9th Trieste–Ljubljana-Zagreb meeting @ Ljubljana

When: Tuesday, 14th Mar, 2023
Where: Jožef Stefan Institute (JSI) – Ljubljana

Link to Jožef Stefan Institute (JSI) webpage

9:55–10:00 Welcome remarks
10:00–10:30 Jaš Bensa (FMF UL)
10:30–11:00 Roberto Verdel Aranda (ICTP)
11:00–11:30 Coffee break
11:30–12:00 Stefano Scopa (SISSA)
12:00–12:30 Sourav Nandy (JSI)
12:30–15:00 Lunch break and Discussion
15:00–15:30 Alberto Giuseppe Catalano (IRB)
15:30–16:00 Coffee break
16:00–16:30 Titas Chanda (ICTP)
16:30–17:00 Nina Javerzat (SISSA)
17:00– Discussion and Social dinner
Phantom eigenvalues
Speaker Jaš Bensa
Abstract In this talk, we investigate the behavior of purity and out-of-time-ordered correlations in random quantum circuits. We show that the time evolution of both quantities can be described by a Markov chain, and their relaxation towards their asymptotic values is not governed by the second largest eigenvalue of the transfer matrix, as one could expect. The exponential relaxation is instead given by an “eigenvalue”, which is not in the spectrum of the transfer matrix at all — a phantom eigenvalue. We shall explore this phenomenon and find that it is rooted in the non-Hermiticity of the transfer matrix and in the locality of the dynamics.
A data-driven approach to the many-body problem: universality far from equilibrium
Speaker Roberto Verdel Aranda
Abstract Programmable quantum devices have demonstrated unparalleled capabilities to probe correlated quantum matter, for example, by resolving many-body wave functions via (generalised) projective measurements. However, dealing with the full information content of the generated output remains a key challenge. In this talk, I will discuss a theoretical framework to address crucial questions in the characterisation of quantum simulator output via non-parametric learning techniques and network theory. In particular, the following three complementary tools are employed: the Kolmogorov complexity, quantified by the intrinsic dimension; spectral entropies obtained via principal component analysis of observables; and a wave function network analysis, to quantify arbitrary correlations between wave function snapshots. I will illustrate this toolbox by analysing both experiments on dynamical properties of Bose-Einstein condensates as well as numerical results for classical many-body spin models. As a main outcome, I will show that our data-driven approach can detect, in an assumption-free manner, universal behaviour in the underlying physical systems, both in and out of equilibrium. I will conclude with general remarks on the applicability of our method and further potential applications.
One-particle density matrix of the out-of-equilibrium Tonks-Girardeau gas: exact results from quantum generalized hydrodynamics
Speaker Stefano Scopa
Abstract Understanding the non-equilibrium dynamics of many-body quantum systems is a notoriously hard task due to the exponential increase of the Hilbert space dimension with the number of the system’s components. This prevented, for a long time, a direct comparison between theory and the available experimental measures with ultracold atoms and ions. In recent years, the advent of Generalized Hydrodynamics enabled significant steps forward, allowing quantitative predictions for some transport properties (e.g. density and current profiles during the dynamics) of experimentally-feasible quantum setups. But despite its great predictive power, Generalized Hydrodynamics (like any hydrodynamic theory) does not capture important quantum effects, such as equal-time correlations among different points and zero-temperature entanglement. A way to account for these missing quantum effects is established by the so-called Quantum Generalized Hydrodynamics, where an effective field theory description of the leading quantum fluctuations is incorporated over the evolving background set by Generalized Hydrodynamics. In this talk, I will present some progresses in the calculation of the out-of-equilibrium one-particle density matrix enabled by the framework of Quantum Generalized Hydrodynamics and comment on their experimental relevance. The focus will be mainly on the 1D Bose gas in the limit of strong repulsion (or Tonks-Girardeau limit).
Spin transport in perturbed quantum integrable chain
Speaker Sourav Nandy
Abstract In the context of quantum transport, the XXZ (or anisotropic Heisenberg) chain is a paradigmatic many-body model, featuring wide spectrum of spin transport behaviour at finite temperature. Although the unperturbed model is analytically solvable, understanding the effects of even weak integrability-breaking perturbations (IBP) remains an open problem. The primary aim of this talk is to highlight the effects of IBP on the spin transport i) in the easy-axis regime and ii) at the isotropic point of the XXZ chain. In particular, I will show that the anomalous (dissipationless) spin diffusion of the integrable easy-axis XXZ chain is replaced by a normal spin diffusion upon the addition of perturbation. Such a fundamental change in the nature of diffusion is reflected via discontinuous variation of the dc diffusion constant as a function of the perturbation. Next, the impact of the symmetry of IBP on the spin superdiffusion at the isotropic point of integrable XXZ chain will be addressed. In this context, our study unveils several remarkable properties: i) the effects of IBP preserving spin isotropy being qualitatively different from anisotropic IBP, ii) isotropic IBP leads to a pronounced maximum of the diffusion constant at the isotropic point as the function of spin anisotropy, and iii) robustness of superdiffusion on finite systems even at appreciable perturbation strengths.

