Publications

We investigate the dynamics of two-dimensional quantum spin systems under the combined effect of random unitary gates and local projective measurements. When considering steady states, a measurement-induced transition occurs between two distinct dynamical phases, one characterized by a volume-law scaling of entanglement entropy, the other by an area law. Employing stabilizer states and Clifford random unitary gates, we numerically investigate square lattices of linear dimension up to L=48 for two distinct measurement protocols. For both protocols, we observe a transition point where the dominant contribution in the entanglement entropy displays multiplicative logarithmic violations to the area law. We obtain estimates of the correlation length critical exponent at the percent level; these estimates suggest universal behavior and are incompatible with the universality class of 3D percolation.

We study the phase diagram, both at zero and finite temperature, in a class of ℤq models with infinite-range interactions. We are able to identify the transitions between a symmetry-breaking and a trivial phase by using a mean-field approach and a perturbative expansion. We perform our analysis on a Hamiltonian with 2p-body interactions and we find first-order transitions for any p > 1; in the case p = 1, the transitions are first-order for q = 3 and second-order otherwise. In the infinite-range case there is no trace of gapless incommensurate phase but, when the transverse field is maximally chiral, the model is in a symmetry-breaking phase for arbitrarily large fields. We analytically study the transition in the limit of infinite q, where the model possesses a continuous U(1) symmetry.

The reduced density matrix of many-body systems possessing an additive conserved quantity can be decomposed in orthogonal sectors which can be independently analyzed. Recently, these have been proven to equally contribute to entanglement entropy for one-dimensional conformal and integrable systems. In this paper, we extend this equipartition theorem to the disordered critical systems by studying the random singlet phase. We analytically compute the disorder averaged symmetry resolved Rényi entropies and show the leading orders are independent of the symmetry sector. Our findings are cross-checked with simulations within the numerical strong disorder renormalization group. We also identify the first subleading term breaking equipartition which is of the form s2/lnℓ where s is the magnetization of a subsystem of length ℓ.

By means of the discrete truncated Wigner approximation, we study dynamical phase transitions arising in the steady state of transverse-field Ising models after a quantum quench. Starting from a fully polarized ferromagnetic initial condition, these transitions separate a phase with nonvanishing magnetization along the ordering direction from a disordered symmetric phase upon increasing the transverse field. We consider two paradigmatic cases, a one-dimensional long-range model with power-law interactions ∞1/rα decaying algebraically as a function of distance r and a two-dimensional system with short-range nearest-neighbor interactions. In the former case, we identify dynamical phase transitions for α≲2 and we extract the critical exponents from a data collapse of the steady-state magnetization for up to 1200 lattice sites. We find identical exponents for α≲0.5, suggesting that the dynamical transitions in this regime fall into the same universality class as the nonergodic mean-field limit. The two-dimensional Ising model is believed to be thermalizing, which we also confirm using exact diagonalization for small system sizes. Thus, the dynamical transition is expected to correspond to the thermal phase transition, which is consistent with our data upon comparing to equilibrium quantum Monte Carlo simulations. We further test the accuracy of the discrete truncated Wigner approximation by comparing against numerically exact methods such as exact diagonalization, tensor network, as well as artificial neural network states and we find good quantitative agreement on the accessible time scales. Finally, our work provides an additional contribution to the understanding of the range and the limitations of qualitative and quantitative applicability of the discrete truncated Wigner approximation.

We report a throughout analysis of the entanglement entropies related to different symmetry sectors in the low-lying primary excited states of a conformal field theory (CFT) with an internal U(1) symmetry. Our findings extend recent results for the ground state. We derive a general expression for the charged moments, i.e. the generalised cumulant generating function, which can be written in terms of correlation functions of the operator that define the state through the CFT operator-state correspondence. We provide explicit analytic computations for the compact boson CFT (aka Luttinger liquid) for the vertex and derivative excitations. The Fourier transform of the charged moments gives the desired symmetry resolved entropies. At the leading order, they satisfy entanglement equipartition, as in the ground state, but we find, within CFT, subleading terms that break it. Our analytical findings are checked against free fermions calculations on a lattice, finding excellent agreement. As a byproduct, we have exact results for the full counting statistics of the U(1) charge in the considered excited states.

