Hidden Caldeira-Leggett dissipation in a Bose-Fermi Kondo model

We show that the Bose-Fermi Kondo model (BFKM), which may find applicability both to certain dissipative mesoscopic qubit devices and to heavy-fermion systems described by the Kondo lattice model, can be mapped exactly onto the Caldeira-Leggett model. This mapping requires an ohmic bosonic bath and an Ising-type coupling between the latter and the impurity spin. This allows us to conclude unambiguously that there is an emergent Kosterlitz-Thouless quantum phase transition in the BFKM with an ohmic bosonic bath. By applying a bosonic numerical renormalization group approach, we thoroughly probe physical quantities close to the quantum phase transition.     

An Anderson Impurity Interacting with the Helical Edge States in a Quantum Spin Hall Insulator

Using the natural orbitals renormalization group(NORG)method,we investigate the screening of the local spin of an Anderson impurity interacting with the helical edge states in a quantum spin Hall insulator.It is found that there is a local spin formed at the impurity site and the local spin is completel.y screened by electrons in the quantum spin Hall insulator.Meanwhile,the local spin is screened dominantly by a single active natural orbital.We then show that the Kondo screening mechanism becomes transparent and simple in the framework of the natural orbitals formalism.We project the active natural orbital respectively into real space and momentum space to characterize its structure.We conilrm the spin-momentum locking property of the edge states based on the occupancy of a Bloch state on the edge to which the impurity couples.Furthermore,we study the dynamical property of the active natural orbital represented by the local density of states,from which we observe the Kondo resonance peak.     

Pseudogap Fermi-Bose Kondo model

We consider a magnetic impurity coupled to both fermionic quasiparticles with a pseudogap density of states and bosonic spin fluctuations. Using renormalization group and large-N calculations we investigate the phase diagram of the resulting Fermi-Bose Kondo model. We show that the Kondo temperature is strongly reduced by low-energy spin fluctuations, and make connections to experiments in cuprate superconductors. Furthermore, we derive an exact exponent for the critical behavior of the conduction electron T matrix, and propose our findings to be relevant for certain scenarios of local quantum criticality in heavy-fermion metals.     

Entanglement and criticality in quantum impurity systems

We investigate the entanglement between a spin and its environment in impurity systems which exhibit a second-order quantum phase transition separating a delocalized and a localized phase for the spin. As an application, we employ the spin-boson model, describing a two-level system (spin) coupled to a sub-Ohmic bosonic bath with power-law spectral density, J(omega) proportional to omega(s) and 0 < s < 1. Combining Wilson's numerical renormalization group method and hyperscaling relations, we demonstrate that the entanglement between the spin and its environment is always enhanced at the quantum phase transition resulting in a visible cusp (maximum) in the entropy of entanglement. We formulate a correspondence between criticality and impurity entanglement entropy, and the relevance of these ideas to nanosystems is outlined.     

Correlated electrons in a dissipative environment

When a system of correlated electrons is embedded in a dissipative environment, new emergent phenomena might occur due to the interplay of correlation and dissipation. Here we focus on quantum impurity systems with coupling to a bosonic bath. For the theoretical investigation we introduce the bosonic numerical renormalization group method which has been initially set up for the spin-boson model. The role of both correlations and dissipation is described in the context of two-electron transfer systems. We also discuss prospects for the investigation of lattice models of correlated electrons with coupling to a dissipative bath.     

Ground state of the parallel double quantum dot system

We resolve the controversy regarding the ground state of the parallel double quantum dot system near half filling. The numerical renormalization group predicts an underscreened Kondo state with residual spin-1/2 magnetic moment, ln2 residual impurity entropy, and unitary conductance, while the Bethe ansatz solution predicts a fully screened impurity, regular Fermi-liquid ground state, and zero conductance. We calculate the impurity entropy of the system as a function of the temperature using the hybridization-expansion continuous-time quantum Monte Carlo technique, which is a numerically exact stochastic method, and find excellent agreement with the numerical renormalization group results. We show that the origin of the unconventional behavior in this model is the odd-symmetry "dark state" on the dots.     

Boundary Quantum Entanglement of the XXZ Spin Chain with Boundary Impurities

The boundary quantum entanglement for the s = 1/2 X X Z spin chain with boundary impurities is studied via the density matrix renormalization group （DMRG） method. It is shown that the entanglement entropy of the boundary bond （the impurity and the chain spin next to it） behaves differently in different phases. The relationship between the singular points of the boundary entropy and boundary quantum critical points is discussed.     

