From Kondo effect to weak-link regime in quantum spin-12 spin chains

Giuliano D., Rossini D., We analyze the crossover from Kondo to weak-link regime by means of a model of tunable bond impurities in the middle of a spin-1/2 XXZ Heisenberg chain. We study the Kondo screening cloud and estimate the Kondo length by combining perturbative renormalization group approach with the exact numerical calculation of the integrated real-space spin-spin correlation functions. We show that, when the spin impurity is symmetrically coupled to the two parts of the chain with realistic values of the Kondo coupling strengths and spin-parity symmetry is preserved, the Kondo length takes values within the reach of nowadays experimental technology in ultracold-atom setups. In the case of nonsymmetric Kondo couplings and/or spin parity broken by a nonzero magnetic field applied to the impurity, we discuss how Kondo screening redistributes among the chain as a function of the asymmetry in the couplings and map out the shrinking of the Kondo length when the magnetic field induces a crossover from Kondo impurity to weak-link physics.

Universal off-diagonal long-range-order behavior for a trapped Tonks-Girardeau gas

Colcelli A., Viti J., The scaling of the largest eigenvalue λ0 of the one-body density matrix of a system with respect to its particle number N defines an exponent C and a coefficient B via the asymptotic relation λ0∼BNC. The case C=1 corresponds to off-diagonal long-range order. For a one-dimensional homogeneous Tonks-Girardeau gas, a well-known result also confirmed by bosonization gives instead C=1/2. Here we investigate the inhomogeneous case, initially addressing the behavior of C in the presence of a general external trapping potential V. We argue that the value C=1/2 characterizes the hard-core system independently of the nature of the potential V. We then define the exponents γ and β, which describe the scaling of the peak of the momentum distribution with N and the natural orbital corresponding to λ0, respectively, and we derive the scaling relation γ+2β=C. Taking as a specific case the power-law potential V(x)2n, we give analytical formulas for γ and β as functions of n. Analytical predictions for the coefficient B are also obtained. These formulas are derived by exploiting a recent field theoretical formulation and checked against numerical results. The agreement is excellent.

Selective insulators and anomalous responses in three-component fermionic gases with broken SU(3) symmetry

Del Re L., We study a three-component fermionic fluid in an optical lattice in a regime of intermediate to strong interactions allowing for optical processes connecting the different components, similar to those used to create artificial gauge fields. Using dynamical mean-field theory, we show that the combined effect of interactions and the external field induces a variety of anomalous phases in which different components of the fermionic fluid display qualitative differences, i.e., the physics is flavor selective. Remarkably, the different components can display huge differences in the correlation effects, measured by their effective masses and nonmonotonic behavior of their occupation number as a function of the chemical potential, signaling a sort of selective instability of the overall stable quantum fluid.

Projective quantum Monte Carlo simulations guided by unrestricted neural network states

Inack E., We investigate the use of variational wave functions that mimic stochastic recurrent neural networks, specifically, unrestricted Boltzmann machines, as guiding functions in projective quantum Monte Carlo (PQMC) simulations of quantum spin models. As a preliminary step, we investigate the accuracy of such unrestricted neural network states as variational Ansätze for the ground state of the ferromagnetic quantum Ising chain. We find that by optimizing just three variational parameters, independently on the system size, accurate ground-state energies are obtained, comparable to those previously obtained using restricted Boltzmann machines with few variational parameters per spin. Chiefly, we show that if one uses optimized unrestricted neural network states as guiding functions for importance sampling, the efficiency of the PQMC algorithms is greatly enhanced, drastically reducing the most relevant systematic bias, namely, the one due to the finite random-walker population. The scaling of the computational cost with the system size changes from the exponential scaling characteristic of PQMC simulations performed without importance sampling, to a polynomial scaling, apparently even at the ferromagnetic quantum critical point. The important role of the protocol chosen to sample hidden-spin configurations, in particular at the critical point, is analyzed. We discuss the implications of these findings for what concerns the problem of simulating adiabatic quantum optimization using stochastic algorithms on classical computers.

