Friedel oscillation in non-Fermi liquid: lesson from exactly solvable Hatsugai-Kohmoto model.

When non-magnetic impurity immerses in Fermi sea, a regular modulation of charge density around impurity will appear and such phenomena is called Friedel oscillation (FO). Although both Luttinger liquid and Landau Fermi liquid show such characteristic oscillation, FO in generic non-Fermi liquid (NFL) phase is still largely unknown. Here, we show that FO indeed exists in NFL state of an exactly solvable model, i.e. the Hatsugai-Kohmoto model which has been intensively explored in recent years. Combining T-matrix approximation and linear-response-theory, an interesting picture emerges, if two interaction-induced quasi-particles bands in NFL are partially occupied, FO in this situation is determined by a novel structure in momentum space, i.e. the 'average Fermi surface' (average over two quasi-particle Fermi surface), which highlights the inter-band particle-hole excitation. We hope our study here provides a counterintuitive example in which FO with Fermi surface coexists with NFL quasi-particle, and it may be useful to detect hidden 'average Fermi surface' structure in other correlated electron systems.

The Microscopic Origin of Second Harmonic Generation Response: The Spatial Structure of Instantaneous Dipole Moments in Electron Excitation.

A deep understanding on the crucial factors of the enhanced macroscopic second harmonic generation (SHG) in some deep-ultraviolet nonlinear optical (NLO) materials is needed to design new NLO materials. Since an optical process relates to the electron excitation and polarization simultaneously, the instantaneous dipole moments and their structures in excitation should be seriously taken account to seek the principal factor in SHG response. In this work, we study the Ba4 B11 O20 F (BBOF), a NLO material, by using the orbital projection technique. From the projected SHG of our theoretic calculation, we recognize the principal dipole moment of the dominant influence on SHG and the relevant atom groups between which the dipole moment is accommodated. With the conclusion that the dipole moment with the most significant influence on SHG is the one between the oxygen-boron polyhedral anion group and barium cation, we predict that Ba4 Al11 O20 F (BAOF) has a comparable SHG response.

Study the mixed valence problem in asymmetric Anderson model: Fano-Kondo resonance around Fermi level.

We numerically calculate the local density of states (LDOS) in asymmetric Anderson model in mixed valence regime using hierarchical equations of motion approach. Based on the idea that the asymmetric line shape of LDOS around Fermi level stems from the interference between the single particle resonance and the Kondo resonance, we perform a fitting. From the fitting results, we obtain the Kondo temperatures and the Fano factors with changing the single particle energy. The tendency of Kondo temperature agrees with the previous analytic expressions and the Fano factors are in an expected variation of Fano resonance. Our study shows that the Fano-Kondo resonance can reasonably explain the asymmetric line shape of the LDOS around the Fermi level.

Erratum: Retrieving Ideal Precision in Noisy Quantum Optical Metrology [Phys. Rev. Lett. 123, 040402 (2019)].

This corrects the article DOI: 10.1103/PhysRevLett.123.040402.

Quantum Phases in a Quantum Rabi Triangle.

The interplay of interactions, symmetries, and gauge fields usually leads to intriguing quantum many-body phases. To explore the nature of emerging phases, we study a quantum Rabi triangle system as an elementary building block for synthesizing an artificial magnetic field. We develop an analytical approach to study the rich phase diagram and the associated quantum criticality. Of particular interest is the emergence of a chiral-coherent phase, which breaks both the Z_{2} and the chiral symmetry. In this chiral phase, photons flow unidirectionally and the chirality can be tuned by the artificial gauge field, exhibiting a signature of broken time-reversal symmetry. The finite-frequency scaling analysis further confirms the associated phase transition to be in the universality class of the Dicke model. This model can simulate a broad range of physical phenomena of light-matter coupling systems, and may have an application in future developments of various quantum information technologies.

Retrieving Ideal Precision in Noisy Quantum Optical Metrology.

Quantum metrology employs quantum effects to attain a measurement precision surpassing the limit achievable in classical physics. However, it was previously found that the precision returns the shot-noise limit (SNL) from the ideal Zeno limit (ZL) due to the photon loss in quantum metrology based on Mech-Zehnder interferometry. Here, we find that not only can the SNL be beaten, but also the ZL can be asymptotically recovered in a long-encoding-time condition when the photon dissipation is exactly studied in its inherent non-Markovian manner. Our analysis reveals that it is due to the formation of a bound state of the photonic system and its dissipative noise. Highlighting the microscopic mechanism of the dissipative noise on the quantum optical metrology, our result supplies a guideline to realize the ultrasensitive measurement in practice by forming the bound state in the setting of reservoir engineering.

Tunable giant magnetoresistance in a single-molecule junction.

