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We study the behavior of the mutual information (MI) in various quadratic fermionic chains, with and without pairing terms and both with short- and long-range hoppings. The models considered include the short-range limit and long-range versions of the Kitaev model as well, and also cases in which the area law for the entanglement entropy is - logarithmically or nonlogarithmically - violated. In all cases surveyed, when the area law is violated at most logarithmically, the MI is a monotonically increasing function of the conformal four-point ratio x. Where nonlogarithmic violations of the area law are present, nonmonotonic features can be observed in the MI, and the four-point ratio, as well as other natural combinations of the parameters, is found not to be sufficient to capture the whole structure of the MI with a collapse onto a single curve. We interpret this behavior as a sign that the structure of peaks is related to a nonuniversal spatial configuration of Bell pairs. For the model exhibiting a perfect volume law, the MI vanishes identically. For the Kitaev model the MI is vanishing for x→0 and it remains zero up to a finite x in the gapped case. In general, a larger range of the pairing corresponds to a reduction of the MI at small x. A discussion of the comparison with the results obtained by the anti-de Sitter/conformal field theory correspondence in the strong-coupling limit is presented.

In the past decades, considerable efforts have been made to understand the critical features of both classical and quantum long-range (LR) interacting models. The case of the Berezinskii-Kosterlitz-Thouless (BKT) universality class, as in the two-dimensional (2D) classical XY model, is considerably complicated by the presence, for short-range interactions, of a line of renormalization group fixed points. In this paper, we discuss a field-theoretical treatment of the 2D XY model with LR couplings, and we compare it with results from the self-consistent harmonic approximation. These methods lead to a rich phase diagram, where both power law BKT scaling and spontaneous symmetry breaking appear for the same (intermediate) decay rates of LR interactions. We also discuss the Villain approximation for the 2D XY model with power law couplings, providing hints that, in the LR regime, it fails to reproduce the correct critical behavior. The obtained results are then applied to the LR quantum XXZ spin chain at zero temperature. We discuss the relation between the phase diagrams of the two models, and we give predictions about the scaling of the order parameter of the quantum chain close to the transition.

We study the nonequilibrium steady-state of a fully-coupled network of N quantum harmonic oscillators, interacting with two thermal reservoirs. Given the long-range nature of the couplings, we consider two setups: one in which the number of particles coupled to the baths is fixed (intensive coupling) and one in which it is proportional to the size N (extensive coupling). In both cases, we compute analytically the heat fluxes and the kinetic temperature distributions using the nonequilibrium Green's function approach, both in the classical and quantum regimes. In the large N limit, we derive the asymptotic expressions of both quantities as a function of N and the temperature difference between the baths. We discuss a peculiar feature of the model, namely that the bulk temperature vanishes in the thermodynamic limit, due to a decoupling of the dynamics of the inner part of the system from the baths. At variance with the usual case, this implies that the steady-state depends on the initial state of the bulk particles. We also show that quantum effects are relevant only below a characteristic temperature that vanishes as 1/N. In the quantum low-temperature regime the energy flux is proportional to the universal quantum of thermal conductance.

Non-differentiable potentials, such as the V-shaped (linear) potential, appear in various areas of physics. For example, the effective action for branons in the framework of the brane world scenario contains a Liouville-type interaction, i.e., an exponential of the V-shaped function. Another example is coming from particle physics when the standard model Higgs potential is replaced by a periodic self-interaction of an N-component scalar field which depends on the length, thus it is O(N) symmetric. We first compare classical and quantum dynamics near non-analytic points and discuss in this context the role of quantum fluctuations. We then study the renormalisation of such potentials, focusing on the Exact Wilsonian Renormalisation approach, and we discuss how quantum fluctuations smoothen the bare singularity of the potential. Applications of these results to the non-differentiable effective branon potential and to the O(N) models when the spatial dimension is varied and to the O(N) extension of the sine-Gordon model in (1+1) dimensions are presented.

Engineered dynamical maps combining coherent and dissipative transformations of quantum states with quantum measurements have demonstrated a number of technological applications, and promise to be a crucial tool in quantum thermodynamic processes. Here we exploit the control on the effective open spin qutrit dynamics of a nitrogen-vacancy center to experimentally realize an autonomous feedback process (Maxwell's demon) with tunable dissipative strength. The feedback is enabled by random measurement events that condition the subsequent dissipative evolution of the qutrit. The efficacy of the autonomous Maxwell's demon is quantified by means of a generalized Sagawa-Ueda-Tasaki relation for dissipative dynamics. To achieve this, we experimentally characterize the fluctuations of the energy exchanged between the system and its the environment. This opens the way to the implementation of a new class of Maxwell's demons, which could be useful for quantum sensing and quantum thermodynamic devices.

