Carlo Vanoni (SISSA)
Filiberto Ares (SISSA)
Jovan Odavić (RBI)
Poetri Tarabunga (ICTP)
Anton Kutlin (ICTP)
Jan Šuntajs (IJS)
(FMF = Faculty of Mathematics and Physics, IJS = Institute Jožef Stefan, IRB = Institute Ruđer Bošković)
Symmetry and symmetry breaking are two pillars of modern quantum physics. However, quantifying how much a symmetry is broken is an issue that has received little attention. In extended quantum systems, this problem is intrinsically bound to the subsystem of interest. In this talk, we will borrow methods from the theory of entanglement in many-body quantum systems to introduce a subsystem measure of symmetry breaking that we dub entanglement asymmetry. As a prototypical illustration, we will study the entanglement asymmetry in a quantum quench of a spin chain in which an initially broken global U(1) symmetry is restored dynamically. We will find, expectedly, that larger is the subsystem, slower is the restoration, but also the counterintuitive result that more the symmetry is initially broken, faster it is restored, a sort of quantum Mpemba effect.
Conventional classification of dynamical phenomena is based on universal hydrodynamic relaxation characterized by algebraic dynamical exponents and asymptotic scaling of the dy- namical structure factor. We argue that dynamical universality classes can instead be naturally distinguished based on their full-counting statistics. As an example we consider a general class of one-dimensional single-file systems of interacting hardcore charged particles. Dynamical con- straints give rise to universal anomalous statistics of cumulative charge currents, manifested both on the timescale characteristic of typical fluctuations and also in the rate function describ- ing rare events. Typical fluctuations in equilibrium are governed by a universal distribution that markedly deviates from the expected Gaussian statistics, whereas large fluctuations are described by a large-deviation rate function featuring an exceptional triple critical point. Far from equilibrium, competition between dynamical phases leads to dynamical phase transitions of first and second order. We point out some connections with charge fluctuations in integrable spin chains.
In this talk, I will present recent results on the topic of integrable topologically frustrated quantum spin chains. In particular, I will discuss entanglement properties of frustrated Ising chains with assumed frustrated boundary conditions that imply periodic boundary conditions, an odd number of spins, and antiferromagnetic coupling. The topologically frustrated ground state is a unique example of a state associated with a local and nearest-neighbor coupling Hamiltonian that violates the area-law scaling of entanglement with the subsystem size. Frustrated boundary conditions induce an excess of long-range entanglement that can be analytically described in the thermodynamic limit using the single-particle interpretation. Using an entanglement cooling (disentangling) algorithm, represented by a particular stochastic quantum circuit, we show that the frustration-induced entanglement is robust against the application of local gates. In this process, we additionally demonstrate, how with different choices of local gates the quantum circuit can induce a transition in the entanglement spectrum from the uncorrelated Poissonian distributed eigenvalue spacings to the correlated Wigner-Dyson distribution. Moreover, we advance the characterization of complexity in quantum many-body systems by examining W -state, a well-known state within the quantum information community. Such a state admits an amount of non-stabilizerness or “magic”(measured as the Stabilizer Rényi Entropy –SRE–) that grows logarithmic with the number of qubits/spins. We show that topologically frustrated ground states have a value of SRE that is the sum of that of the W-state plus an extensive local contribution. Our work reveals that W-states/frustrated ground states display a non-local degree of complexity that can be harvested as a quantum resource and has no counterpart in GHZ states/non-frustrated systems. The talk is based on: arXiv:2209.10541 and arXiv:2210.13495
Over recent years, Rydberg atom arrays has become one of the versatile platforms for the realization of exotic quantum many-body phases, such as topological phases. In this talk, I will discuss recent theoretical proposals to realize two different types of topological phases, namely, (i) Z_2 quantum spin liquids (QSLs) and (ii) (chiral) bosonic Integer Quantum Hall (BIQH) phase in Rydberg atom arrays. In the first case, I will discuss how the strong van der Waals interactions between the Rydberg states can lead to emergent Z_2 gauge symmetries, which is crucial for stabilizing Z_2 QSL. On the other hand, the BIQH phase is predicted in a different setting, where spin-orbit coupling leads to density-dependent hopping of Rydberg states. In this case, the origin of the BIQH phase can be argued to be the Chern-Simons gauge field generated by the density-dependence of the hopping.
I will show how the melting of a smooth interface in the 2D quantum Ising model with transverse and longitudinal fields shows signs of localization. This is done by means of a "holographic" mapping to a 1D integrable model of fermions in the large ferromagnetic coupling J limit and after the systematic introduction of 1/J corrections. I will also discuss the scenario in the presence of a random external field.
It is believed that the two-dimensional (2D) Anderson model exhibits localization for any nonzero disorder in the thermodynamic limit and it is also well known that the finite-size effects are considerable in the weak disorder limit. Here, we numerically study the quantum-chaos to localization transition in finite 2D Anderson models, using standard indicators used in the modern literature, such as the level spacing ratio, spectral form factor, variances of observable matrix elements, participation entropy and the eigenstate entanglement entropy. We show that many features of these indicators may indicate emergence of single-particle quantum chaos at weak disorder. However, we argue that a careful numerical analysis is consistent with the one- 3 parametric scaling theory and predicts the breakdown of quantum chaos at any nonzero disorder value in the thermodynamic limit. Among the hallmarks of this breakdown are the universal behavior of the spectral form factor at weak disorder and the universal scaling of various indi- cators as a function of the parameter u = (W log V )−1 where W is the disorder strength and V is the number of lattice sites.  J. Šuntajs, T. Prosen and L. Vidmar, in preparation.
Due to a series of recent works [1-4], an interest in multifractal states has risen as they are believed to be present in the MBL phase. Inspired by the success of the Rosenzweig-Porter (RP) model with normally distributed transition amplitudes, a similar ensemble but with the fat-tailed distributed amplitudes was proposed [5-9], with claims that it hosts the desired mul- tifractal phase. In the present work, we develop a general (graphical) approach allowing a self-consistent analytical calculation of the spectrum of eigenstate’s fractal dimensions (SFD) for various RP models and investigate what features of the RP Hamiltonians can be responsible for the multifractal phase emergence. We conclude that, for a broad set of models, the only feature contributing to a genuine multifractality is the on-site energies distribution, meaning that no random matrix model with uniformish diagonal and uncorrelated off-diagonal disorder with the convex distribution of the matrix elements’ logarithm can host a genuine multifractal phase and hence model a true MBL.  J. Z. Imbrie, V. Ros, and A. Scardicchio, Ann. Phys. 529, 7, 1600278 (2017).  G. De Tomasi et al., Phys. Rev. B 104, 024202 (2021).  A. Morningstar et al., Phys. Rev. B 105, 174205 (2022).  N. Macé et al., Phys. Rev. Lett., 123,180601 (2019).  C. Monthus, J. Phys. A: Math. & Theor. 50, 29, 295101, (2017).  V. Kravtsov et al., arXiv:2002.02979 (2020).  I. M. Khaymovich et al., Phys. Rev. Research 2, 043346 (2020).  G. Biroli and M. Tarzia, Phys. Rev. B, 103, 104205 (2021).  I. M. Khaymovich and V. E. Kravtsov, SciPost Phys. 11, 045 (2021).