Experimental signature of initial quantum coherence on entropy production

Hernández-Gómez S., Gherardini S., Belenchia A., We report on the experimental quantification of the contribution to non-equilibrium entropy production stemming from the quantum coherence content in the initial state of a qubit exposed to both coherent driving and dissipation. Our experimental demonstration builds on the exquisite experimental control of the spin state of a nitrogen-vacancy defect in diamond and is underpinned, theoretically, by the formulation of a generalized fluctuation theorem designed to track the effects of quantum coherence. Our results provide significant evidence of the possibility to pinpoint the genuinely quantum mechanical contributions to the thermodynamics of non-equilibrium quantum processes in an open quantum systems scenario.

Entanglement asymmetry as a probe of symmetry breaking

Ares F., Murciano S., Symmetry and symmetry breaking are two pillars of modern quantum physics. Still, 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. Hence, in this work, we 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 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 adapt the quasiparticle picture for entanglement evolution to the analytic determination of the entanglement asymmetry. We 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, a phenomenon that we show to occur in a large variety of systems.

Quantum integrability vs experiments: correlation functions and dynamical structure factors

Lencsés M., Integrable Quantum Field Theories can be solved exactly using bootstrap techniques based on their elastic and factorisable S-matrix. While knowledge of the scattering amplitudes reveals the exact spectrum of particles and their on-shell dynamics, the expression of the matrix elements of the various operators allows the reconstruction of off-shell quantities such as two-point correlation functions with a high level of precision. In this review, we summarise results relevant to the contact point between theory and experiment providing a number of quantities that can be computed theoretically with great accuracy. We concentrate on universal amplitude ratios which can be determined from the measurement of generalised susceptibilities, and dynamical structure factors, which can be accessed experimentally e.g. via inelastic neutron scattering or nuclear magnetic resonance. Besides an overview of the subject and a summary of recent advances, we also present new results regarding generalised susceptibilities in the tricritical Ising universality class.

PT breaking and RG flows between multicritical Yang-Lee fixed points

Lencsés M., Miscioscia A., We study a novel class of Renormalization Group flows which connect multicritical versions of the two-dimensional Yang-Lee edge singularity described by the conformal minimal models M (2, 2n + 3). The absence in these models of an order parameter implies that the flows towards and between Yang-Lee edge singularities are all related to the spontaneous breaking of PT symmetry and comprise a pattern of flows in the space of PT symmetric theories consistent with the c-theorem and the counting of relevant directions. Additionally, we find that while in a part of the phase diagram the domains of unbroken and broken PT symmetry are separated by critical manifolds of class M (2, 2n + 3), other parts of the boundary between the two domains are not critical.

Bending stiffness collapse, buckling, topological bands of freestanding twisted bilayer graphene

Wang J., Khosravi A., Silva A., The freestanding twisted bilayer graphene (TBG) is unstable, below a critical twist angle θc∼3.7∘, against a moiré (2×1) buckling distortion at T=0. Realistic simulations reveal the concurrent unexpected collapse of the bending rigidity, an unrelated macroscopic mechanical parameter. An analytical model connects bending and buckling anomalies at T=0, but as temperature rises the former fades, while buckling persists further. The (2×1) electronic properties are also surprising. The magic twist angle narrow bands, now eight in number, fail to show zone boundary splittings despite the different periodicity. Symmetry shows how this is dictated by an effective single-valley physics. These structural, critical, and electronic predictions promise to make the freestanding state of TBG especially interesting.

Generalized Wiedemann-Franz law in a two-site charge Kondo circuit: Lorenz ratio as a manifestation of the orthogonality catastrophe

We show that the transport integrals of the two-site charge Kondo circuits connecting various multichannel Kondo simulators satisfy the generalized Wiedemann-Franz law with the universal Lorenz ratios all greater than 1. The magic Lorenz ratios are directly related to the Anderson's orthogonality catastrophe in quantum simulators providing some additional universal measure for the strong electron-electron correlations. We present a fullly fledged theory for the magic Lorenz ratios and discuss possible routes for the experimental verifications of the theory.