The recent discovery of materials featuring strong Rashba spin-orbit coupling (RSOC) and strong electronic correlation raises questions about the interplay of Mott and Rashba physics. In this work, we employ cluster perturbation theory to investigate the spectral properties of the two-dimensional Hubbard model in the presence of a significant or large RSOC. We show that RSOC strongly favors metallic phases and competes with Mott localization, leading to an unconventional scenario for the Mott transition, which is no longer controlled by the ratio between the Hubbard U and an effective bandwidth. The results show a strong sensitivity to the value of the RSOC.

We study the out-of-equilibrium properties of 1 + 1 dimensional quantum electrodynamics (QED), discretized via the staggered-fermion Schwinger model with an Abelian Zngauge group. We look at two relevant phenomena: first, we analyze the stability of the Dirac vacuum with respect to particle/antiparticle pair production, both spontaneous and induced by an external electric field; then, we examine the string breaking mechanism. We observe a strong effect of confinement, which acts by suppressing both spontaneous pair production and string breaking into quark/antiquark pairs, indicating that the system dynamics displays a number of out-of-equilibrium features.

We introduce and develop a slave-spin mean-field technique for describing generic interacting two-level systems under time-dependent drivings, where an auxiliary S=1 spin is added to describe the localized character of the electrons. We show that the approach efficiently captures the main effects of the strong correlations as well as the dynamical nature of the driving, while remaining simple enough to allow for an analytical treatment. Our formalism provides a flexible solution method, which can be applied to different device configurations at an extremely small numerical cost. Furthermore, it leads to a very practical description of adiabatically driven systems in terms of frozen static solutions.

We consider the time evolution of the gaps of the entanglement spectrum for a block of consecutive sites in finite transverse field Ising chains after sudden quenches of the magnetic field. We provide numerical evidence that, whenever we quench at or across the quantum critical point, the time evolution of the ratios of these gaps allows us to obtain universal information. They encode the low-lying gaps of the conformal spectrum of the Ising boundary conformal field theory describing the spatial bipartition within the imaginary time path integral approach to global quenches at the quantum critical point.

Time dependent Lindblad generators have mostly been studied for discrete variable open quantum systems. We hereby initiate the study of the complete positivity of a continuous one-dimensional quantum system subjected to time-dependent spatial localizations with back-flow of information.

The authors regret an error in the grant number for one of the authors in the Acknowledgements section. The Acknowledgements section should read as follows: This work was partially supported by the ERC Starting Grant ComplexSwimmers (grant no. 677511) and by Vetenskapsrådet (grant no. 2016-03523). A. C. acknowledges partial financial support from TUBITAK (grant no. 116F111). J. P. S. acknowledges partial financial support from FONDECYT (grant no. 1171013). The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and reade

Elucidating the energy transfer between a quantum system and a reservoir is a central issue in quantum nonequilibrium thermodynamics, which could provide novel tools to engineer quantum-enhanced heat engines. The lack of information on the reservoir inherently limits the practical insight that can be gained on the exchange process of open quantum systems. Here we investigate the energy transfer for an open quantum system in the framework of quantum fluctuation relations. As a novel toolbox, we employ a nitrogen-vacancy center spin qubit in diamond, subject to repeated quantum projective measurements and a tunable dissipation channel. In the presence of energy fluctuations originated by dissipation and quantum projective measurements, the experimental results, supplemented by numerical simulations, show the validity of the energy exchange fluctuation relation, where the energy scale factor encodes missing reservoir information in the system out-of-equilibrium steady-state properties. This result is complemented by a theoretical argument showing that, also for an open three-level quantum system, the existence of an out-of-equilibrium steady state dictates a unique time-independent value of the energy scale factor for which the fluctuation relation is verified. Our findings pave the way to the investigation of energy exchange mechanisms in arbitrary open quantum systems.

Despite the striking progress in the field of quantum gases, one of their much anticipated applications - the simulation of quantum Hall states - remains elusive: all experimental approaches so far have failed in reaching a sufficiently small ratio between atom and vortex densities. In this paper we consider rotating Rydberg-dressed atoms in magnetic traps: these gases offer strong and tunable nonlocal repulsive interactions and very low densities; hence they provide an exceptional platform to reach the quantum Hall regime. Based on the Lindemann criterion and the analysis of the interplay of the length scales of the system, we show that there exists an optimal value of the dressing parameters that minimizes the ratio between the filling factor of the system and its critical value to enter the Hall regime, thus making it possible to reach this strongly correlated phase for more than 1000 atoms under realistic conditions.