Phys. Rev. B 106, 245104 (2022), arXiv:2211.17181.

Frustrating quantum batteries
Speaker Alberto Giuseppe Catalano
Abstract We are at the verge of the Quantum Technology Revolution: quantum mechanics allows for phenomena that have no classical counterparts and which can be harvested for new technologies. An example of the emerging quantum technologies are quantum batteries (QB), i.e. quantum mechanical systems that can store and transfer energy in a coherent way. While the practical implementation of such devices is still far from becoming reality, a serious effort is being devoted to understanding their advantages and limitations, using different platforms and protocols. As it has been recently demonstrated that the introduction of topological frustration in one-dimensional spin-1/2 chains can strongly modify the low energy properties of these systems, we investigate the performance of a quantum battery realized through such frustrated chains and introduce a novel, natural, decoherence mechanism that show their superiority compared to their unfrustrated counterpart. We quantify this superiority using the notion of ergotropy, that is, the amount of energy that can be extracted from a battery with a unitary transformation.

Entanglement and photon condensation in cavity QED many-body systems
Speaker Titas Chanda
Abstract In this talk, I will start with discussing our recent work on the critical properties of quantum entanglement in a light-matter hybrid system where coupling to a photonic mode drives a superradiant phase transition in the system. Using both analytical and numerical approaches, we show that the light-matter entanglement displays critical behavior at the transition, and features maximum susceptibility, as demonstrated by a maximal entanglement capacity. Remarkably, such critical behavior of the entanglement provides a direct access to critical exponents, without direct matter probes. On the other hand, the very existence of superradiance phases and transitions in a cavity QED many-body system has recently been put into question when the system respects the gauge-invariance of electromagnetism — resulting in no-go theorems on spontaneous photon condensation. Specifically, the superradiant phase transition is prohibited as long as a purely electrical vector potential is considered, with the transition being analogous to a magnetostatic instability. In the second part of this talk, I will move to another recent work, where, to bypass these no-go theorems, we consider a minimal setting beyond 1D – i.e., a two-leg ladder. In this ladder geometry, the orbital motion of spinless fermions is coupled through Peierls substitution to a non-uniform cavity mode which generates a fluctuating uniform magnetic field. Thanks to the quasi-one dimensional geometry, we scrutinize the accuracy of (mean field) cavity-matter decoupling against large scale density-matrix renormalization group simulations. Our results show that ladder geometries can indeed host a first-order superradiant transition, that corresponds to a sudden change in the fermionic band structure as well as the number of its Fermi points. We find that light-matter entanglement is essential for capturing corrections to matter properties at finite sizes and for the description of the correct photon state.

Phys. Rev. B 106, 155113 (2022), arXiv:2302.09901.

Schramm-Loewner Evolution in 2d Rigidity Percolation
Speaker Nina Javerzat
Abstract Rigidity percolation is a widely used framework in soft matter and biophysics, to describe how amorphous materials acquire mechanical stability as microscopic components are added, undergoing a second-order phase transition from a floppy to a macroscopically rigid phase. Despite the simplicity of its formulation, understanding the universal properties of this long-range correlated percolation model remains a challenge. I will present recent results showing that powerful tools from mathematical physics can be used to probe this critical point: conformal field theory and Schramm-Loewner evolution (SLE). In particular I will explain that the interfaces in rigidity percolation can be consistently described by an $SLE_\kappa$ with an universal diffusion constant $κ_{RP} \sim 2.82$. Relations coming from conformal field theory then provide non-trivial expressions relating critical exponents of rigidity percolation to $\kappa_{RP}$. I’d finally like to discuss recently observed connections between this problem and the standard percolation problem, which might allow to reach a deeper understanding of rigidity percolation in the future.

arXiv:2301.07614, arXiv:2210.06271.

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