Emergent D6 symmetry in fully relaxed magic-angle twisted bilayer graphene

Angeli M., Mandelli D., Valli A., Amaricci A., We present a tight-binding calculation of a twisted bilayer graphene at magic angle θ∼1.08, allowing for full, in- and out-of-plane, relaxation of the atomic positions. The resulting band structure displays, as usual, four narrow minibands around the neutrality point, well separated from all other bands after the lattice relaxation. A thorough analysis of the miniband Bloch functions reveals an emergent D6 symmetry, despite the lack of any manifest point-group symmetry in the relaxed lattice. The Bloch functions at the Γ point are degenerate in pairs, reflecting the so-called valley degeneracy. Moreover, each of them is invariant under C3z, i.e., transforming like a one-dimensional, in-plane symmetric irreducible representation of an "emergent" D6 group. Out of plane, the lower doublet is even under C2x, while the upper doublet is odd, which implies that at least eight Wannier orbitals, two s-like and two pz-like ones for each of the supercell sublattices AB and BA, are necessary but probably not sufficient to describe the four minibands. This unexpected one-electron complexity is likely to play an important role in the still unexplained metal-insulator-superconductor phenomenology of this system.

Phase diagram of the dissipative quantum Ising model on a square lattice

Jin J., Biella A., Viyuela O., Ciuti C., The competition between interactions and dissipative processes in a quantum many-body system can drive phase transitions of different order. Exploiting a combination of cluster methods and quantum trajectories, we show how the systematic inclusion of (classical and quantum) nonlocal correlations at increasing distances is crucial to determine the structure of the phase diagram, as well as the nature of the transitions in strongly interacting spin systems. In practice, we focus on the paradigmatic dissipative quantum Ising model: In contrast to the nondissipative case, its phase diagram is still a matter of debate in the literature. When dissipation acts along the interaction direction, we predict important quantitative modifications of the position of the first-order transition boundary. In the case of incoherent relaxation in the field direction, our approach confirms the presence of a second-order transition, while does not support the possible existence of multicritical points. Potentially, these results can be tested in up-to-date quantum simulators of Rydberg atoms.

Enhanced performance of a quantum-dot-based nanomotor due to Coulomb interactions

Ludovico M., We study the relation between quantum pumping of charge and the work exchanged with the driving potentials in a strongly interacting ac-driven quantum dot. We work in the large-interaction limit and in the adiabatic pumping regime, and we develop a treatment that combines the time-dependent slave-boson approximation with linear response in the rate of change in the ac potentials. We find that the time evolution of the system can be described in terms of equilibrium solutions at every time. We analyze the effect of the electronic interactions on the performance of the dot when operating as a quantum motor. The main two effects of the interactions are a shift of the resonance and an enhancement of the efficiency with respect to a noninteracting dot. This is due to the appearance of additional ac parameters accounting for the interactions that increase the pumping of particles while decreasing the conductance.

Landau-Zener transitions and Rabi oscillations in a Cooper-pair box: Beyond two-level models

Parafilo A.V., We investigate quantum interference effects in a superconducting Cooper-pair box by taking into account the possibility of tunneling processes involving one and two Cooper pairs. The quantum dynamics is analyzed in a framework of three-level model. We compute Landau-Zener probabilities for a linear sweep of the gate charge and investigate Rabi oscillations in a periodically driven three-level system under in- and off-resonance conditions. It was shown that the Landau-Zener probabilities reveal two different patterns: "step"- and "beats"-like behaviors associated with the quantum interference effects. Control on these two regimes is provided by the change of the ratio between two characteristic time scales of the problem. We demonstrate through the analysis of a periodically driven three-level system, that if a direct transition between certain pairs of levels is allowed and fine-tuned to a resonance, the problem is mapped to the two-level Rabi model. If the transition between a pair of levels is forbidden, the off-resonance Rabi oscillations involving second order in tunneling processes are predicted. This effect can be observed by measuring a population difference slowly varying in time between the states of the Cooper-pair box characterized by the same parity.

Measuring quantumness: from theory to observability in interferometric setups

Ferro L., Abstract: We investigate the notion of quantumness based on the noncommutativity of the algebra of observables and introduce a measure of quantumness based on the mutual incompatibility of quantum states. We show that such a quantity can be experimentally measured with an interferometric setup and that, when an arbitrary bipartition of a given composite system is introduced, it detects the one-way quantum correlations restricted to one of the two subsystems. We finally show that, by combining only two projective measurements and carrying out the interference procedure, our measure becomes an efficient universal witness of quantum discord and nonclassical correlations. Graphical abstract: [Figure not available: see fulltext.].

