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We show that tailoring the dissipative environment allows to change the features of continuous quantum phase transitions and, even, induce first order transitions in ferromagnetic spin chains. In particular, using a numerically exact quantum Monte Carlo method for the paradigmatic Ising chain of one-half spins in a transverse magnetic field, we find that spin couplings to local quantum boson baths in the Ohmic regime can drive the transition from the second to the first order even for a low dissipation strength. Moreover, using a variational mean-field approach for the treatment of spin-spin and spin-boson interactions, we point out that phase discontinuities are ascribable to a dissipation induced effective magnetic field which is intrinsically related to the bath quantum fluctuations and vanishes for classical baths. The effective field is able to switch the sign of the magnetization along the direction of spin-spin interactions. The results can be potentially tested in recent quantum simulators and are relevant for quantum sensing since the spin system could not only detect the properties of non-classical baths, but also the effects of weak magnetic fields., Comment: 5 pages, 4 figures

By using worldline Monte Carlo technique, matrix product state and a variational approach \`a la Feynman, we investigate the equilibrium properties and relaxation features of the dissipative quantum Rabi model, where a two level system is coupled to a linear harmonic oscillator embedded in a viscous fluid. We show that, in the Ohmic regime, a Beretzinski-Kosterlitz-Thouless quantum phase transition occurs by varying the coupling strength between the two level system and the oscillator. This is a non perturbative result, occurring even for extremely low dissipation magnitude. By using state-of-the-art theoretical methods, we unveil the features of the relaxation towards the thermodynamic equilibrium, pointing out the signatures of quantum phase transition both in the time and frequency domains. We prove that, for low and moderate values of the dissipation, the quantum phase transition occurs in the deep strong coupling regime. We propose to realize this model by coupling a flux qubit and a damped LC oscillator.

By using worldline and diagrammatic quantum Monte Carlo techniques, matrix product state and a variational approach \`a la Feynman, we investigate the equilibrium properties and relaxation features of a quantum system of $N$ spins antiferromagnetically interacting with each other, with strength $J$, and coupled to a common bath of bosonic oscillators, with strength $\alpha$. We show that, in the Ohmic regime, a Beretzinski-Thouless-Kosterlitz quantum phase transition occurs. While for $J=0$ the critical value of $\alpha$ decreases asymptotically with $1/N$ by increasing $N$, for nonvanishing $J$ it turns out to be practically independent on $N$, allowing to identify a finite range of values of $\alpha$ where spin phase coherence is preserved also for large $N$. Then, by using matrix product state simulations, and the Mori formalism and the variational approach \`a la Feynman jointly, we unveil the features of the relaxation, that, in particular, exhibits a non monotonic dependence on the temperature reminiscent of the Kondo effect. For the observed quantum phase transition we also establish a criterion analogous to that of the metal-insulator transition in solids.

The effectiveness of the variational approach a la Feynman is proved in the spin-boson model, i.e. the simplest realization of the Caldeira-Leggett model able to reveal the quantum phase transition from delocalized to localized states and the quantum dissipation and decoherence effects induced by a heat bath. After exactly eliminating the bath degrees of freedom, we propose a trial, non local in time, interaction between the spin and itself simulating the coupling of the two level system with the bosonic bath. It stems from an Hamiltonian where the spin is linearly coupled to a finite number of harmonic oscillators whose frequencies and coupling strengths are variationally determined. We show that a very limited number of these fictitious modes is enough to get a remarkable agreement, up to very low temperatures, with the data obtained by using an approximation-free Monte Carlo approach, predicting: 1) in the Ohmic regime, a Beretzinski-Thouless-Kosterlitz quantum phase transition exhibiting the typical universal jump at the critical value; 2) in the sub-Ohmic regime ($s \leq 0.5$), mean field quantum phase transitions, with logarithmic corrections for $s=0.5$.

We present a method to measure the von Neumann entanglement entropy of ground states of quantum many-body systems which does not require access to the system wave function. The technique is based on a direct thermodynamic study of entanglement Hamiltonians, whose functional form is available from field theoretical insights. The method is applicable to classical simulations such as quantum Monte Carlo methods, and to experiments that allow for thermodynamic measurements such as the density of states, accessible via quantum quenches. We benchmark our technique on critical quantum spin chains, and apply it to several two-dimensional quantum magnets, where we are able to unambiguously determine the onset of area law in the entanglement entropy, the number of Goldstone bosons, and to check a recent conjecture on geometric entanglement contribution at critical points described by strongly coupled field theories.

