Global Phase Diagram of a Spin-Orbital Kondo Impurity Model and the Suppression of Fermi-Liquid Scale.

Many correlated metallic materials are described by Landau Fermi-liquid theory at low energies, but for Hund metals the Fermi-liquid coherence scale T_{FL} is found to be surprisingly small. In this Letter, we study the simplest impurity model relevant for Hund metals, the three-channel spin-orbital Kondo model, using the numerical renormalization group (NRG) method and compute its global phase diagram. In this framework, T_{FL} becomes arbitrarily small close to two new quantum critical points that we identify by tuning the spin or spin-orbital Kondo couplings into the ferromagnetic regimes. We find quantum phase transitions to a singular Fermi-liquid or a novel non-Fermi-liquid phase. The new non-Fermi-liquid phase shows frustrated behavior involving alternating overscreenings in spin and orbital sectors, with universal power laws in the spin (ω^{-1/5}), orbital (ω^{1/5}) and spin-orbital (ω^{1}) dynamical susceptibilities. These power laws, and the NRG eigenlevel spectra, can be fully understood using conformal field theory arguments, which also clarify the nature of the non-Fermi-liquid phase.

Detecting Kondo Entanglement by Electron Conductance.

Quantum entanglement between an impurity spin and electrons nearby is a key property of the single-channel Kondo effects. We show that the entanglement can be detected by measuring electron conductance through a double quantum dot in an orbital Kondo regime. We derive a relation between the entanglement and the conductance, when the SU(2) spin symmetry of the regime is weakly broken. The relation reflects the universal form of many-body states near the Kondo fixed point. Using it, the spatial distribution of the entanglement-hence, the Kondo cloud-can be detected, with breaking of the symmetry spatially nonuniformly by electrical means.

Nonlocal Entanglement of 1D Thermal States Induced by Fermion Exchange Statistics.

When two identical fermions exchange their positions, their wave function gains a phase factor of -1. We show that this distance-independent effect can induce nonlocal entanglement in one-dimensional (1D) electron systems having Majorana fermions at the ends. It occurs in the system bulk and has a nontrivial temperature dependence. In a system having a single Majorana fermion at each end, the nonlocal entanglement has a Bell-state form at zero temperature and decays as the temperature increases, vanishing suddenly at a certain finite temperature. In a system having two Majorana fermions at each end, it is in a cluster-state form and its nonlocality is more noticeable at a finite temperature. By contrast, the thermal states of corresponding 1D spins do not have nonlocal entanglement.

Macroscopic quantum entanglement of a Kondo cloud at finite temperature.

We propose a variational approach for computing the macroscopic entanglement in a many-body mixed state, based on entanglement witness operators, and compute the entanglement of formation (EoF), a mixed-state generalization of the entanglement entropy, in single- and two-channel Kondo systems at finite temperature. The thermal suppression of the EoF obeys power-law scaling at low temperature. The scaling exponent is halved from the single- to the two-channel system, which is attributed, using a bosonization method, to the non-Fermi liquid behavior of a Majorana fermion, a "half" of a complex fermion, emerging in the two-channel system. Moreover, the EoF characterizes the size and power-law tail of the Kondo screening cloud of the single-channel system.

Anisotropic charge Kondo effect in a triple quantum dot.

We predict that an anisotropic charge Kondo effect appears in a triple quantum dot, when the system has twofold degenerate ground states of (1,1,0) and (0,0,1) charge configurations. Using bosonization and refermionization methods, we find that at low temperature the system has the two different phases of massive charge fluctuations between the two charge configurations and vanishing fluctuations, which are equivalent with the Kondo-screened and ferromagnetic phases of the anisotropic Kondo model, respectively. The phase transition is identifiable by electron conductance measurement, offering the possibility of experimentally exploring the anisotropic Kondo model. Our charge Kondo effect has a similar origin to that in a negative-U Anderson impurity.

How to directly measure a Kondo cloud's length.

We propose a method to directly measure, by electrical means, the Kondo screening cloud formed by an Anderson impurity coupled to semi-infinite quantum wires, on which an electrostatic gate voltage is applied at distance L from the impurity. We show that the Kondo cloud, and hence the Kondo temperature and the electron conductance through the impurity, are affected by the gate voltage, as L decreases below the Kondo cloud length. Based on this behavior, the cloud length can be experimentally identified by changing L with a keyboard type of gate voltage or tuning the coupling strength between the impurity and the wires.

Construction of an optimal witness for unknown two-qubit entanglement.

Whether entanglement in a state can be detected, distilled, and quantified without full state reconstruction is a fundamental open problem. We demonstrate a new scheme encompassing these three tasks for arbitrary two-qubit entanglement, by constructing the optimal entanglement witness for polarization-entangled mixed-state photon pairs without full state reconstruction. With better efficiency than quantum state tomography, the entanglement is maximally distilled by newly developed tunable polarization filters and quantified by the expectation value of the witness, which equals the concurrence. This scheme is extendible to multiqubit Greenberger-Horne-Zeilinger entanglement.