Due to its construction, the nonperturbative renormalization group (RG) evolution of the constant, field-independent term (which is constant with respect to field variations but depends on the RG scale k) requires special care within the Functional Renormalization Group (FRG) approach. In several instances, the constant term of the potential has no physical meaning. However, there are special cases where it receives important applications. In low dimensions (d = 1), in a quantum mechanical model, this term is associated with the ground-state energy of the anharmonic oscillator. In higher dimensions (d = 4), it is identical to the Λ term of the Einstein equations and it plays a role in cosmic inflation. Thus, in statistical field theory, in flat space, the constant term could be associated with the free energy, while in curved space, it could be naturally associated with the cosmological constant. It is known that one has to use a subtraction method for the quantum anharmonic oscillator in d = 1 to remove the k 2 term that appears in the RG flow in its high-energy (UV) limit in order to recover the correct results for the ground-state energy. The subtraction is needed because the Gaussian fixed point is missing in the RG flow once the constant term is included. However, if the Gaussian fixed point is there, no further subtraction is required. Here, we propose a subtraction method for k 4 and k 2 terms of the UV scaling of the RG equations for d = 4 dimensions if the Gaussian fixed point is missing in the RG flow with the constant term. Finally, comments on the application of our results to cosmological models are provided.

In this paper, we discuss the statistical description in non-equilibrium regimes of energy fluctuations originated by the interaction between a quantum system and a measurement apparatus applying a sequence of repeated quantum measurements. To properly quantify the information about energy fluctuations, both the exchanged heat probability density function and the corresponding characteristic function are derived and interpreted. Then, we discuss the conditions allowing for the validity of the fluctuation theorem in Jarzynski form 〈e−βQ〉=1, thus showing that the fluctuation relation is robust against the presence of randomness in the time intervals between measurements. Moreover, also the late-time, asymptotic properties of the heat characteristic function are analyzed, in the thermodynamic limit of many intermediate quantum measurements. In such a limit, the quantum system tends to the maximally mixed state (thus corresponding to a thermal state with infinite temperature) unless the system's Hamiltonian and the intermediate measurement observable share a common invariant subspace. Then, in this context, we also discuss how energy fluctuation relations change when the system operates in the quantum Zeno regime. Finally, the theoretical results are illustrated for the special cases of two- and three-levels quantum systems, now ubiquitous for quantum applications and technologies.

Abstract: We study the few-body dynamics of dipolar bosons in one-dimensional double-wells. By varying the interaction strength and investigating one-body observables, in the considered few-body systems we study tunneling oscillations, self-trapping, and a regime exhibiting an equilibrating behavior. The corresponding two-body correlation dynamics exhibits a strong interplay between the interatomic correlation due to non-local nature of the repulsion and the inter-well coherence. We also study the link between the correlation dynamics and the occupation of natural orbitals of the one-body density matrix. Graphical abstract: [Figure not available: see fulltext.]

We present a reformulation of gauge theories in terms of gauge invariant fields. Focusing on abelian theories, we show that the gauge and matter covariant fields can be recombined to introduce new gauge invariant degrees of freedom. Starting from the (1+1) dimensional case on the lattice, with both periodic and open boundary conditions, we then generalize to higher dimensions and to the continuum limit. To show explicit and physically relevant examples of the reformulation, we apply it to the Hamiltonian of a single particle in a (static) magnetic field, to pure abelian lattice gauge theories, to the Lagrangian of quantum electrodynamics in (3+1) dimensions and to the Hamiltonian of the 2d and the 3d Hofstadter model. In the latter, we show that the particular construction used to eliminate the gauge covariant fields enters the definition of the magnetic Brillouin zone. Finally, we briefly comment on relevance of the presented reformulation to the study of interacting gauge theories.

The main idea of magnetic hyperthermia is to increase locally the temperature of the human body by means of injected superparamagnetic nanoparticles. They absorb energy from a time-dependent external magnetic field and transfer it into their environment. In the so-called superlocalization, the combination of an applied oscillating and a static magnetic field gradient provides even more focused heating since for large enough static field the dissipation is considerably reduced. Similar effect was found in the deterministic study of the rotating field combined with a static field gradient. Here we study theoretically the influence of thermal effects on superlocalization and on heating efficiency. We demonstrate that when time-dependent steady state motions of the magnetization vector are present in the zero temperature limit, then deterministic and stochastic results are very similar to each other. We also show that when steady state motions are absent, the superlocalization is severely reduced by thermal effects. Our most important finding is that in the low frequency range (ω→0) suitable for hyperthermia, the oscillating applied field is shown to result in two times larger intrinsic loss power and specific absorption rate then the rotating one with identical superlocalization ability which has importance in technical realization.