It is commonly accepted that a parametric amplifier can simulate a phase-preserving linear amplifier regardless of how the latter is realized [Caves et al., Phys. Rev. A 86, 063802 (2012)]. If true, this reduces all phase-preserving linear amplifiers to a single familiar model. Here we disprove this claim by constructing two counterexamples. A detailed discussion of the physics of our counterexamples is provided. It is shown that a Heisenberg-picture analysis facilitates a microscopic explanation of the physics. This also resolves a question about the nature of amplifier-added noise in degenerate two-photon amplification., Comment: Comments welcome

We propose a simple method to simulate and detect topological insulators with cold atoms trapped in a one-dimensional bichromatic optical lattice subjected to a time-periodic modulation. The tight-binding form of this shaken system is equivalent to the periodically driven Aubry-Andre model. We demonstrate that this model can be mapped into a two-dimensional Chern insulator model, whose energy spectrum hosts a topological phase within an experimentally accessible parameter regime. By tuning the laser phase adiabatically, such one-dimensional system constitutes a natural platform to realize topological particle pumping. We show that the Chern number characterizing the topological features of this system can be measured by detecting the density shift after one cycle of pumping., Comment: 8 pages, 2 figures

The phase of an optical field inside a linear amplifier is widely known to diffuse with a diffusion coefficient that is inversely proportional to the photon number. The same process occurs in lasers which limits its intrinsic linewidth and makes the phase uncertainty difficult to calculate. The most commonly used simplification is to assume a narrow photon-number distribution for the optical field (which we call the small-noise approximation). For coherent light, this condition is determined by the average photon number. The small-noise approximation relies on (i) the input to have a good signal-to-noise ratio, and (ii) that such a signal-to-noise ratio can be maintained throughout the amplification process. Here we ask: For a coherent input, how many photons must be present in the input to a quantum linear amplifier for the phase noise at the output to be amenable to a small-noise analysis? We address these questions by showing how the phase uncertainty can be obtained without recourse to the small-noise approximation. It is shown that for an ideal linear amplifier (i.e. an amplifier most favourable to the small-noise approximation), the small-noise approximation breaks down with only a few photons on average. Interestingly, when the input strength is increased to tens of photons, the small-noise approximation can be seen to perform much better and the process of phase diffusion permits a small-noise analysis. This demarcates the limit of the small-noise assumption in linear amplifiers as such an assumption is less true for a nonideal amplifier.

We show that a hierarchy of topological phases in one dimension -- a topological Devil's staircase -- can emerge at fractional filling fractions in interacting systems, whose single-particle band structure describes a topological or a crystalline topological insulator. Focusing on a specific example in the BDI class, we present a field-theoretical argument based on bosonization that indicates how the system, as a function of the filling fraction, hosts a series of density waves. Subsequently, based on a numerical investigation of the low-lying energy spectrum, Wilczek-Zee phases, and entanglement spectra, we show that they are symmetry protected topological phases. In sharp contrast to the non-interacting limit, these topological density waves do not follow the bulk-edge correspondence, as their edge modes are gapped. We then discuss how these results are immediately applicable to models in the AIII class, and to crystalline topological insulators protected by inversion symmetry. Our findings are immediately relevant to cold atom experiments with alkaline-earth atoms in optical lattices, where the band structure properties we exploit have been recently realized.

We present an analog of the phenomenon of orthogonality catastrophe in quantum many body systems subject to a local dissipative impurity. We show that the fidelity $F(t)$, giving a measure for distance of the time-evolved state from the initial one, displays a universal scaling form $F(t)\propto t^\theta e^{-\gamma t}$, when the system supports long range correlations, in a fashion reminiscent of traditional instances of orthogonality catastrophe in condensed matter. An exponential fall-off at rate $\gamma$ signals the onset of environmental decoherence, which is critically slowed down by the additional algebraic contribution to the fidelity. This picture is derived within a second order cumulant expansion suited for Liouvillian dynamics, and substantiated for the one-dimensional transverse field quantum Ising model subject to a local dephasing jump operator, as well as for XY and XX quantum spin chains, and for the two dimensional Bose gas deep in the superfluid phase with local particle heating. Our results hint that local sources of dissipation can be used to inspect real-time correlations and to induce a delay of decoherence in open quantum many body systems., Comment: 5+7 pages, 3 figures