Landau-Zener transitions and Rabi oscillations in a Cooper-pair box: Beyond two-level models

Parafilo A., We investigate quantum interference effects in a superconducting Cooper-pair box by taking into account the possibility of tunneling processes involving one and two Cooper pairs. The quantum dynamics is analyzed in a framework of three-level model. We compute Landau-Zener probabilities for a linear sweep of the gate charge and investigate Rabi oscillations in a periodically driven three-level system under in- and off-resonance conditions. It was shown that the Landau-Zener probabilities reveal two different patterns: “step”- and “beats”-like behaviors associated with the quantum interference effects. Control on these two regimes is provided by change of the ratio between two characteristic time scales of the problem. We demonstrate through the analysis of a periodically driven three-level system, that if a direct transition between certain pairs of levels is allowed and fine-tuned to a resonance, the problem is mapped to the two-level Rabi model. If the transition between pair of levels is forbidden, the off-resonance Rabi oscillations involving second order in tunneling processes are predicted. This effect can be observed by measuring a population difference slowly varying in time between the states of the Cooper-pair box characterized by the same parity.

Solution of the sign problem for the half-filled Hubbard-Holstein model

Karakuzu S., Seki K., We show that, by an appropriate choice of auxiliary fields and exact integration of the phonon degrees of freedom, it is possible to define a "sign-free" path integral for the so-called Hubbard-Holstein model at half filling. We use a statistical method, based on an accelerated and efficient Langevin dynamics, for evaluating all relevant correlation functions of the model. Preliminary calculations at U/t=4 and U/t=1, for ω0/t=1, indicate a region around U≃g2ω0 without either antiferromagnetic or charge-density-wave orders that is much wider compared to previous approximate calculations. The elimination of the sign problem in a model without explicit particle-hole symmetry may open different perspectives for strongly correlated models, even away from the purely attractive or particle-hole symmetric cases.

Nontopological parafermions in a one-dimensional fermionic model with even multiplet pairing

Mazza L., Iemini F., We discuss a one-dimensional fermionic model with a generalized ZN even multiplet pairing extending Kitaev Z2 chain. The system shares many features with models believed to host localized edge parafermions, the most prominent being a similar bosonized Hamiltonian and a ZN symmetry enforcing an N-fold degenerate ground state robust to certain disorders. Interestingly, we show that the system supports a pair of parafermions but they are nonlocal instead of being boundary operators. As a result, the degeneracy of the ground state is only partly topological and coexists with spontaneous symmetry breaking by a (two-particle) pairing field. Each symmetry-breaking sector is shown to possess a pair of Majorana edge modes encoding the topological twofold degeneracy. Surrounded by two band insulators, the model exhibits for N=4 the dual of an 8π fractional Josephson effect highlighting the presence of parafermions.

Persistent currents by reservoir engineering

Keck M., Rossini D., We demonstrate that persistent currents can be induced in a quantum system in contact with a structured reservoir, without the need of any applied gauge field. The working principle of the mechanism leading to their presence is based on the extension to the many-body scenario of nonreciprocal Lindblad dynamics, recently put forward by Metelmann and Clerk, Phys. Rev. X 5, 021025 (2015)10.1103/PhysRevX.5.021025: Nonreciprocity can be generated by suitably balancing coherent interactions with their corresponding dissipative version, induced by the coupling to a common structured environment, so as to make the total interactions directional. Specifically, we consider an interacting spin- (or boson-) model in a ring-shaped one-dimensional lattice coupled to an external bath. By employing a combination of cluster mean-field, exact diagonalization, and matrix-product-operator techniques, we show that solely dissipative effects suffice to engineer steady states with a persistent current that survives in the limit of large systems. We also verify the robustness of such current in the presence of additional dissipative or Hamiltonian perturbation terms.

Quantization of the Hall conductivity in the Harper-Hofstadter model

Wauters M., We study the robustness of the quantization of the Hall conductivity in the Harper-Hofstadter model towards the details of the protocol with which a longitudinal uniform driving force Fx(t) is turned on. In the vector potential gauge, through Peierls substitution, this involves the switching on of complex time-dependent hopping amplitudes e-iAx(t) in the ◯ direction such that ∂tAx(t)=Fx(t). The switching on can be sudden, Fx(t)=θ(t)F, where F is the steady driving force, or more generally smooth Fx(t)=f(t/t0)F, where f(t/t0) is such that f(0)=0 and f(1)=1. We investigate how the time-averaged (steady-state) particle current density jy in the ŷ direction deviates from the quantized value jyh/F=n due to the finite value of F and the details of the switching-on protocol. Exploiting the time periodicity of the Hamiltonian Ĥ(t), we use Floquet techniques to study this problem. In this picture the (Kubo) linear response F→0 regime corresponds to the adiabatic limit for Ĥ(t). In the case of a sudden quench jyh/F shows F2 corrections to the perfectly quantized limit. When the switching on is smooth, the result depends on the switch-on time t0: For a fixed t0 we observe a crossover force F∗ between a quadratic regime for FF∗. The crossover F∗ decreases as t0 increases, eventually recovering the topological robustness. These effects are in principle amenable to experimental tests in optical lattice cold atomic systems with synthetic gauge fields.

