Emergent quasiparticles at Luttinger surfaces

In periodic systems of interacting electrons, Fermi and Luttinger surfaces refer to the locations within the Brillouin zone of poles and zeros, respectively, of the single-particle Green’s function at zero energy and temperature. Such difference in analytic properties underlies the emergence of well-defined quasiparticles close to a Fermi surface, in contrast to their supposed non-existence close to a Luttinger surface, where the single-particle density-of-states vanishes at zero energy. We here show that, contrary to such common belief, dispersive ‘quasiparticles’ with infinite lifetime do exist also close to a pseudo-gapped Luttinger surface. Thermodynamic and dynamic properties of such ‘quasiparticles’ are just those of conventional ones. For instance, they yield well-defined quantum oscillations in Luttinger surface and linear-in-temperature specific heat, which is striking given the vanishing density of states of physical electrons, but actually not uncommon in strongly correlated materials.

Confinement in the tricritical Ising model

Lencsés M., We study the leading and sub-leading magnetic perturbations of the thermal E7 integrable deformation of the tricritical Ising model. In the low-temperature phase, these magnetic perturbations lead to the confinement of the kinks of the model. The resulting meson spectrum can be obtained using the semi-classical quantisation, here extended to include also mesonic excitations composed of two different kinks. An interesting feature of the integrable sub-leading magnetic perturbation of the thermal E7 deformation of the model is the possibility to swap the role of the two operators, i.e. the possibility to consider the model as a thermal perturbation of the integrable A3 model associated to the sub-leading magnetic deformation. Due to the occurrence of vacuum degeneracy unrelated to spontaneous symmetry breaking in A3, the confinement pattern shows novel features compared to previously studied models. Interestingly enough, the validity of the semi-classical description in terms of the A3 endpoint extends well beyond small fields, and therefore the full parameter space of the joint thermal and sub-leading magnetic deformation is well described by a combination of semi-classical approaches. All predictions are verified by comparison to finite volume spectrum resulting from truncated conformal space.

Pattern capacity of a single quantum perceptron

Recent developments in quantum machine learning have seen the introduction of several models to generalize the classical perceptron to the quantum regime. The capabilities of these quantum models need to be determined precisely in order to establish if a quantum advantage is achievable. Here we use a statistical physics approach to compute the pattern capacity of a particular model of quantum perceptron realized by means of a continuous variable quantum system.

Phase diagram of Rydberg-dressed atoms on two-leg square ladders: Coupling supersymmetric conformal field theories on the lattice

Tsitsishvili M., Chanda T., Votto M., Fromholz P., We investigate the phase diagram of hard-core bosons in two-leg ladders in the presence of soft-shoulder potentials. We show how the competition between local and nonlocal terms gives rise to a phase diagram with liquid phases with dominant cluster, spin-, and density-wave quasi-long-range ordering. These phases are separated by Berezinskii-Kosterlitz-Thouless, Gaussian, and supersymmetric (SUSY) quantum critical transitions. For the latter, we provide a phenomenological description of coupled SUSY conformal field theories, whose predictions are confirmed by matrix product state simulations. Our results are motivated by, and directly relevant to, recent experiments with Rydberg-dressed atoms in optical lattices, where ladder dynamics has already been demonstrated, and emphasize the capabilities of these setups to investigate exotic quantum phenomena such as cluster liquids and coupled SUSY conformal field theories.

Two-dimensional t-t′ Holstein model

Araújo M.V., De Lima J.P., The competition and interplay between charge-density wave and superconductivity have become a central subject for quasi-two-dimensional compounds. Some of these materials, such as the transition-metal dichalcogenides, exhibit strong electron-phonon coupling, an interaction that may favor both phases, depending on the external parameters, such as hydrostatic pressure. In view of this, here we analyze the single-band t-t′ Holstein model in the square lattice, adding a next-nearest neighbor hopping t′ in order to play the role of the external pressure. To this end, we perform unbiased quantum Monte Carlo simulations with an efficient inversion sampling technique appropriately devised for this model. Such a methodology drastically reduces the autocorrelation time and increases the efficiency of the Monte Carlo approach. By investigating the charge-charge correlation functions, we obtain the behavior of the critical temperature as a function of t′ and, from compressibility analysis, we show that a first-order metal-to-insulator phase transition occurs. We also provide a low-temperature phase diagram for the model.