Driven-dissipative quantum many-body systems have attracted increasing interest in recent years as they lead to novel classes of quantum many-body phenomena. In particular, mean-field calculations predict limit cycle phases, slow oscillations instead of stationary states, in the long-time limit for a number of driven-dissipative quantum many-body systems. Using a cluster mean-field and a self-consistent Mori projector approach, we explore the persistence of such limit cycles as short range quantum correlations are taken into account in a driven-dissipative Heisenberg model., Comment: 13 pages, 7 figures

In this work we introduce {\it boundary time-crystals}. Here {\it continuous} time-translation symmetry breaking occurs only in a macroscopic fraction of a many-body quantum system. After introducing their definition and properties, we analyse in detail a solvable model where an accurate scaling analysis can be performed. The existence of the boundary time crystals is intimately connected to the emergence of a time-periodic steady state in the thermodynamic limit of a many-body open quantum system. We also discuss connections to quantum synchronisation., Comment: 6 + 9 pages, 4 + 7 figures

The realization of the Hofstadter model in a strongly anisotropic ladder geometry has now become possible in one-dimensional optical lattices with a synthetic dimension. In this work, we show how the Hofstadter Hamiltonian in such ladder configurations hosts a topological phase of matter which is radically different from its two-dimensional counterpart. This topological phase stems directly from the hybrid nature of the ladder geometry, and is protected by a properly defined inversion symmetry. We start our analysis considering the paradigmatic case of a three-leg ladder which supports a topological phase exhibiting the typical features of topological states in one dimension: robust fermionic edge modes, a degenerate entanglement spectrum and a non-zero Zak phase; then, we generalize our findings - addressable in the state-of-the-art cold atom experiments - to ladders with an higher number of legs.

We present a quantum heat switch based on coupled superconducting qubits, connected to two $LC$ resonators that are terminated by resistors providing two heat baths. To describe the system we use a standard second order master equation with respect to coupling to the baths. We find that this system can act as an efficient heat switch controlled by the applied magnetic flux. The flux influences the energy level separations of the system, and under some conditions, the finite coupling of the qubits enhances the transmitted power between the two baths, by an order of magnitude under realistic conditions. At the same time, the bandwidth at maximum power of the switch formed of the coupled qubits is narrowed.

We show how angular momentum conservation can stabilise a symmetry-protected quasi-topological phase of matter supporting Majorana quasi-particles as edge modes in one-dimensional cold atom gases. We investigate a number-conserving four-species Hubbard model in the presence of spin-orbit coupling. The latter reduces the global spin symmetry to an angular momentum parity symmetry, which provides an extremely robust protection mechanism that does not rely on any coupling to additional reservoirs. The emergence of Majorana edge modes is elucidated using field theory techniques, and corroborated by density-matrix-renormalization-group simulations. Our results pave the way toward the observation of Majorana edge modes with alkaline-earth-like fermions in optical lattices, where all basic ingredients for our recipe - spin-orbit coupling and strong inter-orbital interactions - have been experimentally realized over the last two years., Comment: 12 pages (6 + 6 supplementary material)

We explore critical properties of two-dimensional lattices of spins interacting via an anisotropic Heisenberg Hamiltonian and subject to incoherent spin flips. We determine the steady-state solution of the master equation for the density matrix via the corner-space renormalization method. We investigate the finite-size scaling and critical exponent of the magnetic linear susceptibility associated to a dissipative ferromagnetic transition. We show that the Von Neumann entropy increases across the critical point, revealing a strongly mixed character of the ferromagnetic phase. Entanglement is witnessed by the quantum Fisher information which exhibits a critical behavior at the transition point, showing that quantum correlations play a crucial role in the transition even though the system is in a mixed state., Comment: Accepted for publication on Phys. Rev. B (6 pages, 5 figures)

We introduce a simple method to realize and detect photonic topological Chern insulators with one-dimensional circiut quantum electrodynamics arrays. By periodically modulating the couplings of the array, we show that this one-dimensional model can be mapped into a two-dimensional Chern insulator model. In addition to allowing the study of photonic Chern insulators, this approach also provides a natural platform to realise experimentally Laughlin's pumping argument. Based on scattering theory of topological insulators and input-output formalism, we show that the photonic edge state can be probed directly and the topological invariant can be detected from the winding number of the reflection coefficient phase., Comment: 5 pages, 3 figures

