Correlations at PT-Symmetric Quantum Critical Point.

We consider a PT-symmetric Fermi gas with an exceptional point, representing the critical point between PT-symmetric and symmetry broken phases. The low energy spectrum remains linear in momentum and is identical to that of a Hermitian Fermi gas. The fermionic Green's function decays in a power law fashion for large distances, as expected from gapless excitations, although the exponent is reduced from -1 due to the quantum Zeno effect. In spite of the gapless nature of the excitations, the ground state entanglement entropy saturates to a finite value, independent of the subsystem size due to the non-Hermitian correlation length intrinsic to the system. Attractive or repulsive interaction drives the system into the PT-symmetry broken regime or opens up a gap and protects PT symmetry, respectively. Our results challenge the concept of universality in non-Hermitian systems, where quantum criticality can be masked due to non-Hermiticity.

Kubo Formula for Non-Hermitian Systems and Tachyon Optical Conductivity.

Linear response theory plays a prominent role in various fields of physics and provides us with extensive information about the thermodynamics and dynamics of quantum and classical systems. Here we develop a general theory for the linear response in non-Hermitian systems with nonunitary dynamics and derive a modified Kubo formula for the generalized susceptibility for an arbitrary (Hermitian and non-Hermitian) system and perturbation. We use this to evaluate the dynamical response of a non-Hermitian, one-dimensional Dirac model with imaginary and real masses, perturbed by a time-dependent electric field. The model has a rich phase diagram, and in particular, features a tachyon phase, where excitations travel faster than an effective speed of light. Surprisingly, we find that the dc conductivity of tachyons is finite, and the optical sum rule is exactly satisfied for all masses. Our results highlight the peculiar properties of the Kubo formula for non-Hermitian systems and are applicable for a large variety of settings.

Kondo Cloud in a Superconductor.

Magnetic impurities embedded in a metal are screened by the Kondo effect, signaled by the formation of an extended correlation cloud, the so-called Kondo or screening cloud. In a superconductor, the Kondo state turns into subgap Yu-Shiba-Rusinov states, and a quantum phase transition occurs between screened and unscreened phases once the superconducting energy gap Δ exceeds sufficiently the Kondo temperature, T_{K}. Here we show that, although the Kondo state does not form in the unscreened phase, the Kondo cloud does exist in both quantum phases. However, while screening is complete in the screened phase, it is only partial in the unscreened phase. Compensation, a quantity introduced to characterize the integrity of the cloud, is universal, and shown to be related to the magnetic impurities' g factor, monitored experimentally by bias spectroscopy.

Topologically Protected Correlated End Spin Formation in Carbon Nanotubes.

For most chiralities, semiconducting nanotubes display topologically protected end states of multiple degeneracies. We demonstrate using density matrix renormalization group based quantum chemistry tools that the presence of Coulomb interactions induces the formation of robust end spins. These are the close analogs of ferromagnetic edge states emerging in graphene nanoribbons. The interaction between the two ends is sensitive to the length of the nanotube, its dielectric constant, and the size of the end spins: for S=1/2 end spins, their interaction is antiferromagnetic, while for S>1/2, it changes from antiferromagnetic to ferromagnetic as the nanotube length increases. The interaction between end spins can be controlled by changing the dielectric constant of the environment, thereby providing a possible platform for two-spin quantum manipulations.

Dissipation-Induced Luttinger Liquid Correlations in a One-Dimensional Fermi Gas.

We study a one-dimensional Fermi gas in the presence of dissipative coupling to environment through the Lindblad equation. The dissipation involves energy exchange with the environment and favours the relaxation of electrons to excitations. After switching on the dissipation, the system approaches a steady state, which is described by a generalized Gibbs ensemble. The fermionic single particle density matrix resembles deceivingly to that in a hermitian interaction quench. It decays inversely with the distance for short times due to the fermionic correlations in the initial state, which changes into a noninteger power law decay for late times, representing dissipation-induced Luttinger liquid behavior. However, the crossover between the two regions occurs due to dissipation-induced damping, and is unrelated to the propagation of excitations. The velocity of information spreading is set by the dissipative coupling, and differs significantly from the original sound velocity. The thermodynamic entropy grows as -t ln t initially, and saturates to an extensive value. Our results can be tested experimentally in one-dimensional Dirac systems.

Quantum Quench in PT-Symmetric Luttinger Liquid.

A Luttinger liquid (LL) describes low energy excitations of many interacting one dimensional systems, and exhibits universal response both in and out of equilibrium. We analyze its behavior in the non-Hermitian realm after quantum quenching to a PT-symmetric LL by focusing on the fermionic single particle density matrix. For short times, we demonstrate the emergence of unique phenomena, characteristic to non-Hermitian systems, that correlations propagate faster than the conventional maximal speed, known as the Lieb-Robinson bound. These emergent supersonic modes travel with velocities that are multiples of the conventional light cone velocity. This behavior is argued to be generic for correlators in non-Hermitian systems. In the long time limit, we find typical LL behavior, extending the LL universality to the nonequilibrium, non-Hermitian case. Our analytical results are benchmarked numerically and indicate that the dispersal of quantum information is much faster in non-Hermitian systems.