Negativity Hamiltonian: An Operator Characterization of Mixed-State Entanglement

Murciano S., Vitale V., In the context of ground states of quantum many-body systems, the locality of entanglement between connected regions of space is directly tied to the locality of the corresponding entanglement Hamiltonian: the latter is dominated by local, few-body terms. In this work, we introduce the negativity Hamiltonian as the (non-Hermitian) effective Hamiltonian operator describing the logarithm of the partial transpose of a many-body system. This allows us to address the connection between entanglement and operator locality beyond the paradigm of bipartite pure systems. As a first step in this direction, we study the structure of the negativity Hamiltonian for fermionic conformal field theories and a free-fermion chain: in both cases, we show that the negativity Hamiltonian assumes a quasilocal functional form, that is captured by simple functional relations.

Dynamics of the order parameter statistics in the long range Ising model

Ranabhat N., We study the relaxation of the local ferromagnetic order in the transverse field quantum Ising chain with power-law decaying interactions ∼ 1/rα. We prepare the system in the GHZ state and study the time evolution of the probability distribution function (PDF) of the order parameter within a block of when quenching the transverse field. The model is known to support long range order at finite temperature for α ≤ 2.0. In this regime, quasi-localized topological magnetic defects are expected to strongly affect the equilibration of the full probability distribution. We highlight different dynamical regimes where gaussification mechanism may be slowed down by confinement and eventually breaks. We further study the PDF dynamics induced by changing the effective dimensionality of the system; we mimic this by quenching the range of the interactions. As a matter of fact, the behavior of the system crucially depends on the value of α governing the unitary evolution.

EDIpack: A parallel exact diagonalization package for quantum impurity problems

Amaricci A., Crippa L., Scazzola A., Petocchi F., Mazza G., de Medici L., We present EDIpack, an exact diagonalization package to solve generic quantum impurity problems. The algorithm includes a generalization of the look-up method introduced in Ref. [1] and enables a massively parallel execution of the matrix-vector linear operations required by Lanczos and Arnoldi algorithms. We show that a suitable Fock basis organization is crucial to optimize the inter-processors communication in a distributed memory setup and to reach sub-linear scaling in sufficiently large systems. We discuss the algorithm in details indicating how to deal with multiple orbitals and electron-phonon coupling. Finally, we outline the download, installation and functioning of the package. Program summary: Program title: EDIpack CPC Library link to program files: https://doi.org/10.17632/2hxhw9zjg9.1 Code Ocean capsule: https://codeocean.com/capsule/3537659 Licensing provisions: GPLv3 Programming language: Fortran, Python External dependencies: CMake (>=3.0.0), Scifortran, MPI Nature of problem: The solution of multi-orbital quantum impurity systems at zero or low temperatures, including the effective description of lattice models of strongly correlated electrons, are difficult to determine. Solution method: Use parallel exact diagonalization algorithm to compute the low lying spectrum and evaluate dynamical correlation functions.

QMC study of the chiral Heisenberg Gross-Neveu universality class

Otsuka Y., Seki K., We investigate a quantum criticality of an antiferromagnetic phase transition in the Hubbard model on a square lattice with a d-wave pairing field by large-scale auxiliary-field quantum Monte Carlo simulations. Since the d-wave pairing filed induces Dirac cones in the non-interacting single-particle spectrum, the quantum criticality should correspond to the chiral Heisenberg universality class in terms of the Gross-Neveu theory, which is the same as those expected in the Hubbard model on the honeycomb lattice, despite the unit cells being different (e.g., they contain one and two sites, respectively). We show that both the two phase transitions, expected to occur on the square and on the honeycomb lattices, indeed have the same quantum criticality. We also argue that details of the models, i.e., the way of counting the total number N of fermion components and the anisotropy of the Dirac cones, do not change the critical exponents.

Quenches and confinement in a Heisenberg-Ising spin ladder

Lagnese G., Surace F.M., Kormos M., We consider the quantum quench dynamics of a Heisenberg-Ising spin ladder which is an archetypal model in which confinement of elementary excitations is triggered by internal interactions rather than an external field. We show that the confinement strongly affects the light cone structure of correlation functions providing signatures of the velocities of the mesons of the model. We also show that the meson masses can be measured from the real time analysis of the evolution of the order parameter.