Quantum phase diagram of a spin-1/2 antiferromagnetic chain with magnetic impurity

We present the renormalization group (RG) flow diagram of a spin-half antiferromagnetic chain with magnetic impurity and one altered link. In this two parameters (competing interactions) model, one can find the complex phase diagram with many interesting fixed points. There is no evidence of intermediate stable fixed point in weak coupling phase. It may arise at the strong coupling phase. Depending on the strength of couplings the phases correspond either to a decoupled spin with Curie law behavior or a logarithmically diverging impurity susceptibility as in the two channel Kondo problem.     

Quantum bit commitment is weaker than quantum bit seals

We investigate the reduced dynamics of a central spin coupled to a spin environment with non-uniform coupling. Through using the method of time-dependent density-matrix renormalization group (t-DMRG), we nonperturbatively show the dissipative dynamics of the central spin beyond the case of uniform coupling between the central spin and the environment spins. It is shown that only when the system-environment coupling is weak enough, the central spin system shows Markovian effect and will finally reach the steady state; otherwise, the reduced dynamics is non-Markovian and exhibits a quasi-periodic oscillation. The frequency spectrum and the correlation between the central spin system and the environment are also studied to elucidate the dissipative dynamics of the central spin system for different coupling strengths.     

Numerical renormalization group at marginal spectral density: application to tunneling in Luttinger liquids

Many quantum mechanical problems (such as dissipative phase fluctuations in metallic and superconducting nanocircuits or impurity scattering in Luttinger liquids) involve a continuum of bosonic modes with a marginal spectral density diverging as the inverse of energy. We construct a numerical renormalization group in this singular case, with a manageable violation of scale separation at high energy, capturing reliably the low energy physics. The method is demonstrated by a nonperturbative solution over several energy decades for the dynamical conductance of a Luttinger liquid with a single static defect.     

Quantum spin chains with various defects

Using the density matrix renormalization group (DMRG) method, we study the quantum coherence in one‐dimensional disordered spin chains and Fermi systems. We consider in detail spinless fermions on a ring, and compare the influence of several kinds of impurities in a gapless and a dimerized, gapped system. In the translation‐invariant system a so‐called site‐impurity, which can be realized by a local potential or a modification of one link, increases for repulsive interaction, and decreases for attractive interaction, upon renormalization. The weakening of two neighbouring bonds, which is a realization of a so‐called bond‐impurity, on the other hand, is healed for repulsive interaction, but enhanced for intermediate attractive interactions. This leads to a strong suppression of the quantum coherence measured by the phase sensitivity, but not to localization. Adding a local distortion to a dimerized system, we find that even the presence of a single site‐impurity increases the metallic region found in the dimerized model. For a strong dimerization and a high barrier, an additional sharp maximum, is seen in the phase sensitivity as a function of interaction, already for systems with about 100 sites. A bond‐impurity in the dimerized system also opens a small metallic window in the otherwise isolating regime.     

Variational numerical renormalization group: bridging the gap between NRG and density matrix renormalization group

The numerical renormalization group (NRG) is rephrased as a variational method with the cost function given by the sum of all the energies of the effective low-energy Hamiltonian. This allows us to systematically improve the spectrum obtained by NRG through sweeping. The ensuing algorithm has a lot of similarities to the density matrix renormalization group (DMRG) when targeting many states, and this synergy of NRG and DMRG combines the best of both worlds and extends their applicability. We illustrate this approach with simulations of a quantum spin chain and a single impurity Anderson model where the accuracy of the effective eigenstates is greatly enhanced as compared to the NRG, especially in the transition to the continuum limit.     

The exchange interaction effect in the scanning tunneling spectroscopy of a two-orbital Anderson impurity on metallic surface

We investigate the scanning tunneling spectroscopy (STS) of a two-orbital Anderson impurity adsorbed on a metallic surface by using the numerical renormalization group (NRG) method. The density of state of magnetic impurity and the local conduction electron are calculated. We obtain the Fano resonance line shape in the STM conductance at zero temperature. For the impurity atom with antiferromagnetic inter-orbital exchange interaction and a spin singlet ground state, we show that a dip in the STM spectra around zero bias voltage regime and side peaks of spin excitation can be observed. The spin excitation energy is proportional to the exchange interaction strength. As the exchange interaction is ferromagnetic, the underscreened Kondo effect dominates the low energy properties of this system, and it gives rise to drastically different STM spectra as compared with the spin singlet case.     