Gauge theories are the cornerstone of our understanding of fundamental interactions among elementary particles. Their properties are often probed in dynamical experiments, such as those performed at ion colliders and high-intensity laser facilities. Describing the evolution of these strongly coupled systems is a formidable challenge for classical computers and represents one of the key open quests for quantum simulation approaches to particle physics phenomena. In this work, we show how recent experiments done on Rydberg atom chains naturally realize the real-time dynamics of a lattice gauge theory at system sizes at the boundary of classical computational methods. We prove that the constrained Hamiltonian dynamics induced by strong Rydberg interactions maps exactly onto the one of a U(1) lattice gauge theory. Building on this correspondence, we show that the recently observed anomalously slow dynamics corresponds to a string-inversion mechanism, reminiscent of the string breaking typically observed in gauge theories. This underlies the generality of this slow dynamics, which we illustrate in the context of one-dimensional quantum electrodynamics on the lattice. Within the same platform, we propose a set of experiments that generically show long-lived oscillations, including the evolution of particle-antiparticle pairs, and discuss how a tunable topological angle can be realized, further affecting the dynamics following a quench. Our work shows that the state of the art for quantum simulation of lattice gauge theories is at 51 qubits and connects the recently observed slow dynamics in atomic systems to archetypal phenomena in particle physics.

We investigate the out-of-equilibrium physics of monodisperse bosonic ensembles on a square lattice. The effective Hamiltonian description of these systems is given in terms of an extended Hubbard model with cluster-forming interactions relevant to experimental realizations with cold Rydberg-dressed atoms. The ground state of the model, recently investigated in [Phys. Rev. Lett. 123, 045301 (2019)10.1103/PhysRevLett.123.045301], features, aside from a superfluid and a stripe crystalline phase occurring at small and large interaction strength V, respectively, a rare first-order transition between an isotropic and an anisotropic stripe supersolid at intermediate V. By means of quantum Monte Carlo calculations we show that the equilibrium crystal may be turned into a glass by simulated temperature quenches and that out-of-equilibrium isotropic (super)solid states may emerge also when their equilibrium counterparts are anisotropic. These out-of-equilibrium states are of experimental interest, their excess energy with respect to the ground state being within the energy window typically accessed in cold atom experiments. We find, after quenching, no evidence of coexistence between superfluid and glassy behavior. Such an absence of superglassiness is qualitatively explained.

As a contribution to a viable candidate for a standard model of cosmology, we here show that pre-inflationary quantum fluctuations can provide a scenario for the long-sought initial conditions for the inflaton field. Our proposal is based on the assumption that at very high energies (higher than the energy scale of inflation) the vacuum-expectation value (VeV) of the field is trapped in a false vacuum and then, due to renormalization-group (RG) running, the potential starts to flatten out toward low energy, eventually tending to a convex one which allows the field to roll down to the true vacuum. We argue that the proposed mechanism should apply to large classes of inflationary potentials with multiple concave regions. Our findings favor a particle physics origin of chaotic, large-field inflationary models as we eliminate the need for large field fluctuations at the GUT scale. In our analysis, we provide a specific example of such an inflationary potential, whose parameters can be tuned to reproduce the existing cosmological data with good accuracy.