Controlling electronic transport through a single-molecule junction is crucial for molecular electronics or spintronics. In magnetic molecular devices, the spin degree-of-freedom can be used to this end since the magnetic properties of the magnetic ion centers fundamentally impact the transport through the molecules. Here we demonstrate that the electron pathway in a single-molecule device can be selected between two molecular orbitals by varying a magnetic field, giving rise to a tunable anisotropic magnetoresistance up to 93%. The unique tunability of the electron pathways is due to the magnetic reorientation of the transition metal center, resulting in a re-hybridization of molecular orbitals. We obtain the tunneling electron pathways by Kondo effect, which manifests either as a peak or a dip line shape. The energy changes of these spin-reorientations are remarkably low and less than one millielectronvolt. The large tunable anisotropic magnetoresistance could be used to control electronic transport in molecular spintronics.

Long-range overlapping of Kondo clouds in open triple quantum dots.

We study the phenomena of overlapping of Kondo clouds in an open triple quantum dots (OTQDs) system by using the dissipaton equation of motion (DEOM) theory. Motivated by the long-rang interaction of the TQDs system demonstrated in Cheng et al (2017 Phys. Rev. B 95 155417), we present a comprehensive picture of the long-range overlapping behavior of Kondo clouds via investigation of the spectral functions, spin-spin correlation, dot occupancies and susceptibility. For the configuration [Formula: see text], a conduction electron peak occurs in the spectral function of intermediate QD in the Kondo regime. This peak results from the overlapping of the two Kondo clouds forming from between the two peripheral QDs and leads, enhances with decreasing temperature and increasing dot-lead coupling. Both the spin-spin correlations between the two adjacent QDs and the two peripheral QDs own negative values. It also confirms the physical picture of the overlapping between left and right Kondo clouds via the intermediate QD. To understand the physical insight, we examine also the electron occupacies and the spectral functions, with their dependence on the temperature and dot-lead coupling. In addition, a distinct nonmonotonic behavior of the susceptibility associated with the Kondo clouds is characterized.

[Formula: see text] classification for a novel antiferromagnetic topological insulating phase in three-dimensional topological Kondo insulator.

Antiferromagnetic topological insulator (AFTI) is a topological matter that breaks time-reversal symmetry. Since its proposal, explorations of AFTI in strong-correlated systems are still lacking. In this paper, we show for the first time that a novel AFTI phase can be realized in three-dimensional topological Kondo insulator (TKI). In a wide parameter region, the ground states of TKI undergo a second-order transition to antiferromagnetic insulating phases which conserve a combined symmetry of time reversal and a lattice translation, allowing us to derive a [Formula: see text]-classification formula for these states. By calculating the [Formula: see text] index, the antiferromagnetic insulating states are classified into AFTI or non-topological antiferromagnetic insulator (nAFI) in different parameter regions. On the antiferromagnetic surfaces in AFTI, we find topologically protected gapless Dirac cones inside the bulk gap, leading to metallic Fermi rings exhibiting helical spin texture with weak spin-momentum locking. Depending on model parameters, the magnetic transitions take place either between AFTI and strong topological insulator, or between nAFI and weak topological insulator. By varying some model parameters, we find a topological transition between AFTI and nAFI, driving by closing of bulk gap. Our work may account for the pressure-induced magnetism in TKI compound SmB6, and helps to explore richer AFTI phases in heavy-fermion systems as well as in other strong-correlated systems.

Universal Scaling and Critical Exponents of the Anisotropic Quantum Rabi Model.

We investigate the quantum phase transition of the anisotropic quantum Rabi model, in which the rotating and counterrotating terms are allowed to have different coupling strengths. The model interpolates between two known limits with distinct universal properties. Through a combination of analytic and numerical approaches, we extract the phase diagram, scaling functions, and critical exponents, which determine the universality class at finite anisotropy (identical to the isotropic limit). We also reveal other interesting features, including a superradiance-induced freezing of the effective mass and discontinuous scaling functions in the Jaynes-Cummings limit. Our findings are extended to the few-body quantum phase transitions with N>1 spins, where we expose the same effective parameters, scaling properties, and phase diagram. Thus, a stronger form of universality is established, valid from N=1 up to the thermodynamic limit.

Magnetization jump in one dimensional J - Q 2 model with anisotropic exchange.