有限温度张量重正化群方法及其在阻挫量子磁性研究中的应用

阻挫量子磁体中的新奇物态与效应是凝聚态物理研究的重要前沿方向,因其与高温超导、拓扑量子计算等的密切联系,近年来吸引了人们浓厚的研究兴趣。实验上,阻挫自旋液体候选材料的 新进展层出不穷,人们系统地研究了若干三角晶格、笼目晶格和六角Kitaev 阻挫磁体等材料,发 现其在一定条件下展现出自旋液体态的特征,但澄清其中的量子物态是充满挑战的量子多体问题。 作者最近的工作指出,可以从有限温度张量重正化群多体计算入手,开展热力学性质的精确计算 与分析,确定阻挫磁体的微观自旋模型,做出进一步理论预言并开展实验验证,从而建立量子磁性 系统的多体计算精确研究方案。有限温度张量重正化群方法是计算大尺寸二维阻挫量子自旋模型 有限温度性质的有力工具,在本文中作者首先介绍新近发展的系列张量重正化群方法,包括线性 和指数张量重正化群等。随后,作者讨论有限温度张量方法在三角晶格量子伊辛磁体TmMgGaO4 和六角晶格Kitaev 磁体α-RuCl3 的微观自旋模型中的具体应用：通过高精度和全面的多体计算, 揭示出其中存在演生U(1) 对称性与拓扑相变,以及高场量子自旋液体态等新颖的结论,这些理 论预言也陆续被实验所证实。通过上述实例,作者展示了有限温度张量重正化群计算方法在自旋 液体候选材料研究中的应用价值,并期待这些方法能在强关联量子物质研究中发挥重要作用。     

Theory of smeared quantum phase transitions

We present an analytical strong-disorder renormalization group theory of the quantum phase transition in the dissipative random transverse-field Ising chain. For Ohmic dissipation, we solve the renormalization flow equations analytically, yielding asymptotically exact results for the low-temperature properties of the system. We find that the interplay between quantum fluctuations and Ohmic dissipation destroys the quantum critical point by smearing. We also determine the phase diagram and the behavior of observables in the vicinity of the smeared quantum phase transition.     

Phase diagram of an impurity in the spin-1/2 chain: two-channel Kondo effect versus Curie law

We consider a magnetic S = 1/2 impurity in the antiferromagnetic spin chain as a function of two coupling parameters: the symmetric coupling of the impurity to two sites in the chain J1 and the coupling between the two sites J2. By using field theory arguments and numerical calculations we can identify all possible fixed points and classify the renormalization flow between them, which leads to a nontrivial phase diagram. Depending on the detailed choice of the two (frustrating) coupling strengths, the stable phases correspond either to a decoupled spin with Curie law behavior or to a non-Fermi-liquid fixed point with a logarithmically diverging impurity susceptibility as in the two-channel Kondo effect. Our results resolve a controversy about the renormalization flow.     

Efficient approximation of the dynamics of one-dimensional quantum spin systems

In this Letter we show that an arbitrarily good approximation to the propagator e(itH) for a 1D lattice of n quantum spins with Hamiltonian H may be obtained with polynomial computational resources in n and the error epsilon and exponential resources in |t|. Our proof makes use of the finitely correlated state or matrix product state formalism exploited by numerical renormalization group algorithms like the density matrix renormalization group. There are two immediate consequences of this result. The first is that Vidal's time-dependent density matrix renormalization group will require only polynomial resources to simulate 1D quantum spin systems for logarithmic |t|. The second consequence is that continuous-time 1D quantum circuits with logarithmic |t| can be simulated efficiently on a classical computer, despite the fact that, after discretization, such circuits are of polynomial depth.     

Theory of inelastic scattering from magnetic impurities

We use the numerical renormalization group method to calculate the single-particle matrix elements T of the many-body T matrix of the conduction electrons scattered by a magnetic impurity at T=0 temperature. Since T determines both the total and the elastic, spin-diagonal scattering cross sections, we are able to compute the full energy, spin, and magnetic field dependence of the inelastic scattering cross section sigma(inel)(omega). We find an almost linear frequency dependence of sigma(inel)(omega) below the Kondo temperature T(K), which crosses over to a omega(2) behavior only at extremely low energies. Our method can be generalized to other quantum impurity models.     

Numerical renormalization group for bosonic systems and application to the sub-ohmic spin-boson model

We describe the generalization of Wilson's numerical renormalization group method to quantum impurity models with a bosonic bath, providing a general nonperturbative approach to bosonic impurity models which can access exponentially small energies and temperatures. As an application, we consider the spin-boson model, describing a two-level system coupled to a bosonic bath with power-law spectral density, J(omega) proportional to omega(s). We find clear evidence for a line of continuous quantum phase transitions for sub-Ohmic bath exponents 0相似文献