Diagrammatic method for many-body non-Markovian dynamics: Memory effects and entanglement transitions

Chiriacò G., Tsitsishvili M., Poletti D., We study the quantum dynamics of a many-body system subject to coherent evolution and coupled to a non-Markovian bath. We propose a technique to unravel the non-Markovian dynamics in terms of quantum jumps, a connection that was so far only understood for single-body systems. We develop a systematic method to calculate the probability of a quantum trajectory and formulate it in a diagrammatic structure. We find that non-Markovianity renormalizes the probability of realizing a quantum trajectory and that memory effects can be interpreted as a perturbation on top of the Markovian dynamics. We show that the diagrammatic structure is akin to that of a Dyson equation and that the probability of the trajectories can be calculated analytically. We then apply our results to study the measurement-induced entanglement transition in random unitary circuits. We find that non-Markovianity does not significantly shift the transition but stabilizes the volume law phase of the entanglement by shielding it from transient strong dissipation.

Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders

Beradze B., Tsitsishvili M., Tirrito E., We consider a system of interacting spinless fermions on a two-leg triangular ladder with π/2 magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge and a discrete Z2 symmetry - a product of parity transformation and chain permutation. Using bosonization, we show that, in the low-energy limit, the system is described by the quantum double-frequency sine-Gordon model. On the basis of this correspondence, a rich phase diagram of the system is obtained. It includes trivial and topological band insulators for weak interactions, separated by a Gaussian critical line, whereas at larger interactions a strongly correlated phase with spontaneously broken Z2 symmetry sets in, exhibiting a net charge imbalance and nonzero total current. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry. This non-Abelian symmetry, absent in the microscopic description, is realized at low energies as a combined effect of the magnetic flux, frustration, and many-body correlations. The criticality belongs to the SU(2)1 Wess-Zumino-Novikov-Witten universality class. The critical point bifurcates into two Ising critical lines that separate the band insulators from the strong-coupling symmetry broken phase. We establish an analytical connection between the low-energy description of our model around the critical bifurcation point on one hand and the Ashkin-Teller model and a weakly dimerized XXZ spin-1/2 chain on the other. We complement our field-theory understanding via tensor network simulations, providing compelling quantitative evidences of all bosonization predictions. Our findings are of interest to up-to-date cold atom experiments utilizing Rydberg dressing that have already demonstrated correlated ladder dynamics.

Classification and emergence of quantum spin liquids in chiral Rydberg models

Tarabunga P.S., Giudici G., Chanda T., We investigate the nature of quantum phases arising in chiral interacting Hamiltonians recently realized in Rydberg atom arrays. We classify all possible fermionic chiral spin liquids with U(1) global symmetry using parton construction on the honeycomb lattice. The resulting classification includes six distinct classes of gapped quantum spin liquids: the corresponding variational wavefunctions obtained from two of these classes accurately describe the Rydberg many-body ground state at 1/2 and 1/4 particle density. Complementing this analysis with tensor network simulations, we conclude that both particle filling sectors host a spin liquid with the same topological order of a ν=1/2 fractional quantum Hall effect. At density 1/2, our results clarify the phase diagram of the model, while at density 1/4, they provide an explicit construction of the ground-state wavefunction with almost unit overlap with the microscopic one. These findings pave the way to the use of parton wavefunctions to guide the discovery of quantum spin liquids in chiral Rydberg models.

Massive superfluid vortices and vortex necklaces on a planar annulus

Caldara M., Richaud A., We study a superfluid in a planar annulus hosting vortices with massive cores. An analytical point-vortex model shows that the massive vortices may perform radial oscillations on top of the usual uniform precession of their massless counterpart. Beyond a critical vortex mass, this oscillatory motion becomes unstable and the vortices are driven towards one of the edges. The analogy with the motion of a charged particle in a static electromagnetic field leads to the development of a plasma orbit theory that provides a description of the trajectories which remains accurate even beyond the regime of small radial oscillations. These results are confirmed by the numerical solution of coupled two-component Gross-Pitaevskii equations. The analysis is then extended to a necklace of vortices symmetrically arranged within the annulus.

Nonequilibrium steady states of long-range coupled harmonic chains

Andreucci F., Lepri S., Ruffo S., We perform a numerical study of transport properties of a one-dimensional chain with couplings decaying as an inverse power r-(1+σ) of the intersite distance r and open boundary conditions, interacting with two heat reservoirs. Despite its simplicity, the model displays highly nontrivial features in the strong long-range regime -1<σ<0. At weak coupling with the reservoirs, the energy flux departs from the predictions of perturbative theory and displays anomalous superdiffusive scaling of the heat current with the chain size. We trace this behavior back to the transmission spectrum of the chain, which displays a self-similar structure with a characteristic σ-dependent fractal dimension.