Entanglement dynamics in confining spin chains

Scopa S., The confinement of elementary excitations induces distinctive features in the non-equilibrium quench dynamics. One of the most remarkable is the suppression of entanglement entropy, which in several instances turns out to oscillate rather than grow indefinitely. While the qualitative physical origin of this behavior is clear, till now no quantitative understanding away from the field theory limit was available. Here we investigate this problem in the weak quench limit, when mesons are excited at rest, hindering entropy growth and exhibiting persistent oscillations. We provide analytical predictions of the entire entanglement dynamics based on a Gaussian approximation of the many-body state, which captures numerical data with great accuracy and is further simplified to a semiclassical quasiparticle picture in the regime of weak confinement. Our methods are valid in general and we apply explicitly to two prototypical models: the Ising chain in a tilted field and the experimentally relevant long-range Ising model.

Thermoelectrics of a two-channel charge Kondo circuit: Role of electron-electron interactions in a quantum point contact

Parafilo A.V., Nguyen T.K.T., In this Letter we investigate the properties of a quantum impurity model in the presence of additional many-body interactions between mobile carriers. The fundamental question which is addressed here is how the interactions in the charge and spin sectors of an itinerant system affect the quantum impurity physics in the vicinity of the intermediate coupling fixed point. To illustrate the general answer to this question we discuss a two-channel charge Kondo circuit model. We show that the electron-electron interactions resulting in the formation of a massive spin mode in an itinerant electron subset drive the system away from the unstable non-Fermi-liquid (NFL) fixed point to the stable Fermi-liquid (FL) regime. We discuss the thermoelectric response as a benchmark for the NFL-FL crossover.

Quantum physics in space

Belenchia A., Carlesso M., Bayraktar Ö., Dequal D., Derkach I., Gasbarri G., Herr W., Li Y.L., Rademacher M., Sidhu J., Oi D.K.L., Seidel S.T., Kaltenbaek R., Marquardt C., Ulbricht H., Usenko V.C., Wörner L., Xuereb A., Paternostro M., Advances in quantum technologies are giving rise to a revolution in the way fundamental physics questions are explored at the empirical level. At the same time, they are the seeds for future disruptive technological applications of quantum physics. Remarkably, a space-based environment may open many new avenues for exploring and employing quantum physics and technologies. Recently, space missions employing quantum technologies for fundamental or applied studies have been proposed and implemented with stunning results. The combination of quantum physics and its space application is the focus of this review: we cover both the fundamental scientific questions that can be tackled with quantum technologies in space and the possible implementation of these technologies for a variety of academic and commercial purposes.

Vacuum energy and renormalization of the field-independent term

Márián I.G., Jentschura U.D., Defenu N., 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.

Symmetry-resolved dynamical purification in synthetic quantum matter

Vitale V., Elben A., Kueng R., Neven A., Carrasco J., Kraus B., Zoller P., When a quantum system initialized in a product state is subjected to either coherent or incoherent dynamics, the entropy of any of its connected partitions generically increases as a function of time, signalling the inevitable spreading of (quantum) information throughout the system. Here, we show that, in the presence of continuous symmetries and under ubiquitous experimental conditions, symmetry-resolved information spreading is inhibited due to the competition of coherent and incoherent dynamics: in given quantum number sectors, entropy decreases as a function of time, signalling dynamical purification. Such dynamical purification bridges between two distinct short and intermediate time regimes, characterized by a log-volume and log-area entropy law, respectively. It is generic to symmetric quantum evolution, and as such occurs for different partition geometry and topology, and classes of (local) Liouville dynamics. We then develop a protocol to measure symmetry-resolved entropies and negativities in synthetic quantum systems based on the random unitary toolbox, and demonstrate the generality of dynamical purification using experimental data from trapped ion experiments [Brydges et al., Science 364, 260 (2019)]. Our work shows that symmetry plays a key role as a magnifying glass to characterize many-body dynamics in open quantum systems, and, in particular, in noisy-intermediate scale quantum devices.

Branch point twist field form factors in the sine-Gordon model II: Composite twist fields and symmetry resolved entanglement

Horváth D.X., In this paper we continue the program initiated in Part I, that is the study of entanglement measures in the sine-Gordon model. In both parts, we have focussed on one specific technique, that is the well-known connection between branch point twist field correlators and measures of entanglement in 1+1D integrable quantum field theory. Our papers apply this technique for the first time to a non-diagonal theory with an involved particle spectrum, the sine-Gordon model. In this Part II we focus on a different entanglement measure, the symmetry resolved entanglement, and develop its associated twist field description, exploiting the underlying U(1) symmetry of the theory. In this context, conventional branch point twist fields are no longer the fields required, but instead we must work with one of their composite generalisations, which can be understood as the field resulting from the fusion of a standard branch point twist field and the sine-Gordon exponential field associated with U(1) symmetry. The resulting composite twist field has correlators which as usual admit a form factor expansion. In this paper we write the associated form factor equations and solve them for various examples in the breather sector by using the method of angular quantisation. We show that, in the attractive regime, this is the sector which provides the leading contribution to the symmetry resolved entropies, both Rényi and von Neumann. We compute the latter in the limit of a large region size and show that they satisfy the property of equipartition, that is the leading contribution to the symmetry resolved entanglement is independent of the symmetry sector.