We investigate the adiabatic magnetization process of the one-dimensional J - Q 2 model with XXZ anisotropy g in an external magnetic field h by using density matrix renormalization group (DMRG) method. According to the characteristic of the magnetization curves, we draw a magnetization phase diagram consisting of four phases. For a fixed nonzero pair coupling Q, (i) when g < -1, the ground state is always ferromagnetic in spite of h; (ii) when g > -1 but still small, the whole magnetization curve is continuous and smooth; (iii) if further increasing g, there is a macroscopic magnetization jump from partially- to fully-polarized state; (iv) for a sufficiently large g, the magnetization jump is from non- to fully-polarized state. By examining the energy per magnon and the correlation function, we find that the origin of the magnetization jump is the condensation of magnons and the formation of magnetic domains. We also demonstrate that while the experienced states are Heisenberg-like without long-range order, all the jumped-over states have antiferromagnetic or Néel long-range orders, or their mixing.

Corrected Kondo temperature beyond the conventional Kondo scaling limit.

In the Kondo systems such as the magnetic impurity screened by the conduction electrons in a metal host, as well as the quantum dots connected by the leads, the low energy behaviors have universal dependence on the [Formula: see text] or [Formula: see text], where [Formula: see text] is the conventional Kondo temperature. However, it was shown that this scaling behavior is only valid at low-energy; this is called the Kondo scaling limit. Here we explore the extention of the scaling parameter range by introducing the corrected Kondo temperature T K, which may depend on the temperature and bias, as well as the other external parameters. We define the corrected Kondo temperature by scaling the local density of states near the Fermi level, obtained by accurate hierarchy of equations of motion approach at finite temperature and finite bias, and thus obtain a phenomenological expression of the corrected Kondo temperature. By using the corrected Kondo temperature as a characteristic energy scale, the conductance of the quantum dot can be well scaled in a wide parameter range, even two orders beyond the conventional scaling parameter range. Our work indicates that the Kondo scaling, although dominated by the conventional Kondo temperature in the low-energy of the Kondo system, could be extended to a higher energy regime, which is useful for analyzing the physics of the Kondo transport in non-equilibrium or high temperature cases.

Thermoelectric unipolar spin battery in a suspended carbon nanotube.

A quantum dot formed in a suspended carbon nanotube exposed to an external magnetic field is predicted to act as a thermoelectric unipolar spin battery which generates pure spin current. The built-in spin flip mechanism is a consequence of the spin-vibration interaction resulting from the interplay between the intrinsic spin-orbit coupling and the vibrational modes of the suspended carbon nanotube. On the other hand, utilizing thermoelectric effect, the temperature difference between the electron and the thermal bath to which the vibrational modes are coupled provides the driving force. We find that both magnitude and direction of the generated pure spin current are dependent on the strength of spin-vibration interaction, the sublevel configuration in dot, the temperatures of electron and thermal bath, and the tunneling rate between the dot and the pole. Moreover, in the linear response regime, the kinetic coefficient is non-monotonic in the temperature T and it reaches its maximum when [Formula: see text] is about one phonon energy. The existence of a strong intradot Coulomb interaction is irrelevant for our spin battery, provided that high-order cotunneling processes are suppressed.

Kondo peak splitting and Kondo dip induced by a local moment.

Many features like spin-orbit coupling, bias and magnetic fields applied, and so on, can strongly influence the Kondo effect. One of the consequences is Kondo peak splitting. However, Kondo peak splitting led by a local moment has not been investigated systematically. In this research we study theoretically electronic transport through a single-level quantum dot exchange coupled to a local magnetic moment in the Kondo regime. We focus on the Kondo peak splitting induced by an anisotropic exchange coupling between the quantum dot and the local moment, which shows rich splitting behavior. We consider the cases of a local moment with S = 1/2 and S = 1. The longitudinal (z-component) coupling plays a role of multivalued magnetic fields and the transverse (x, y-components) coupling lifts the degeneracy of the quantum dot, both of which account for the fine Kondo peak splitting structures. The inter-level or intra-level transition processes are identified in detail. Moreover, we find a Kondo dip at the Fermi level under the proper parameters. The possible experimental observations of these theoretical results should deepen our understanding of Kondo physics.

Topological incommensurate magnetization plateaus in quasi-periodic quantum spin chains.

Uncovering topologically nontrivial states in nature is an intriguing and important issue in recent years. While most studies are based on the topological band insulators, the topological state in strongly correlated low-dimensional systems has not been extensively explored due to the failure of direct explanation from the topological band insulator theory on such systems and the origin of the topological property is unclear. Here we report the theoretical discovery of strongly correlated topological states in quasi-periodic Heisenberg spin chain systems corresponding to a series of incommensurate magnetization plateaus under the presence of the magnetic field, which are uniquely determined by the quasi-periodic structure of exchange couplings. The topological features of plateau states are demonstrated by the existence of non-trivial spin-flip edge excitations, which can be well characterized by nonzero topological invariants defined in a two-dimensional parameter space. Furthermore, we demonstrate that the topological invariant of the plateau state can be read out from a generalized Streda formula and the spin-flip excitation spectrum exhibits a similar structure of the Hofstadter's butterfly spectrum for the two-dimensional quantum Hall system on a lattice.