Dynamical manifestation of the Gibbs paradox after a quantum quench

We study the propagation of entanglement after quantum quenches in the nonintegrable paramagnetic quantum Ising spin chain. Tuning the parameters of the system, we observe a sudden increase in the entanglement production rate, which we show to be related to the appearance of new quasiparticle excitations in the postquench spectrum. We argue that the phenomenon is the nonequilibrium version of the well-known Gibbs paradox related to mixing entropy and demonstrate that its characteristics fit the expectations derived from the quantum resolution of the paradox in systems with a nontrivial quasiparticle spectrum.

Entanglement entropy of two disjoint intervals and the recursion formula for conformal blocks

Ruggiero P., We reconsider the computation of the entanglement entropy of two disjoint intervals in a (1+1) dimensional conformal field theory by conformal block expansion of the 4-point correlation function of twist fields. We show that accurate results may be obtained by taking into account several terms in the operator product expansion of twist fields and by iterating the Zamolodchikov recursion formula for each conformal block. We perform a detailed analysis for the Ising conformal field theory and for the free compactified boson. Each term in the conformal block expansion can be easily analytically continued and so this approach also provides a good approximation for the von Neumann entropy.

Quantum detailed balance conditions and fluctuation relations for thermalizing quantum dynamics

Ramezani M., Quantum detailed balance conditions and quantum fluctuation relations are two important concepts in the dynamics of open quantum systems: both concern how such systems behave when they thermalize because of interaction with an environment. We prove that for thermalizing quantum dynamics the quantum detailed balance conditions yield validity of a quantum fluctuation relation (where only forward-time dynamics is considered). This implies that to have such a quantum fluctuation relation (which in turn enables a precise formulation of the second law of thermodynamics for quantum systems) it suffices to fulfill the quantum detailed balance conditions. We, however, show that the converse is not necessarily true; indeed, there are cases of thermalizing dynamics which feature the quantum fluctuation relation without satisfying detailed balance. We illustrate our results with three examples.

Energy transport in a disordered spin chain with broken U(1) symmetry: Diffusion, subdiffusion, and many-body localization

Schulz M., Taylor S.R., Hooley C.A., We explore the physics of the disordered XYZ spin chain using two complementary numerical techniques: exact diagonalization (ED) on chains of up to 17 spins, and time-evolving block decimation (TEBD) on chains of up to 400 spins. Our principal findings are as follows. First, we verify that the clean XYZ spin chain shows ballistic energy transport for all parameter values that we investigated. Second, for weak disorder there is a stable diffusive region that persists up to a critical disorder strength that depends on the XY anisotropy. Third, for disorder strengths above this critical value, energy transport becomes increasingly subdiffusive. Fourth, the many-body localization transition moves to significantly higher disorder strengths as the XY anisotropy is increased. We discuss these results, and their relation to our current physical picture of subdiffusion in the approach to many-body localization.

Return probability for the Anderson model on the random regular graph

Bera S., De Tomasi G., Khaymovich I.M., We study the return probability for the Anderson model on the random regular graph and give evidence of the existence of two distinct phases: a fully ergodic and nonergodic one. In the ergodic phase, the return probability decays polynomially with time with oscillations, being the attribute of the Wigner-Dyson-like behavior, while in the nonergodic phase the decay follows a stretched exponential decay. We give a phenomenological interpretation of the stretched exponential decay in terms of a classical random walker. Furthermore, comparing typical and mean values of the return probability, we show how to differentiate an ergodic phase from a nonergodic one. We benchmark this method first in two random matrix models, the power-law random banded matrices, and the Rosenzweig-Porter matrices, which host both phases. Second, we apply this method to the Anderson model on the random regular graph to give further evidence of the existence of the two phases.

Full counting statistics of the two-stage Kondo effect

Karki D., We developed a theoretical framework which extends the method of full counting statistics (FCS) from conventional single-channel Kondo screening schemes to a multichannel Kondo paradigm. The developed idea of FCS has been demonstrated considering an example of a two-stage Kondo (2SK) model. We analyzed the charge-transferred statistics in the strong-coupling regime of a 2SK model using a nonequilibrium Keldysh formulation. A bounded value of the Fano factor, 1≤F≤5/3, confirmed the crossover regimes of charge-transferred statistics in the 2SK effect, from Poissonian to super-Poissonian. An innovative way of measuring the transport properties of the 2SK effect, by the independent measurements of charge current and noise, has been proposed.