Growth of entanglement entropy under local projective measurements

Coppola M., Tirrito E., Karevski D., Nonequilibrium 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 an abrupt change in the scaling law of the bipartite entanglement entropy, thus suggesting the existence of different nonequilibrium regimes. However, our understanding of how these regimes appear and whether they survive in the thermodynamic limit is much less established. Here we investigate these questions on a one-dimensional quadratic fermionic model: this allows us to reach system sizes relevant in the thermodynamic sense. We show that local projective measurements induce a qualitative modification of the time growth of the entanglement entropy which changes from linear to logarithmic. However, in the stationary regime, the logarithmic behavior of the entanglement entropy does not survive in the thermodynamic limit and, for any finite value of the measurement rate, we numerically show the existence of a single area-law phase for the entanglement entropy. Finally, exploiting the quasiparticle picture, we further support our results by analyzing the fluctuations of the stationary entanglement entropy and its scaling behavior.

Heat rectification through single and coupled quantum dots

Tesser L., Bhandari B., Erdman P.A., Paladino E., We study heat rectification through quantum dots in the Coulomb blockade regime using a master equation approach. We consider both cases of two-terminal and four-terminal devices. In the two-terminal configuration, we analyze the case of a single quantum dot with either a doubly-degenerate level or two non-degenerate levels. In the sequential tunneling regime we analyze the behaviour of heat currents and rectification as functions of the position of the energy levels and of the temperature bias. In particular, we derive an upper bound for rectification in the closed-circuit setup with the doubly-degenerate level. We also prove the absence of a bound for the case of two non-degenerate levels and identify the ideal system parameters to achieve nearly perfect rectification. The second part of the paper deals with the effect of second-order cotunneling contributions, including both elastic and inelastic processes. In all cases we find that there exists ranges of values of parameters (such as the levels' position) where rectification is enhanced by cotunneling. In particular, in the doubly-degenerate level case we find that cotunneling corrections can enhance rectification when they reduce the magnitude of the heat currents. For the four-terminal configuration, we analyze the non-local situation of two Coulomb-coupled quantum dots, each connected to two terminals: the temperature bias is applied to the two terminals connected to one quantum dot, while the heat currents of interest are the ones flowing in the other quantum dot. Remarkably, in this situation we find that non-local rectification can be perfect as a consequence of the fact that the heat currents vanish for properly tuned parameters.

H→0 limit of the entanglement entropy

Entangled quantum states share properties that do not have classical analogs; in particular, they show correlations that can violate Bell inequalities. It is, therefore, an interesting question to see what happens to entanglement measures - such as the entanglement entropy for a pure state - taking the semiclassical limit, where the naive expectation is that they may become singular or zero. This conclusion is, however, incorrect. In this paper, we determine the ℏ→0 limit of the bipartite entanglement entropy for a one-dimensional system of N quantum particles in an external potential and we explicitly show that this limit is finite. Moreover, if the particles are fermionic, we show that the ℏ→0 limit of the bipartite entanglement entropy coincides with the Shannon entropy of N bits.

Taking the temperature of a pure quantum state

Mitchison M.T., Purkayastha A., Brenes M., Temperature is a deceptively simple concept that still raises deep questions at the forefront of quantum physics research. The observation of thermalization in completely isolated quantum systems, such as cold-atom quantum simulators, implies that a temperature can be assigned even to individual, pure quantum states. Here, we propose a scheme to measure the temperature of such pure states through quantum interference. Our proposal involves interferometry of an auxiliary qubit probe, which is prepared in a superposition state and subsequently decoheres due to weak coupling with a closed, thermalized many-body system. Using only a few basic assumptions about chaotic quantum systems, namely, the eigenstate thermalization hypothesis and the emergence of hydrodynamics at long times, we show that the qubit undergoes pure exponential decoherence at a rate that depends on the temperature of its surroundings. We verify our predictions by numerical experiments on a quantum spin chain that thermalizes after absorbing energy from a periodic drive. Our Letter provides a general method to measure the temperature of isolated, strongly interacting systems under minimal assumptions.