For many years, the Luttinger liquid theory has served as a useful paradigm for the description of one-dimensional (1D) quantum fluids in the limit of low energies. This theory is based on a linearization of the dispersion relation of the particles constituting the fluid. We review the recent progress in understanding 1D quantum fluids beyond the low-energy limit, where the nonlinearity of the dispersion relation becomes essential. The novel methods which have been developed to tackle such systems combine phenomenology built on the ideas of the Fermi edge singularity and the Fermi liquid theory, perturbation theory in the interaction strength, and new ways of treating finitesize properties of integrable models. These methods can be applied to a wide variety of 1D fluids, from 1D spin liquids to electrons in quantum wires to cold atoms confined by 1D traps. We review existing results for various dynamic correlation functions, in particular the dynamic structure factor and the spectral function. Moreover, we show how a dispersion nonlinearity leads to finite particle lifetimes, and its impact on the transport properties of 1D systems at finite temperatures is discussed. The conventional Luttinger liquid theory is a special limit of the new theory, and we explain the relation between the two.

We evaluate the low-temperature conductance of a weakly interacting one-dimensional helical liquid without axial spin symmetry. The lack of that symmetry allows for inelastic backscattering of a single electron, accompanied by forward scattering of another. This joint effect of weak interactions and potential scattering off impurities results in a temperature-dependent deviation from the quantized conductance, δG ∝ T4. In addition, δG is sensitive to the position of the Fermi level. We determine numerically the parameters entering our generic model for the Bernevig-Hughes-Zhang Hamiltonian of a HgTe/CdTe quantum well in the presence of Rashba spin-orbit coupling.

We study the growth of entanglement entropy in density matrix renormalization group calculations of the real-time quench dynamics of the Anderson impurity model. We find that with appropriate choice of basis, the entropy growth is logarithmic in both the interacting and noninteracting single-impurity models. The logarithmic entropy growth is understood from a noninteracting chain model as a critical behavior separating regimes of linear growth and saturation of entropy, corresponding respectively to an overlapping and gapped energy spectra of the set of bath states. We find that with an appropriate choices of basis (energy-ordered bath orbitals), logarithmic entropy growth is the generic behavior of quenched impurity models. A noninteracting calculation of a double-impurity Anderson model supports the conclusion in the multi-impurity case. The logarithmic growth of entanglement entropy enables studies of quench dynamics to very long times.

We analyze the full counting statistics (FCS) of a single-site quantum dot coupled to a local Holstein phonon for arbitrary transmission and weak electron-phonon coupling. We identify explicitly the contributions due to quasielastic and inelastic transport processes in the cumulant generating function and discuss their influence on the transport properties of the dot. We find that in the low-energy sector, i.e. for bias voltage and phonon frequency much smaller than the dot-electrode contact transparency, the inelastic term causes a sign change in the shot noise correction at certain universal values of the transmission. Furthermore, we show that when the correction to the current due to inelastic processes vanishes, all the odd order cumulants vanish as well.

We consider the dynamic response functions of interacting one dimensional spin-1/2 fermions at arbitrary momenta. We build a nonperturbative zero-temperature theory of the threshold singularities using mobile impurity Hamiltonians. The interaction induced low-energy spin-charge separation and power-law threshold singularities survive away from Fermi points. We express the threshold exponents in terms of the spinon spectrum.PACS numbers: 71.10.PmThe low-energy excitations of interacting spin-1/2 fermions confined to one dimension (1D) is well represented by two collective bosonic modes. These modes are the quantized waves of spin and charge densities. Their spectra are linear; the corresponding velocities, v s and v c , differ from each other. A microscopic consideration [1,2] of the repulsive interaction between spinful fermions leads to v c > v s .The spectra of the collective modes can be probed in a momentum-resolved tunneling [3,4] or in an ARPES [5] or photoemission [6] experiment. In these methods, a spin-1/2 fermion with a given momentum tunnels into or out of the studied system. The tunneling inevitably perturbs each of the two collective modes. For example, in the case of a low-energy particle (k F ≫ k − k F > 0), the small difference k − k F is shared between the excitations of the two modes. The Luttinger liquid (LL) theory predicts [2] that at given k the tunneling probability is singular at energies v s (k−k F ) and v c (k−k F ), corresponding to the entire momentum k − k F given to the "spinon" or "holon" belonging to the spin and charge mode, respectively. The exponents of the two power-law singularities depend on a single number, the LL parameter K c for the charge mode. The two sharp peaks in the momentumresolved tunneling probability at energies associated with excitation of the two modes, ω = v s,c · (k − k F ), are the hallmark of the spin-charge separation in the LL.The momentum-resolved tunneling rate is proportional to the fermionic spectral functionRecently, considerable progress was achieved in the analytical theory of dynamic responses of a 1D system away from the Fermi points for spinless fermions [7][8][9][10][11]. The developed methods map the 1D dynamic response problem near the edge of support onto the "mobile quantum impurity" effective Hamiltonian [12]. For spinless fermions in the weak-interaction limit, one may consider the generic spectrum of free fermions exactly, while treating their interaction perturbatively [7,8]. For example, at |k| < k F the threshold coincides with the spectrum of a hole, which can be thought of as a mobile quantum impurity. Because of the interactions, it "shakes up" the fermions in the vicinity of Fermi points, leading to the orthogonality catastrophe and to the power-law behavior of A(k, ω) at the threshold [7,8]. The perturbation theory allows one to identify the quantum numbers of the impurity and to match the phenomenological theory of threshold exponents [10] valid at any interaction strength with the weak-interaction limit.In this Letter we bui...