Canonical versus noncanonical equilibration dynamics of open quantum systems.

In statistical mechanics, any quantum system in equilibrium with its weakly coupled reservoir is described by a canonical state at the same temperature as the reservoir. Here, by studying the equilibration dynamics of a harmonic oscillator interacting with a reservoir, we evaluate microscopically the condition under which the equilibration to a canonical state is valid. It is revealed that the non-Markovian effect and the availability of a stationary state of the total system play a profound role in the equilibration. In the Markovian limit, the conventional canonical state can be recovered. In the non-Markovian regime, when the stationary state is absent, the system equilibrates to a generalized canonical state at an effective temperature; whenever the stationary state is present, the equilibrium state of the system cannot be described by any canonical state anymore. Our finding of the physical condition on such noncanonical equilibration might have significant impact on statistical physics. A physical scheme based on circuit QED is proposed to test our results.

Kondo effect of cobalt adatoms on a graphene monolayer controlled by substrate-induced ripples.

The Kondo effect, a widely studied phenomenon in which the scattering of conduction electrons by magnetic impurities increases as the temperature T is lowered, depends strongly on the density of states at the Fermi energy. It has been predicted by theory that magnetic impurities on free-standing monolayer graphene exhibit the Kondo effect and that control of the density of states at the Fermi level by external means can be used to switch the effect on and off. However, though transport data for Co adatoms on graphene monolayers on several substrates have been reported, there exists no evidence for a Kondo effect. Here we probe the role of the substrate on the Kondo effect of Co on graphene by combining low-temperature scanning tunneling microscopy and spectroscopy measurements with density functional theory calculations. We use a Ru(0001) substrate that is known to cause graphene to ripple, yielding a moiré superlattice. The experimental data show a sharp Kondo resonance peak near the Fermi energy from only Co adatoms at the edge of atop regions of the moiré pattern. The theoretical results show that the variation of the distance from the graphene to the Ru substrate, which controls the spin polarization and local density of states at the Fermi energy, is the key factor for the appearance of the Kondo resonance. The results suggest that rippling of graphene by suitable substrates is an additional lever for tuning and selectively switching the appearance of the Kondo effect.

Inhomogeneity of the phase space of the damped harmonic oscillator under Lévy noise.

The damped harmonic oscillator under symmetric Lévy white noise shows inhomogeneous phase space, which is in contrast to the homogeneous phase space of the same oscillator under the Gaussian white noise, as shown in a recent paper [Sokolov, Ebeling, and Dybiec, Phys. Rev. E 83, 041118 (2011)]. The inhomogeneity of the phase space shows correlation between the coordinate and the velocity of the damped oscillator under symmetric Lévy white noise. In the present work we further explore the physical origin of these distinguished features and find that it is due to the combination of the damped effect and heavy tail of the noise. We directly demonstrate this in the reduced coordinate x[over ̃] versus velocity v[over ̃] plots and identify the physics of the antiassociation of the coordinate and velocity.

Engineering integrable nonautonomous nonlinear Schrödinger equations.

We investigate Painlevé integrability of a generalized nonautonomous one-dimensional nonlinear Schrödinger (NLS) equation with time- and space-dependent dispersion, nonlinearity, and external potentials. Through the Painlevé analysis some explicit requirements on the dispersion, nonlinearity, dissipation/gain, and the external potential as well as the constraint conditions are identified. It provides an explicit way to engineer integrable nonautonomous NLS equations at least in the sense of Painlevé integrability. Furthermore analytical solutions of this class of integrable nonautonomous NLS equations can be obtained explicitly from the solutions of the standard NLS equation by a general transformation. The result provides a significant way to control coherently the soliton dynamics in the corresponding nonlinear systems, as that in Bose-Einstein condensate experiments. We analyze explicitly the soliton dynamics under the nonlinearity management and the external potentials and discuss its application in the matter-wave dynamics. Some comparisons with the previous works have also been discussed.

Kondo effect in carbon nanotube quantum dots with spin-orbit coupling.

Motivated by recent experimental observation of spin-orbit coupling in carbon nanotube quantum dots [F. Kuemmeth, Nature (London) 452, 448 (2008)], we investigate in detail its influence on the Kondo effect. The spin-orbit coupling intrinsically lifts out the fourfold degeneracy of a single electron in the dot, thereby breaking the SU(4) symmetry and splitting the Kondo resonance even at zero magnetic field. When the field is applied, the Kondo resonance further splits and exhibits fine multipeak structures resulting from the interplay of spin-orbit coupling and the Zeeman effect. A microscopic cotunneling process for each peak can be uniquely identified. Finally, a purely orbital Kondo effect in the two-electron regime is also predicted.