISSA)
11:00–11:30 Coffee break
11:30–12:00 Gianpaolo Torre (IRB)
12:00–12:30 Jacopo Niedda (ICTP)
12:30–14:00 Lunch break and Discussion
14:00–14:30 Andrea Solfanelli (SISSA)
14:30–15:00 Iris Ulčakar (IJS)
15:00–15:30 Zeno Bacciconi (ICTP)
15:30– Coffee and discussions

FMF = Faculty of Mathematics and Physics (Ljubljana)
IJS = Jožef Stefan Institute (Ljubljana)
IRB = Ruđer Bošković Institute (Zagreb)
SISSA = International School for Advanced Studies (Trieste)
ICTP = International Centre for Theoretical Physics (Trieste)

Abstracts
Aspects of entanglement, chaos, and hydro in quantum many- body systems
Speaker Cheryne Dea Jonay (FMF)
Abstract In this short talk, I will introduce three recent works addressing quantum thermalization, chaos, and hydrodynamics in 1-d spin chains. The first work addresses the microscopic process driving thermalization in a generic class of quantum circuits. The main result is that there is a competition between emergent modes, resulting in multi-stage thermalization of observables and entanglement. The second introduces a framework to quantify chaos by comparing eigen- state entanglement entropy distributions to random matrix theory, enabling a more fine-grained metric than the usual spectral diagnostics. In the third part, I will introduce a recent idea to use insights from holography to study the hydrodynamics of chaotic boundary models. The bulk theory simplifies the identification of hydrodynamic variables through emergent dynamics of a simple (local and unitary) quantum circuit.
Negativity Hamiltonian from pure to mixed states
Speaker Federico Rottoli (SISSA)
Abstract The entanglement Hamiltonian, defined as the logarithm of the reduced density matrix, pro- vides the most complete characterisation of bipartite entanglement in pure states. In analogy with this quantity, recently the Negativity Hamiltonian has been introduced as a non-Hermitian operator which characterises entanglement in mixed states. We review the concept of Negativity Hamiltonian and we present analytical results in both the ground and in a thermal state of the massless Dirac fermion field theory in 1+1 dimensions, highlighting the main features and the differences with respect to the Entanglement Hamiltonian. We finally compute numerically the Negativity Hamiltonian in a critical lattice model, comparing the lattice results with the asymptotic QFT prediction. A proper comparison requires a non-trivial continuum limit which takes into account couplings between fermions at all distances.
Topologically Frustrated ANNNI Chain
Speaker Gianpaolo Torre (IRB)
Abstract Frustration originates from the impossibility of minimizing simultaneously all the local energy
constraints. In 1D spin chains with nearest-neighbor interaction, frustration can be introduced by applying a ring geometry with appropriate boundary conditions. When paired with anti- ferromagnetic interactions, this frustration has been proven to modify several system properties, such as the closing of the energy gap in traditionally gapped phases, the emergence of long-range correlations, and the vanishing (or spatial dependence) of the order parameters. In this talk, we study the interplay between the boundary-condition induced topological frustration and that of local nature due to the presence of competing next-to-nearest neighbor interactions. We consider the 1D ANNNI model since it allows us to explore both kinds of frustrations by tuning the cou- plings and the boundary conditions. In particular, we focus on the degree of entanglement within the system as measured by the entanglement entropy (EE). In the antiphase, we find that topo- logical effects are present with the EE violating the area law, providing a non-diverging extensive contribution that depends on the subsystem length. Furthermore, in the thermodynamic limit, the local and topological contributions are decoupled, and the EE can be expressed as the sum of the two terms. In contrast to the systems in which only the Topological frustration is present, this phenomenology cannot be interpreted in terms of a delocalized excitation within the system.
Glass and pseudo-localization transitions in random lasers
Speaker Jacopo Niedda (ICTP)
Abstract Optical waves in active disordered media display the typical phenomenology of complex sys- tems. The multiple scattering of light with randomly placed scatterers inside a material confines the electromagnetic field and entails the existence of well-defined cavity modes with long life- times competing for amplification. The presence of modes in random lasers can be revealed from the highly structured spectra measured in experiments. If one takes several spectral shots from the same piece of material, the position of the intensity peaks changes from shot to shot, meaning that there is no specific frequency which is preferred in the lasing phenomenon, but depending on the initial state, with the disorder kept fixed, the modes gaining the highest inten- sity change every time. In order to explain this behaviour, a statistical mechanics model derived from spin-glass theory has been developed, where the light modes are described as non-linearly interacting phasors on the so-called mode-locked diluted graph [1]. In this talk we present re- cent results from numerical simulations of the mode-locked glassy random laser. The presence of a phenomenology compatible with a glass transition when tuning the optical power of the system above a threshold value is put in evidence from the divergence of the specific heat and a non-trivial structure of the Parisi overlap distribution function. By means of a refined finite-size scaling analysis of the critical region, the transition is assessed to be compatible with a mean- field universality class [2]. A pseudo-localization transition to a phase where the intensity of light is neither properly localized on a single mode nor equiparted among all modes is revealed from the measurement of the inverse participation ratio and of the spectral entropy [3]. The two transitions occur at the same temperature as different manifestations of the same underlying phenomenon, the breaking of ergodicity.