We study the out-of-equilibrium properties of the antiferromagnetic Hamiltonian Mean-Field model at low energy. In this regime, the Hamiltonian dynamics exhibits the presence of a long-lived metastable state where the rotators are gathered in a bicluster. This state is not predicted by equilibrium statistical mechanics in the microcanonical ensemble. Performing a low kinetic energy approximation, we derive the explicit expression of the magnetization vector as a function of time. We find that the latter displays coherent oscillations, and we show numerically that the probability distribution for its phase is bimodal or quadrimodal. We then look at the individual rotator dynamics as a motion in an external time-dependent potential, given by the magnetization. This dynamics exhibits two distinct time scales, with the fast one associated to the oscillations of the global magnetization vector. Performing an average over the fast oscillations, we derive an expression for the effective force acting on the individual rotator. This force is always bimodal, and determines a low frequency oscillation of the rotators. Our approach leads to a self-consistent theory linking the time-dependence of the magnetization to the motion of the rotators, providing a heuristic explanation for the formation of the bicluster.

We show that in three-dimensional (3D) topological metals, a subset of the van Hove singularities of the density of states sits exactly at the transitions between topological and trivial gapless phases. We may refer to these as topological van Hove singularities. By investigating two minimal models, we show that they originate from energy saddle points located between Weyl points with opposite chiralities, and we illustrate their topological nature through their magnetotransport properties in the ballistic regime. We exemplify the relation between van Hove singularities and topological phase transitions in Weyl systems by analyzing the 3D Hofstadter model, which offers a simple and interesting playground to consider different kinds of Weyl metals and to understand the features of their density of states. In this model, as a function of the magnetic flux, the occurrence of topological van Hove singularities can be explicitly checked.

We discuss the role of quantum coherence in the energy fluctuations of open quantum systems. To this aim, we introduce a protocol to which we refer as the end-point measurement scheme, allowing us to define the statistics of energy changes as a function of energy measurements performed only after the evolution of the initial state. At the price of an additional uncertainty on the initial energies, this approach prevents the loss of initial quantum coherences and enables the estimation of their effects on energy fluctuations. We demonstrate our findings by running an experiment on the IBM Quantum Experience superconducting qubit platform.

The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a quasiordered phase, characterized by a power-law scaling of the correlation functions at low temperature, is disrupted by the proliferation of topological excitations above the critical temperature TBKT. In this Letter, we consider the effect of long-range decaying couplings ∼r-2-σ on the BKT transition. After pointing out the relevance of this nontrivial problem, we discuss the phase diagram, which is far richer than the corresponding short-range one. It features - for 7/4<σ<2 - a quasiordered phase in a finite temperature range TcTBKT. The transition temperature Tc displays unique universal features quite different from those of the traditional, short-range XY model. Given the universal nature of our findings, they may be observed in current experimental realizations in 2D atomic, molecular, and optical quantum systems.

We study the critical properties of the 3d O(2) universality class in bounded domains through Monte Carlo simulations of the clock model. We use an improved version of the latter, chosen to minimize finite-size corrections at criticality, with 8 orientations of the spins and in the presence of vacancies. The domain chosen for the simulations is the slab configuration with fixed spins at the boundaries. We obtain the universal critical magnetization profile and two-point correlations, which favorably compare with the predictions of the critical geometry approach based on the Yamabe equation. The main result is that the correlations, once the dimensionful contributions are factored out with the critical magnetization profile, are shown to depend only on the distance between the points computed using a metric found solving the corresponding fractional Yamabe equation. The quantitative comparison with the corresponding results for the Ising model at criticality is shown and discussed. Moreover, from the magnetization profiles the critical exponent η is extracted and found to be in reasonable agreement with up-to-date results.

Ultracold fermionic atoms are proposed to be used in 1D optical lattices to quantum simulate the electronic transport in quantum cascade laser (QCL) structures. The competition between the coherent tunneling among (and within) the wells and the dissipative decay at the basis of lasing is discussed. In order to validate the proposed simulation scheme, such competition is quantitatively addressed in a simplified 1D model. The existence of optimal relationships between the model parameters is shown, maximizing the particle current, the population inversion (or their product), and the stimulated emission rate. This substantiates the concept of emulating the QCL operation mechanisms in cold-atom optical lattice simulators, laying the groundwork for addressing open questions, such as the impact of electron–electron scattering and the origin of transport-induced noise, in the design of new-generation QCLs.

