Unified role of Green's function poles and zeros in correlated topological insulators

Blason A., Green's function zeros, which can emerge only if correlation is strong, have been for long overlooked and believed to be devoid of any physical meaning, unlike Green's function poles. Here, we prove that Green's function zeros instead contribute on the same footing as poles to determine the topological character of an insulator. The key to the proof, worked out explicitly in two dimensions but easily extendable in three dimensions, is to express the topological invariant in terms of a quasiparticlethermal Green's function matrix G∗(iϵ,k)=1/[iϵ-H∗(ϵ,k)], with Hermitian H∗(ϵ,k), by filtering out the positive-definite quasiparticle residue. In that way, the topological invariant is easily found to reduce to the Thouless, Kohmoto, Nightingale, and den Nijs formula for quasiparticles described by the noninteracting Hamiltonian H∗(0,k). Since the poles of the quasiparticle Green's function G∗(ϵ,k) on the real frequency axis correspond to poles and zeros of the physical-particle Green's function G(ϵ,k), both of them equally determine the topological character of an insulator.

Thermodynamic uncertainty relations for systems with broken time reversal symmetry: The case of superconducting hybrid systems

Taddei F., We derive bounds to the thermodynamic uncertainty relations in the linear-response regime for steady-state transport in two-terminal systems when time reversal symmetry is broken. We find that such bounds are different for charge and heat currents and depend on the details of the system, through the Onsager coefficients, and on the ratio between applied voltage and temperature difference. As a function of such a ratio, the bounds can take any positive values. The bounds are then calculated for a hybrid coherent superconducting system using the scattering approach, and the concrete case of an Andreev interferometer is explored. Interestingly, we find that the bound on the charge current is always smaller than 2 when the system operates as a heat engine, while the bound on the heat current is always larger than 2 when the system operates as a refrigerator.

Deep learning nonlocal and scalable energy functionals for quantum Ising models

Costa E., Density functional theory (DFT) is routinely employed in material science and quantum chemistry to simulate weakly correlated electronic systems. Recently, deep learning (DL) techniques have been adopted to develop promising functionals for the strongly correlated regime. DFT can be applied to quantum spin models too, but functionals based on DL have not been developed yet. Here, we investigate DL-based DFTs for random quantum Ising chains, both with nearest-neighbor and up to next-nearest-neighbor couplings. Our neural functionals are trained and tested on data produced via the Jordan-Wigner transformation, exact diagonalization, and tensor-network methods. An economical gradient-descent optimization is used to find the ground-state properties of previously unseen Hamiltonian instances. Notably, our nonlocal functionals drastically improve upon the common local density approximations, and they are designed to be scalable, allowing us to simulate chain sizes much larger than those used for training. The prediction accuracy is analyzed, paying attention to the spatial correlations of the learned functionals and to the role of quantum criticality. Our findings indicate a suitable strategy to extend the reach of other computational methods with a controllable accuracy.

Quantum effects on the synchronization dynamics of the Kuramoto model

Delmonte A., Romito A., The Kuramoto model serves as a paradigm for describing spontaneous synchronization in a system of classical interacting rotors. In this paper, we extend this model to the quantum domain by coupling quantum interacting rotors to external baths following the Caldeira-Leggett approach. Studying the mean-field model in the overdamped limit using Feynman-Vernon theory, we show how quantum mechanics modifies the phase diagram. Specifically, we demonstrate that quantum fluctuations hinder the emergence of synchronization, albeit not entirely suppressing it. We examine the phase transition into the synchronized phase at various temperatures, revealing that classical results are recovered at high temperatures while a quantum phase transition occurs at zero temperature. Additionally, we derive an analytical expression for the critical coupling, highlighting its dependence on the model parameters, and examine the differences between classical and quantum behavior.

First-order photon condensation in magnetic cavities: A two-leg ladder model

Bacciconi Z., Andolina G.M., Chanda T., Chiriacò G., Schirò M., We consider a model of free fermions in a ladder geometry coupled to a non-uniform cavity mode via Peierls substitution. Since the cavity mode generates a magnetic field, no-go theorems on spontaneous photon condensation do not apply, and we indeed observe a phase transition to a photon condensed phase characterized by finite circulating currents, alternatively referred to as the equilibrium superradiant phase. We consider both square and triangular ladder geometries, and characterize the transition by studying the energy structure of the system, light-matter entanglement, the properties of the photon mode, and chiral currents. The transition is of first order and corresponds to a sudden change in the fermionic band structure as well as the number of its Fermi points. 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. 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. The latter remains Gaussian in the the thermodynamic limit both in the normal and photon condensed phases.

Lack of symmetry restoration after a quantum quench: An entanglement asymmetry study

Ares F., Murciano S., Vernier E., We consider the quantum quench in the XX spin chain starting from a tilted Néel state which explicitly breaks the U(1) symmetry of the post-quench Hamiltonian. Very surprisingly, the U(1) symmetry is not restored at large time because of the activation of a non- Abelian set of charges which all break it. The breaking of the symmetry can be effectively and quantitatively characterised by the recently introduced entanglement asymmetry. By a combination of exact calculations and quasi-particle picture arguments, we are able to exactly describe the behaviour of the asymmetry at any time after the quench. Furthermore we show that the stationary behaviour is completely captured by a non-Abelian generalised Gibbs ensemble. While our computations have been performed for a noninteracting spin chain, we expect similar results to hold for the integrable interacting case as well because of the presence of non-Abelian charges also in that case.