[1] F. Antenucci, C. Conti, A. Crisanti, L. Leuzzi, Phys. Rev. Lett. 114, 043901 (2015).
[2] J. Niedda, G. Gradenigo, L. Leuzzi, G. Parisi, SciPost Phys. 14, 144 (2023).
[3] J. Niedda, L. Leuzzi, G. Gradenigo, J. Stat. Mech. 053302 (2023).

Exploring discrete floquet time crystals in long-range interacting quantum systems: from theoretical foundations to digital duantum simulations
Speaker Andrea Solfanelli (SISSA)
Abstract Discrete Floquet time crystals (DFTCs) are unique nonequilibrium many-body phases char- acterized by the breaking of the discrete time translation symmetry of the Floquet driving, and by an order parameter displaying persistent oscillations with a period that is an integer multiple of the driving period. The talk explores their potential generation in clean systems, with a focus on long-range interacting models. In the first part, I will introduce a novel order parameter to detect discrete time crystalline phases in quantum systems with strong long-range interac- tions. This tool is applied to characterize the out-of-equilibrium phase diagram of the long-range kicked Ising model, revealing a rich landscape with self-similar fractal boundaries. The second part presents outcomes from a digital quantum simulation effort, addressing qubit connectivity limitations in noisy intermediate-scale quantum devices. By exploiting the universality of native quantum processor gates, I will show how to implement couplings among physically disconnected qubits. Finally, I will present the results from a quantum simulation on IBM superconducting quantum processors benchmarking the prethermal stabilization of discrete Floquet time crys- talline response with increasing interaction range.
Iterative construction of conserved quantities in dissipative nearly integrable systems
Speaker Iris Ulčakar (IJS)
Abstract Integrable systems offer rare examples of solvable many-body problems in the quantum world, but due to their fine-tuned structure, the effects of integrability in nature are observed only tran- siently. One way to overcome this limitation is to weakly couple nearly integrable systems to baths and driving: these will stabilize integrable effects up to arbitrary time and encode them in the stationary state approximated by a generalized Gibbs ensemble. However, the description of such driven dissipative nearly integrable models is challenging and no exact analytical methods have been proposed so far. In this talk, I will present an iterative scheme in which integrability breaking perturbations (baths) determine the conserved quantities that play the leading role in a truncated generalized Gibbs ensemble description. I will first benchmark our approach on the paradigmatic transverse field Ising and Heisenberg models coupled to Lindblad baths. For the former, I will show how to evaluate the scheme for thermodynamically large systems and obtain a non-thermal steady state despite infinitesimal couplings to baths.

[1] I. Ulčakar and Z. Lenarčič, arXiv:2310.03809 (2023).

Cavity control of the fractional quantum Hall effect
Speaker Zeno Bacciconi (ICTP)
Abstract In recent years the possibility of controlling properties of quantum many body systems by means of cavity embedding has attracted a lot of attention. Among these efforts, recent exper- imental results have shown that vacuum fluctuations of an extended cavity mode are able to affect transport properties in the Integer Quantum Hall regime. From a fundatmental point of view, the effect of strongly coupled extended cavity modes challenges the understanding of re- silience to local perturbations of topological states of matter. In this talk I will present results [1] concerning the coupling of a realistic cavity set-up to a Fractional Quantum Hall state. We find that for a finite regime of coupling strengths the topological order of the state is stable. Only at strong coupling the quantum fluctuations of the cavity mode drive a transition to a charge density wave state.

[1] Z. Bacciconi, T. Chanda, H. Xavier, M. Dalmonte, in preparation.

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