Universality in Anderson localization on random graphs with varying connectivity

Sierant P., Lewenstein M., We perform a thorough and complete analysis of the Anderson localization transition on several models of random graphs with regular and random connectivity. The unprecedented precision and abundance of our exact diagonalization data (both spectra and eigenstates), together with new finite size scaling and statistical analysis of the graph ensembles, unveils a universal behavior which is described by two simple, integer, scaling exponents. A by-product of such analysis is a reconciliation of the tension between the results of perturbation theory coming from strong disorder and earlier numerical works, which seemed to suggest that there should be a non-ergodic region above a given value of disorder WE which is strictly less than the Anderson localization critical disorder WC, and that of other works which suggest that there is no such region. We find that, although no separate WE exists from WC, the length scale at which fully developed ergodicity is found diverges like |W−WC|−1, while the critical length over which delocalization develops is ∼ |W−WC|−1/2. The separation of these two scales at the critical point allows for a true non-ergodic, delocalized region. In addition, by looking at eigenstates and studying leading and sub-leading terms in system size-dependence of participation entropies, we show that the former contain information about the non-ergodicity volume which becomes non-trivial already deep in the delocalized regime. We also discuss the quantitative similarities between the Anderson transition on random graphs and many-body localization transition.

Competition of Quasiparticles and Magnetization Noise in Hybrid Ferromagnetic Transmon Qubits

Ahmad H.G., Brosco V., Miano A., Di Palma L., Arzeo M., Satariano R., Ferraiuolo R., Lucignano P., Vettoliere A., Granata C., Parlato L., Ausanio G., Montemurro D., Pepe G.P., The coexistence between ferromagnetic ordering and superconducting transport in tunnel ferromagnetic Josephson junctions (SFS JJs) accounts for a wide range of unconventional physical properties. The integration of both insulating ferromagnets or multi-layered insulator-ferromagnet barriers allows to combine ferromagnetic switching properties with peculiar low quasiparticle dissipation, which could enhance the capabilities of SFS JJs as active elements in quantum circuits. Here we show that split-transmon qubits based on tunnel ferromagnetic JJs realize an ideal playground to study noise fluctuations in ferromagnetic Josephson devices. By considering the transport properties of measured Al-based tunnel SFS JJs, we report on a theoretical study of the competition between intrinsic magnetization fluctuations in the barrier and quasiparticles dissipation, thus providing specific operation regimes to identify and disentangle the two noise sources, depending on the peculiar properties of the F layer and F/S interface.

Can multipartite entanglement be characterized by two-point connected correlation functions?

Lepori L., We discuss under which conditions multipartite entanglement in mixed quantum states can be characterized only in terms of two-point connected correlation functions, as it is the case for pure states. In turn, the latter correlations are defined via a suitable combination of (disconnected) one- and two-point correlation functions. In contrast to the case of pure states, conditions to be satisfied turn out to be rather severe. However, we were able to identify some interesting cases, as when the point-independence is valid of the one-point correlations in each possible decomposition of the density matrix, or when the operators that enter in the correlations are (semi-)positive/negative defined.

Strange correlators for topological quantum systems from bulk-boundary correspondence

Lepori L., Burrello M., "Strange"correlators provide a tool to detect topological phases arising in many-body models by computing the matrix elements of suitably defined two-point correlations between the states under investigation and trivial reference states. Their effectiveness depends on the choice of the adopted operators. In this paper, we give a systematic procedure for this choice, discussing the advantages of choosing operators using the bulk-boundary correspondence of the systems under scrutiny. Via the scaling exponents, we directly relate the algebraic decay of the strange correlators with the scaling dimensions of gapless edge modes operators. We begin our analysis with lattice models hosting symmetry-protected topological phases and we analyze the sums of the strange correlators, pointing out that integrating their moduli substantially reduces cancellations and finite-size effects. We also analyze instances of systems hosting intrinsic topological order, as well as strange correlators between states with different nontrivial topologies. Our results for both translational and nontranslational invariant cases, and in the presence of on-site disorder and long-range couplings, extend the validity of the strange correlator approach for the diagnosis of topological phases of matter and indicate a general procedure for their optimal choice.