The joint action of a synthetic gauge potential and of atomic contact repulsion in a one-dimensional alkaline-earth(-like) fermionic gas with nuclear spin I leads to the existence of a hierarchy of fractional insulating and conducting states with intriguing properties. We unveil the existence and the features of those phases by means of both analytical bosonization techniques and numerical methods based on the density-matrix renormalization group algorithm. In particular, we show that the gapless phases can support helical modes, whereas the gapped states, which appear under certain conditions, are characterised both by density and magnetic order. Several distinct features emerge solely for spin I larger than 1/2, thus making their study with cold-atoms unique. We will finally argue that these states are related to the properties of an unconventional fractional quantum Hall effect in the thin-torus limit. The properties of this hierarchy of states can be experimentally studied in state-of-the-art cold-atom laboratories., Comment: (8 pages, 5 figures; Supplementary Material: 4 pages, 5 figures)

We explore the phase diagram of the dissipative Rabi-Hubbard model, as could be realized by a Raman-pumping scheme applied to a coupled cavity array. There exist various exotic attractors, including ferroelectric, antiferroelectric, and inccomensurate fixed points, as well as regions of persistent oscillations. Many of these features can be understood analytically by truncating to the two lowest lying states of the Rabi model on each site. We also show that these features survive beyond mean-field, using Matrix Product Operator simulations., Comment: 5pages, 3 figures, plus supplementary material. Final version, as published

Spontaneous synchronization is a fundamental phenomenon, important in many theoretical studies and applications. Recently this effect has been analyzed and observed in a number of physical systems close to the quantum mechanical regime. In this work we propose the mutual information as a useful order parameter which can capture the emergence of synchronization in very different contexts, ranging from semi-classical to intrinsically quantum mechanical systems. Specifically we first study the synchronization of two coupled Van der Pol oscillators in both classical and quantum regimes and later we consider the synchronization of two qubits inside two coupled optical cavities. In all these contexts, we find that mutual information can be used as an appropriate figure of merit for determining the synchronization phases, independently of the specific details of the system.

We investigate the mean-field dynamics of a system of interacting photons in an array of coupled cavities in presence of dissipation and disorder. We follow the evolution of on an initially prepared Fock state, and show how the interplay between dissipation and disorder affects the coherence properties of the cavity emission and that these properties can be used as signatures of the many-body phase of the whole array., Comment: 8 pages, 10 figures, new reference added

We extend the concept of superadiabatic dynamics, or transitionless quantum driving, to quantum open systems whose evolution is governed by a master equation in the Lindblad form. We provide the general framework needed to determine the control strategy required to achieve superadiabaticity. We apply our formalism to two examples consisting of a two-level system coupled to environments with time-dependent bath operators., Comment: 11 pages, no Figures; accepted for publication in New Journal of Physics

We study the photon transfer along a linear array of three coupled cavities where the central one contains an interacting two-level system in the strong and ultrastrong coupling regimes. We find that an inhomogeneously coupled array forbids a complete single-photon transfer between the external cavities when the central one performs a Jaynes-Cummings dynamics. This is not the case in the ultrastrong coupling regime, where the system exhibits singularities in the photon transfer time as a function of the cavity-qubit coupling strength. Our model can be implemented within the state-of-the-art circuit quantum electrodynamics technology and it represents a building block for studying photon state transfer through scalable cavity arrays., Comment: 5 pages, 5 figures, supplemental material

We introduce and characterize two different measures which quantify the level of synchronization of interacting continuous variable quantum systems. The two measures allow to extend to the quantum domain the notions of complete and phase synchronization. The Heisenberg principle sets a universal bound to complete synchronization. The measure of phase synchronization is in principle unbounded, however in the absence of quantum resources (e.g. squeezing) the synchronization level is bounded below a certain threshold. We elucidate some interesting connections between entanglement and synchronization and, finally, discuss an application based on quantum opto-mechanical systems., Comment: 5+1 pages, 2 figures

We propose an experimental scheme to verify the quantum non-equilibrium fluctuation relations using current technology. Specifically, we show that the characteristic function of the work distribution for a non-equilibrium quench of a general quantum system can be extracted from Ramsey interferometry of a single probe qubit. Our scheme paves the way for the full characterisation of non-equilibrium processes in a variety of complex quantum systems ranging from single particles to many-body atomic systems and spin chains. We demonstrate our idea using a time-dependent quench of the motional state of a trapped ion, where the internal pseudo-spin provides a convenient probe qubit., Comment: 4.5 pages. 2 Figures. See related paper "Measuring the characteristic function of the work distribution" by L. Mazzola et al. This version - additional analysis undertaken