Memory-induced oscillations of a driven particle in a dissipative correlated medium

Venturelli D., The overdamped dynamics of a particle is in general affected by its interaction with the surrounding medium, especially out of equilibrium, and when the latter develops spatial and temporal correlations. Here we consider the case in which the medium is modeled by a scalar Gaussian field with relaxational dynamics, and the particle is dragged at constant velocity through the medium by a moving harmonic trap. This mimics the setting of an active microrheology experiment conducted in a near-critical medium. When the particle is displaced from its average position in the nonequilibrium steady state, its subsequent relaxation is shown to feature damped oscillations. This is similar to what has been recently predicted and observed in viscoelastic fluids, but differs from what happens in the absence of driving or for an overdamped Markovian dynamics, in which cases oscillations cannot occur. We characterize these oscillating modes in terms of the parameters of the underlying mesoscopic model for the particle and the medium, confirming our analytical predictions via numerical simulations.

Subdiffusive spin transport in disordered classical Heisenberg chains

McRoberts A.J., Balducci F., Moessner R., We study the transport and equilibration properties of a classical Heisenberg chain, whose couplings are random variables drawn from a one-parameter family of power-law distributions. The absence of a scale in the couplings makes the system deviate substantially from the usual paradigm of diffusive spin hydrodynamics and exhibit a regime of subdiffusive transport with an exponent changing continuously with the parameter of the distribution. We propose a solvable phenomenological model that correctly yields the subdiffusive exponent, thereby linking local fluctuations in the coupling strengths to the long-time, large-distance behavior. It also yields the finite-time corrections to the asymptotic scaling, which can be important in fitting the numerical data. We show how such exponents undergo transitions as the distribution of the coupling gets wider, marking the passage from diffusion to a regime of slow diffusion, and finally to subdiffusion.

Jastrow wave function for the spin-1 Heisenberg chain: The string order revealed by the mapping to the classical Coulomb gas

Piccioni D., Apostoli C., Becca F., Mazzola G., Parola A., We show that a two-body Jastrow wave function is able to capture the ground-state properties of the S=1 Heisenberg chain with nearest-neighbor superexchange J and single-ion anisotropy term D, in both the topological and large-D phases (with D/J≥0). Here, the optimized Jastrow pseudopotential assumes a very simple form in Fourier space, i.e., vq≈1/q2, which is able to give rise to a finite string-order parameter in the topological regime. The results are analyzed by using an exact mapping from the quantum expectation values over the variational state to the classical partition function of the one-dimensional Coulomb gas of particles with charge q=±1. Here, two phases are present at low temperatures: the first one is a diluted gas of dipoles (bound neutral pairs of particles), which are randomly oriented (describing the large-D phase); the other one is a dense liquid of dipoles, which are aligned thanks to the residual dipole-dipole interactions (describing the topological phase, with the finite string order being related to the dipole alignment). Our results provide an insightful interpretation of the ground-state nature of the spin-1 antiferromagnetic Heisenberg model.

Work statistics, quantum signatures, and enhanced work extraction in quadratic fermionic models

Santini A., Solfanelli A., Gherardini S., In quadratic fermionic models, we determine a quantum correction to the work statistics after both a sudden quench and a time-dependent driving. Such a correction lies in the noncommutativity of the initial quantum state and the time-dependent Hamiltonian, and is revealed via the Kirkwood-Dirac quasiprobability (KDQ) approach to two-times correlators. Thanks to the latter, one can assess the onset of nonclassical signatures in the KDQ distribution of work, in the form of negative and complex values that no classical theory can reveal. By applying these concepts on the one-dimensional transverse-field Ising model, we relate nonclassical behaviors of the KDQ statistics of work in correspondence of the critical points of the model. Finally, we also prove the enhancement of the extracted work in nonclassical regimes where the noncommutativity takes a role.

Full counting statistics as probe of measurement-induced transitions in the quantum Ising chain

Tirrito E., Santini A., Non-equilibrium dynamics of many-body quantum systems under the effect of measurement protocols is attracting an increasing amount of attention. It has been recently revealed that measurements may induce different non-equilibrium regimes and an abrupt change in the scaling-law of the bipartite entanglement entropy. However, our understanding of how these regimes appear, how they affect the statistics of local quantities and, finally whether they survive in the thermodynamic limit, is much less established. Here we investigate measurement-induced phase transitions in the Quantum Ising chain coupled to a monitoring environment. In particular we show that local projective measurements induce a quantitative modification of the out-of-equilibrium probability distribution function of the local magnetization. Starting from a GHZ state, the relaxation of the paramagnetic and the ferromagnetic order is analysed. In particular we describe how the probability distributions associated to them show different behaviour depending on the measurement rate.

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.