Time-dependent ghost Gutzwiller nonequilibrium dynamics

Guerci D., We introduce the time-dependent ghost Gutzwiller approximation (TD-gGA), a nonequilibrium extension of the ghost Gutzwiller approximation (gGA), a powerful variational approach which systematically improves on the standard Gutzwiller method by including auxiliary degrees of freedom. We demonstrate the effectiveness of TD-gGA by studying the quench dynamics of the single-band Hubbard model as a function of the number of auxiliary parameters. Our results show that TD-gGA captures the relaxation of local observables, in contrast with the time-dependent Gutzwiller method. This systematic and qualitative improvement leads to an accuracy comparable with time-dependent dynamical mean-field theory which comes at a much lower computational cost. These findings suggest that TD-gGA has the potential to enable extensive and accurate theoretical investigations of multiorbital correlated electron systems in nonequilibrium situations, with potential applications in the field of quantum control, Mott solar cells, and other areas where an accurate account of the nonequilibrium properties of strongly interacting quantum systems is required.

Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum

Zerba C., We study dynamical phase transitions occurring in the stationary state of the dynamics of integrable many-body non-hermitian Hamiltonians, which can be either realized as a no-click limit of a stochastic Schrödinger equation or using spacetime duality of quantum circuits. In two specific models, the Transverse Field Ising Chain and the Long Range Kitaev Chain, we observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the nonhermitian Hamiltonian: bounded entanglement entropy when the imaginary part of the quasi-particle spectrum is gapped and a logarithmic growth for gapless imaginary spectrum. This observation suggests the possibility to generalize the area-law theorem to non-Hermitian Hamiltonians.

One-particle density matrix and momentum distribution of the out-of-equilibrium one-dimensional Tonks-Girardeau gas: Analytical results at large N

Scopa S., Ruggiero P., In one-dimensional (1D) quantum gases, the momentum distribution (MD) of the atoms is a standard experimental observable, routinely measured in various experimental setups. The MD is sensitive to correlations, and it is notoriously hard to compute theoretically for large numbers of atoms N, which often prevents direct comparison with experimental data. Here we report significant progress on this problem for the 1D Tonks-Girardeau (TG) gas in the asymptotic limit of large N, at zero temperature and driven out of equilibrium by a quench of the confining potential. We find an exact analytical formula for the one-particle density matrix (ψ †(x)ψ(x′)) of the out-of-equilibrium TG gas in the N→∞ limit, valid on distances |x-x′| much larger than the interparticle distance. By comparing with time-dependent Bose-Fermi mapping numerics, we demonstrate that our analytical formula can be used to compute the out-of-equilibrium MD with great accuracy for a wide range of momenta (except in the tails of the distribution at very large momenta). For a quench from a double-well potential to a single harmonic well, which mimics a "quantum Newton cradle"setup, our method predicts the periodic formation of peculiar, multiply peaked, momentum distributions.

Full counting statistics and symmetry resolved entanglement for free conformal theories with interface defects

Capizzi L., Murciano S., We consider the ground state of two species of one-dimensional critical free theories coupled together via a conformal interface. They have an internal U(1) global symmetry and we investigate the quantum fluctuations of the total charge on one side of the interface, giving analytical predictions for the full counting statistics, the charged moments of the reduced density matrix and the symmetry resolved Rényi entropies. Our approach is based on the relation between the geometry with the defect and the homogeneous one, and it provides a way to characterize the spectral properties of the correlation functions restricted to one of the two species. Our analytical predictions are tested numerically, finding a perfect agreement.

A hydrodynamic approach to Stark localization

Capizzi L., Vanoni C., When a free Fermi gas on a lattice is subject to the action of a linear potential it does not drift away, as one would naively expect, but it remains spatially localized. Here we revisit this phenomenon, known as Stark localization, within the recently proposed framework of generalized hydrodynamics. In particular, we consider the dynamics of an initial state in the form of a domain wall and we recover known results for the particle density and the particle current, while we derive analytical predictions for relevant observables such as the entanglement entropy and the full counting statistics. Then, we extend the analysis to generic potentials, highlighting the relationship between the occurrence of localization and the presence of peculiar closed orbits in phase space, arising from the lattice dispersion relation. We also compare our analytical predictions with numerical calculations and with the available results, finding perfect agreement. This approach paves the way for an exact treatment of the interacting case known as Stark many-body localization.