The interplay between bulk spin-orbit coupling and electron-electron interactions produces umklapp scattering in the helical edge states of a two-dimensional topological insulator. If the chemical potential is at the Dirac point, umklapp scattering can open a gap in the edge state spectrum even if the system is time-reversal invariant. We determine the zero-energy bound states at the interfaces between a section of a helical liquid which is gapped out by the superconducting proximity effect and a section gapped out by umklapp scattering. We show that these interfaces pin charges which are multiples of e/2, giving rise to a Josephson current with 8π periodicity. Moreover, the bound states, which are protected by time-reversal symmetry, are fourfold degenerate and can be described as Z 4 parafermions. We determine their braiding statistics and show how braiding can be implemented in topological insulator systems. Introduction. The one-dimensional edge states of timereversal (TR) invariant two-dimensional (2D) topological insulators [1,2] are helical: electrons with opposite spins propagate in opposite directions [3,4]. This property has several interesting consequences which are currently attracting the attention of theorists and experimentalists alike. On the one hand, Kramers theorem forbids elastic backscattering, so the edge states remain gapless even in the presence of disorder and weak interactions [5][6][7]. On the other hand, inducing superconductivity in helical or quasihelical [8][9][10][11][12] systems has been predicted to give rise to exotic zeroenergy bound states such as Majorana fermions [13][14][15][16][17] and parafermions [18,19], which could have important applications in topological quantum computation [20,21].

We analyze the nonequilibrium transport properties of a quantum dot with a harmonic degree of freedom (Holstein phonon) coupled to metallic leads, and derive its full counting statistics (FCS). Using the Lang-Firsov (polaron) transformation, we construct a diagrammatic scheme to calculate the cumulant generating function. The electron-phonon interaction is taken into account exactly, and the employed approximation represents a summation of a diagram subset with respect to the tunneling amplitude. By comparison to Monte Carlo data the formalism is shown to capture the basic properties of the strong coupling regime.PACS numbers: 73.63. Kv, 72.10.Pm, In the past decades, the miniaturization of electric circuits has crossed the divide between the microscale and the nanoscale. Molecular and atomic electronics are no longer mere theoretical concepts. A wide variety of experimental setups has been developed for the exploration of the electronic and mechanical properties of nanometersized objects like carbon nanotubes, C 60 -fullerenes and complex molecules. It has become possible to connect these samples to mesoscopic environments and to investigate their transport properties. 1-11The electronic structure of these nanosized objects is best captured by the concept of a quantum dot, i.e., by an arrangement of energy levels which correspond to the molecular orbitals of the device. One of the most prominent and fundamental models for the theoretical description of quantum dots is the Anderson impurity model, which accounts for the tunnel coupling to noninteracting electron reservoirs and for the local Coulomb interaction between the electrons populating the quantum dot.12 In the case of contacted molecules, where charging is often accompanied by structural deformations of the molecule itself, however, this model is often an oversimplification. For a more realistic description, an explicit consideration of the coupling to vibrational degrees of freedom is necessary. This is accomplished by the Anderson-Holstein model (AHM). 13,14In its full extent, the AHM captures a huge variety of physical phenomena. Its physical properties depend on several energy scales, e.g., temperature, charging energy, hybridization energy, level spacing and electron-phonon interaction strength. These define many interesting and physically distinct regimes in parameter space. In this paper we are mainly interested in the effect of electronphonon interactions on the charge transport through a contacted molecule. The model can therefore be simplified to contain a single electronic level (thus neglecting the spin degree of freedom as well as the charging energy) linearly coupled to a local (Holstein) phonon, i.e., a bosonic oscillator degree of freedom with a single frequency. Even this simplified model, which in the following will be referred to as AHM, offers rich physics. Whereas the conductance and the nonlinear I − Vcharacteristic of such a system can be approached by a number of methods, such as diagrammatic Monte Carlo schemes, 15 rate equations...

We establish a theoretical method which goes beyond the weak-coupling and Markovian approximations while remaining intuitive, using a quantum master equation in a larger Hilbert space. The method is applicable to all impurity Hamiltonians tunnel coupled to one (or multiple) baths of free fermions. The accuracy of the method is in principle not limited by the system-bath coupling strength, but rather by the shape of the spectral density and it is especially suited to study situations far away from the wide-band limit. In analogy to the bosonic case, we call it the fermionic reaction coordinate mapping. As an application, we consider a thermoelectric device made of two Coulomb-coupled quantum dots. We pay particular attention to the regime where this device operates as an autonomous Maxwell demon shoveling electrons against the voltage bias thanks to information. Contrary to previous studies, we do not rely on a Markovian weak-coupling description. Our numerical findings reveal that in the regime of strong coupling and non-Markovianity, the Maxwell demon is often doomed to disappear except in a narrow parameter regime of small power output.