The quest for a satisfactory understanding of systems at criticality in dimensions d > 2 is a major field of research. We devise here a geometric description of bounded systems at criticality in any dimension d. This is achieved by altering the flat metric with a space dependent scale factor γ(x), x belonging to a bounded domain Ω. γ(x) is chosen in order to have a scalar curvature to be constant and matching the one of the hyperbolic space, the proper notion of curvature being-as called in the mathematics literature-the fractional Q-curvature. The equation for γ(x) is found to be the fractional Yamabe equation (to be solved in Ω) that, in absence of anomalous dimension, reduces to the usual Yamabe equation in the same domain. From the scale factor γ(x) we obtain novel predictions for the scaling form of one-point order parameter correlation functions. A (necessary) virtue of the proposed approach is that it encodes and allows to naturally retrieve the purely geometric content of two-dimensional boundary conformal field theory. From the critical magnetization profile in presence of boundaries one can extract the scaling dimension of the order parameter, Δ φ . For the 3D Ising model we find Δ φ = 0.518 142(8) which favorably compares (at the fifth decimal place) with the state-of-the-art estimate. A nontrivial prediction is the structure of two-point spin-spin correlators at criticality. They should depend on the fractional Q-hyperbolic distance calculated from the metric, in turn depending only on the shape of the bounded domain and on Δ φ . Numerical simulations of the 3D Ising model on a slab geometry are found to be in agreement with such predictions.

TurboRVB is a computational package for ab initio Quantum Monte Carlo (QMC) simulations of both molecular and bulk electronic systems. The code implements two types of well established QMC algorithms: Variational Monte Carlo (VMC) and diffusion Monte Carlo in its robust and efficient lattice regularized variant. A key feature of the code is the possibility of using strongly correlated many-body wave functions (WFs), capable of describing several materials with very high accuracy, even when standard mean-field approaches [e.g., density functional theory (DFT)] fail. The electronic WF is obtained by applying a Jastrow factor, which takes into account dynamical correlations, to the most general mean-field ground state, written either as an antisymmetrized geminal power with spin-singlet pairing or as a Pfaffian, including both singlet and triplet correlations. This WF can be viewed as an efficient implementation of the so-called resonating valence bond (RVB) Ansatz, first proposed by Pauling and Anderson in quantum chemistry [L. Pauling, The Nature of the Chemical Bond (Cornell University Press, 1960)] and condensed matter physics [P.W. Anderson, Mat. Res. Bull 8, 153 (1973)], respectively. The RVB Ansatz implemented in TurboRVB has a large variational freedom, including the Jastrow correlated Slater determinant as its simplest, but nontrivial case. Moreover, it has the remarkable advantage of remaining with an affordable computational cost, proportional to the one spent for the evaluation of a single Slater determinant. Therefore, its application to large systems is computationally feasible. The WF is expanded in a localized basis set. Several basis set functions are implemented, such as Gaussian, Slater, and mixed types, with no restriction on the choice of their contraction. The code implements the adjoint algorithmic differentiation that enables a very efficient evaluation of energy derivatives, comprising the ionic forces. Thus, one can perform structural optimizations and molecular dynamics in the canonical NVT ensemble at the VMC level. For the electronic part, a full WF optimization (Jastrow and antisymmetric parts together) is made possible, thanks to state-of-the-art stochastic algorithms for energy minimization. In the optimization procedure, the first guess can be obtained at the mean-field level by a built-in DFT driver. The code has been efficiently parallelized by using a hybrid MPI-OpenMP protocol, which is also an ideal environment for exploiting the computational power of modern Graphics Processing Unit accelerators.

The CSL model predicts a progressive breakdown of the quantum superposition principle, with a noise randomly driving the state of the system towards a localized one, thus accounting for the emergence of a classical world within a quantum framework. In the original model the noise is supposed to be white, but since white noises do not exist in nature, it becomes relevant to identify some of its spectral properties. Experimental data set an upper bound on its frequencies, while in this paper we bound it from below. We do so in two ways: by considering a 'minimal' measurement setup, requiring that the collapse is completed within the measurement time; and in a measurement modeling-independent way, by requiring that the fluctuations average to zero before the measurement time.

We study the dynamics of the fluctuations of the variance s of the order parameter of the Gaussian model, following a temperature quench of the thermal bath. At each time t, there is a critical value s c(t) of s such that fluctuations with s > sc (t) are realized by condensed configurations of the systems, i.e., a single degree of freedom contributes macroscopically to s. This phenomenon, which is closely related to the usual condensation occurring on average quantities, is usually referred to as condensation of fluctuations. We show that the probability of fluctuations with s < inft[sc (t)], associated to configurations that never condense, after the quench converges rapidly and in an adiabatic way towards the new equilibrium value. The probability of fluctuations with s > inft[sc (t)], instead, displays a slow and more complex behavior, because the macroscopic population of the condensing degree of freedom is involved.