We demonstrate that arbitrary time evolutions of many-body quantum systems can be reversed even in cases when only part of the Hamiltonian can be controlled. The reversed dynamics obtained via optimal control --contrary to standard time-reversal procedures-- is extremely robust to external sources of noise. We provide a lower bound on the control complexity of a many-body quantum dynamics in terms of the dimension of the manifold supporting it, elucidating the role played by integrability in this context., Comment: 4.5 pages, 5 figures

We show that the dynamics of a driven quantum system weakly coupled to the environment can exhibit two distinct regimes. While the relaxation basis is usually determined by the system+drive Hamiltonian (system-governed dynamics), we find that under certain conditions it is determined by specific features of the environment, such as, the form of the coupling operator (environment-governed dynamics). We provide an effective coupling parameter describing the transition between the two regimes and discuss how to observe the transition in a superconducting charge pump., Comment: 5+1 pages, 3 figures

We illustrate a reverse Von Neumann measurement scheme in which a geometric phase induced on a quantum harmonic oscillator is measured using a microscopic qubit as a probe. We show how such a phase, generated by a cyclic evolution in the phase space of the harmonic oscillator, can be kicked back on the qubit, which plays the role of a quantum interferometer. We also extend our study to finite-temperature dissipative Markovian dynamics and discuss potential implementations in micro and nano-mechanical devices coupled to an effective two-level system., Comment: RevTeX4, 4 pages, 2 figures

We introduce an algorithm to perform an optimal adiabatic evolution that operates without an apriori knowledge of the system spectrum. By probing the system gap locally, the algorithm maximizes the evolution speed, thus minimizing the total evolution time. We test the algorithm on the Landau-Zener transition and then apply it on the quantum adiabatic computation of 3-SAT: The result is compatible with an exponential speed-up for up to twenty qubits with respect to classical algorithms. We finally study a possible algorithm improvement by combining it with the quantum Zeno effect., Comment: 4 pages, 4 figures

The number of defects which are generated on crossing a quantum phase transition can be minimized by choosing properly designed time-dependent pulses. In this work we determine what are the ultimate limits of this optimization. We discuss under which conditions the production of defects across the phase transition is vanishing small. Furthermore we show that the minimum time required to enter this regime is $T\sim \pi/\Delta$, where $\Delta$ is the minimum spectral gap, unveiling an intimate connection between an optimized unitary dynamics and the intrinsic measure of the Hilbert space for pure states. Surprisingly, the dynamics is non-adiabatic, this result can be understood by assuming a simple two-level dynamics for the many-body system. Finally we classify the possible dynamical regimes in terms of the action $s=T\Delta$., Comment: 6 pages, 6 figures

We investigate the coherent mixing of co-propagating edge channels in a quantum Hall bar produced by step potentials. In the case of two edge channels it is found that, although a single step induces only a few percent mixing, a series of steps could yield 50% mixing. In addition, a strong mixing is found when the potential height of a single step allows a different number of edge channels on the two sides of the step. Charge density probability has been also calculated even for the case where the step is smoothened., Comment: final version: 7 pages, 6 figures

Three different implementations of interaction-free measurements (IFMs) in solid-state nanodevices are discussed. The first one is based on a series of concatenated Mach-Zehnder interferometers, in analogy to optical-IFM setups. The second one consists of a single interferometer and concatenation is achieved in the time domain making use of a quantized electron emitter. The third implementation consists of an asymmetric Aharonov-Bohm ring. For all three cases we show that the presence of a dephasing source acting on one arm of the interferometer can be detected without degrading the coherence of the measured current. Electronic implementations of IFMs in nanoelectronics may play a fundamental role as very accurate and noninvasive measuring schemes for quantum devices., Comment: 12 pages, 10 figures

The multiscale entanglement renormalization ansatz is applied to the study of boundary critical phenomena. We compute averages of local operators as a function of the distance from the boundary and the surface contribution to the ground state energy. Furthermore, assuming a uniform tensor structure, we show that the multiscale entanglement renormalization ansatz implies an exact relation between bulk and boundary critical exponents known to exist for boundary critical systems., Comment: 6 pages, 4 figures; for a related work see arXiv:0912.1642

Many-body states whose wave-function admits a representation in terms of a uniform binary-tree tensor decomposition are shown to obey to power-law two-body correlations functions. Any such state can be associated with the ground state of a translational invariant Hamiltonian which, depending on the dimension of the systems sites, involve at most couplings between third-neighboring sites. A detailed analysis of their spectra shows that they admit an exponentially large ground space., Comment: 6 pages, 2 figures