Atomtronics deals with matter-wave circuits of ultracold atoms manipulated through magnetic or laser-generated guides with different shapes and intensities. In this way, new types of quantum networks can be constructed in which coherent fluids are controlled with the know-how developed in the atomic and molecular physics community. In particular, quantum devices with enhanced precision, control, and flexibility of their operating conditions can be accessed. Concomitantly, new quantum simulators and emulators harnessing on the coherent current flows can also be developed. Here, the authors survey the landscape of atomtronics-enabled quantum technology and draw a roadmap for the field in the near future. The authors review some of the latest progress achieved in matter-wave circuits' design and atom-chips. Atomtronic networks are deployed as promising platforms for probing many-body physics with a new angle and a new twist. The latter can be done at the level of both equilibrium and nonequilibrium situations. Numerous relevant problems in mesoscopic physics, such as persistent currents and quantum transport in circuits of fermionic or bosonic atoms, are studied through a new lens. The authors summarize some of the atomtronics quantum devices and sensors. Finally, the authors discuss alkali-earth and Rydberg atoms as potential platforms for the realization of atomtronic circuits with special features.

We study the heat statistics of a multilevel N-dimensional quantum system monitored by a sequence of projective measurements. The late-time, asymptotic properties of the heat characteristic function are analyzed in the thermodynamic limit of a high, ideally infinite, number M of measurements (M→∞). In this context, the conditions allowing for an infinite-temperature thermalization (ITT), induced by the repeated monitoring of the quantum system, are discussed. We show that ITT is identified by the fixed point of a symmetric random matrix that models the stochastic process originated by the sequence of measurements. Such fixed point is independent on the nonequilibrium evolution of the system and its initial state. Exceptions to ITT, which we refer to as partial thermalization, take place when the observable of the intermediate measurements is commuting (or quasicommuting) with the Hamiltonian of the quantum system or when the time interval between measurements is smaller or comparable with the system energy scale (quantum Zeno regime). Results on the limit of infinite-dimensional Hilbert spaces (N→∞), describing continuous systems with a discrete spectrum, are also presented. We show that the order of the limits M→∞ and N→∞ matters: When N is fixed and M diverges, then ITT occurs. In the opposite case, the system becomes classical, so that the measurements are no longer effective in changing the state of the system. A nontrivial result is obtained fixing M/N2 where instead partial ITT occurs. Finally, an example of partial thermalization applicable to rotating two-dimensional gases is presented.

We study the connection between the magnetization profiles of models described by a scalar field with marginal interaction term in a bounded domain and the solutions of the so-called Yamabe problem in the same domain, which amounts to finding a metric having constant curvature. Taking the slab as a reference domain, we first study the magnetization profiles at the upper critical dimensions d=3, 4, 6 for different (scale-invariant) boundary conditions. By studying the saddle-point equations for the magnetization, we find general formulas in terms of Weierstrass elliptic functions, extending exact results known in literature and finding ones for the case of percolation. The zeros and poles of the Weierstrass elliptic solutions can be put in direct connection with the boundary conditions. We then show that, for any dimension d, the magnetization profiles are solution of the corresponding integer Yamabe equation at the same d and with the same boundary conditions. The magnetization profiles in the specific case of the four-dimensional Ising model with fixed boundary conditions are compared with Monte Carlo simulations, finding good agreement. These results explicitly confirm at the upper critical dimension recent results presented in Gori and Trombettoni [J. Stat. Mech: Theory Exp. (2020) 0632101742-546810.1088/1742-5468/ab7f32].

We discuss a method to compute the microcanonical entropy at fixed magnetization without direct counting. Our approach is based on the evaluation of a saddle-point leading to an optimization problem. The method is applied to a benchmark Ising model with simultaneous presence of mean-field and nearest-neighbour interactions for which direct counting is indeed possible, thus allowing a comparison. Moreover, we apply the method to an Ising model with mean-field, nearest-neighbour and next-nearest-neighbour interactions, for which direct counting is not straightforward. For this model, we compare the solution obtained by our method with the one obtained from the formula for the entropy in terms of all correlation functions. This example shows that for general couplings our method is much more convenient than direct counting methods to compute the microcanonical entropy at fixed magnetization.