Large spatial extension of the zero-energy Yu-Shiba-Rusinov state in a magnetic field.

Various promising qubit concepts have been put forward recently based on engineered superconductor subgap states like Andreev bound states, Majorana zero modes or the Yu-Shiba-Rusinov (Shiba) states. The coupling of these subgap states via a superconductor strongly depends on their spatial extension and is an essential next step for future quantum technologies. Here we investigate the spatial extension of a Shiba state in a semiconductor quantum dot coupled to a superconductor. With detailed transport measurements and numerical renormalization group calculations we find a remarkable more than 50 nm extension of the zero energy Shiba state, much larger than the one observed in very recent scanning tunneling microscopy measurements. Moreover, we demonstrate that its spatial extension increases substantially in a magnetic field.

Vaporization Dynamics of a Dissipative Quantum Liquid.

We investigate the stability of a Luttinger liquid, upon suddenly coupling it to a dissipative environment. Within the Lindblad equation, the environment couples to local currents and heats the quantum liquid up to infinite temperatures. The single particle density matrix reveals the fractionalization of fermionic excitations in the spatial correlations by retaining the initial noninteger power law exponents, accompanied by an exponential decay in time with an interaction dependent rate. The spectrum of the time evolved density matrix is gapped, which collapses gradually as -ln(t). The von Neumann entropy crosses over from the early time -tln(t) behavior to ln(t) growth for late times. The early time dynamics is captured numerically by performing simulations on spinless interacting fermions, using several numerically exact methods. Our results could be tested experimentally in bosonic Luttinger liquids.

Quantum Criticality and Formation of a Singular Fermi Liquid in the Attractive SU(N>2) Anderson Model.

While much is known about repulsive quantum impurity models, significantly less attention has been devoted to their attractive counterparts. This motivated us to study the attractive SU(N) Anderson impurity model. While for the repulsive case the phase diagram features mild N dependence and the ground state is always a Fermi liquid, in the attractive case a Kosterlitz-Thouless charge localization phase transition is revealed for N>2. Beyond a critical value of attractive interaction, an abrupt jump appears in the number of particles at the impurity site, and a singular Fermi liquid state emerges, where the scattering of quasiparticles is found to exhibit power law behavior with fractional power. The capacity diverges exponentially at the quantum critical point, signaling the Kosterlitz-Thouless transition.

Statistics and Dynamics of the Center-of-Mass Coordinate in a Quantum Liquid.

Motivated by recent experiments in ultracold gases, we focus on the properties of the center-of-mass coordinate of an interacting one-dimensional Fermi gas, displaying several distinct phases. While the variance of the center of mass vanishes in insulating phases such as phase-separated and charge density wave phases, it remains finite in the metallic phase, which realizes a Luttinger liquid. By combining numerics with bosonization, we demonstrate that the autocorrelation function of the center-of-mass coordinate is universal throughout the metallic phase. It exhibits persistent oscillations, and its short time dynamics reveal important features of the quantum liquid, such as the Luttinger liquid parameter and the renormalized velocity. The full counting statistics of the center of mass follows a normal distribution already for small systems. Our results apply to nonintegrable systems as well and are within experimental reach for, e.g., carbon nanotubes and cold atomic gases.

Noise of a Chargeless Fermi Liquid.

We construct a Fermi liquid theory to describe transport in a superconductor-quantum dot-normal metal junction close to the singlet-doublet (parity changing) transition of the dot. Though quasiparticles do not have a definite charge in this chargeless Fermi liquid, in the case of particle-hole symmetry, a mapping to the Anderson model unveils a hidden U(1) symmetry and a corresponding pseudocharge. In contrast to other correlated Fermi liquids, the back scattering noise reveals an effective charge equal to the charge of Cooper pairs, e^{*}=2e. In addition, we find a strong suppression of noise when the linear conductance is unitary, even for its nonlinear part.

Hybrid Semiclassical Theory of Quantum Quenches in One-Dimensional Systems.

We develop a hybrid semiclassical method to study the time evolution of one-dimensional quantum systems in and out of equilibrium. Our method handles internal degrees of freedom completely quantum mechanically by a modified time-evolving block decimation method while treating orbital quasiparticle motion classically. We can follow dynamics up to time scales well beyond the reach of standard numerical methods to observe the crossover between preequilibrated and locally phase equilibrated states. As an application, we investigate the quench dynamics and phase fluctuations of a pair of tunnel-coupled one-dimensional Bose condensates. We demonstrate the emergence of soliton-collision-induced phase propagation, soliton-entropy production, and multistep thermalization. Our method can be applied to a wide range of gapped one-dimensional systems.