We show that an Aharonov-Bohm (AB) ring with asymmetric electron injection can act as a coherent detector of electron dephasing. The presence of a dephasing source in one of the two arms of a moderately-to-highly asymmetric ring changes the response of the system from total reflection to complete transmission while preserving the coherence of the electrons propagating from the ring, even for strong dephasing. We interpret this phenomenon as an implementation of an interaction-free measurement., Comment: 4 pages, 3 figures

We determine the conditions under which topological order survives a rapid quantum quench. Specifically, we consider the case where a quantum spin system is prepared in the ground state of the Toric Code Model and, after the quench, it evolves with a Hamiltonian that does not support topological order. We provide analytical results supported by numerical evidence for a variety of quench Hamiltonians. The robustness of topological order under non-equilibrium situations is tested by studying the topological entropy and a novel dynamical measure, which makes use of the similarity between partial density matrices obtained from different topological sectors., Comment: 4 pages, 3 figures; published version (PRA Rapid Communication)

We analyze the non-equilibrium dynamics of a gas of interacting photons in an array of coupled dissipative nonlinear cavities driven by a pulsed external coherent field. Using a mean-field approach, we show that the system exhibits a phase transition from a Mott-insulator-like to a superfluid regime. For a given single-photon nonlinearity, the critical value of the photon tunneling rate at which the phase transition occurs increases with the increasing photon loss rate. We checked the robustness of the transition by showing its insensitivity to the initial state prepared by the the pulsed excitation. We find that the second-order coherence of cavity emission can be used to determine the phase diagram of an optical many-body system without the need for thermalization., Comment: 4 pages, 4 figures

We study theoretically the electronic entropy and specific heat in diffusive superconductor-normal metal-superconductor (SNS) Josephson junctions. In particular, we consider the influence of non-idealities occurring in an actual experiment, such as the presence of barriers at the NS interfaces, the spin-flip and inelastic scattering in the N region and quasiparticle subgap states in the superconductors. We find that spin-flip and inelastic scattering do not have, for typical parameters values, a large effect. On the contrary, the presence of barriers suppresses the superconducting correlations in the N region, with the consequence that the entropy and the specific heat get reduced eventually to those in the absence of superconductivity for opaque interfaces. Finally we suggest an experiment and check that it is possible, under realistic conditions, to measure the dependence of electronic specific heat on the phase difference between the superconductors., Comment: 8 pages, 10 color figures

Homogeneous Multi-scale Entanglement Renormalization Ansazt (MERA) state have been recently introduced to describe quantum critical systems. Here we present an extensive analysis of the properties of such states by clarifying the definition of their transfer super-operator whose structure is studied within a informational theoretical approach. Explicit expressions for computing the expectation values of symmetric observables are given both in the case of finite size systems and in the thermodynamic limit of infinitely many particles., Comment: 13 pages, 5 figures

We introduce a new technique to probe the properties of an interacting cold atomic gas that can be viewed as a dynamical compressibility measurement. We apply this technique to the study of the superfluid to Mott insulator quantum phase transition in one and three dimensions for a bosonic gas trapped in an optical lattice. Excitations of the system are detected by time-of-flight measurements. The experimental data for the one-dimensional case are in good agreement with the results of a time-dependent density matrix renormalization group calculation., Comment: 5 pages, 5 figures

An algorithm for optimizing the MERA tensor network in an infinite system is presented. Using this technique we compute the critical exponents of Ising and XXZ model., Comment: 4 pages, 4 figures

We study the influence of superconducting correlations on the electronic specific heat in a diffusive superconductor-normal metal-superconductor Josephson junction. We present a description of this system in the framework of the diffusive-limit Green's function theory, taking into account finite temperatures, phase difference as well as junction parameters. We find that proximity effect may lead to a substantial deviation of the specific heat as compared to that in the normal state, and that it can be largely tuned in magnitude by changing the phase difference between the superconductors. A measurement setup to confirm these predictions is also suggested., Comment: 4+ pages, 4 figures

We study the multi-spin entanglement for the 1D anisotropic XY model concentrating on the simplest case of three-spin entanglement. As compared to the pairwise entanglement, three-party quantum correlations have a longer range and they are more robust on increasing the temperature. We find regions of the phase diagram of the system where bound entanglement occurs, both at zero and finite temperature. Bound entanglement in the ground state can be obtained by tuning the magnetic field. Thermal bound entanglement emerges naturally due to the effect of temperature on the free ground state entanglement., Comment: 7 pages, 3 figures; some typos corrected, references added