Motivated by recent scanning tunneling microscopy experiments on chains of Co adatoms on Cu surfaces, we investigate the physics of a spin-
3/2 Heisenberg chain with single-ion anisotropy (
D) on metallic and semi-metallic surfaces. In the strong Kondo coupling (
Jk) limit, a perturbative analysis maps the system onto a Haldane spin-1 chain with single-ion anisotropy, ferromagnetically coupled to the metallic surface. This Haldane state, arising from underscreening of the
S=3/2 chain, is stable against small
D and characterized by topological edge modes. The nature of the
D-driven transitions out of this state depends on the environment. Coupling to a metal (semi-metal) is a relevant (irrelevant) perturbation at the decoupled fixed point between the spin-1 chain and the two-dimensional electron gas. In the large positive
D limit, the system maps onto an anisotropic spin-
1/2 Kondo system. For large negative
D, in the Ising phase, spins are frozen. For small
Jk, the nature of the metallic phase dominates. On a two-dimensional semi-metal, the Kondo coupling is irrelevant at the decoupled fixed point (
Jk=0), leading to a Kondo breakdown phase at weak coupling, irrespective of
D. In contrast, on a two-dimensional metal, the resulting dissipative Ohmic bath is a marginally relevant perturbation, inducing antiferromagnetic ordering along the chain. In this case,
D drives a spin-flop transition between Ising and XY ordered phases. At
D=0, we observe continuous transitions between the Kondo breakdown or dissipation-induced long-range ordered phases and the underscreened Haldane phase. These phase diagrams are supported by scaling arguments and sign-free auxiliary-field quantum Monte Carlo simulations.
We study the low energy physics of a Kondo chain where electrons from a one-dimensional band interact with magnetic moments via an anisotropic exchange interaction. It is demonstrated that the anisotropy gives rise to two different phases which are separated by a quantum phase transition. In the phase with easy plane anisotropy, Z_{2} symmetry between sectors with different helicity of the electrons is broken. As a result, localization effects are suppressed and the dc transport acquires (partial) symmetry protection. This effect is similar to the protection of the edge transport in time-reversal invariant topological insulators. The phase with easy axis anisotropy corresponds to the Tomonaga-Luttinger liquid with a pronounced spin-charge separation. The slow charge density wave modes have no protection against localization.
We consider a two-dimensional quantum spin system described by a Heisenberg model that is embedded in a three-dimensional metal. The two systems couple via an antiferromagnetic Kondo interaction. In such a setup, the ground state generically remains metallic down to the lowest temperatures and allows us to study magnetic quantum phase transitions in metallic environments. From the symmetry point of view, translation symmetry is present in two out of three lattice directions such that crystal momentum is only partially conserved. Importantly, the construction provides a route to study, with negative-sign-free auxiliary-field quantum Monte Carlo methods, the physics of local moments in metallic environments. Our large-scale numerical simulations show that as a function of the Kondo coupling, the system has two metallic phases. In the limit of strong Kondo coupling, a paramagnetic heavy-fermion phase emerges. Here, the spin degree of freedom is screened by means of the formation of a composite quasiparticle that participates in the Luttinger count. At weak Kondo coupling, magnetic order is present. This phase is characterized by Landau-damped Goldstone modes. Furthermore, the aforementioned composite quasiparticle remains intact across the quantum phase transition.
Using numerical renormalization-group techniques, we study static and dynamic properties of a family of single-channel Kondo impurity models with axial magnetic anisotropy
DSz2 terms; such models are appropriate to describe magnetic impurity atoms adsorbed on nonmagnetic surfaces, which may exhibit surface Kondo effect. We show that for positive anisotropy
D and for any spin
S, the systems behave at low temperatures as regular Fermi liquids with fully compensated impurity spin. The approach to the stable fixed point depends on the value of the spin
S and on the ratio
D/TK(0), where
TK(0) is the Kondo temperature in the absence of the anisotropy. For
S=1, the screening occurs in two stages if
D<TK(0); the second Kondo temperature is exponentially reduced in this case. More generally, there is an effective spin-1/2 Kondo effect for any integer
S if
D<TK(0) and for any half-integer
S if
D>TK(0). For negative anisotropy
D, the system is a non-Fermi liquid with residual anisotropic exchange interaction. However, the presence of transverse magnetic anisotropy $E({S}_{x}^{2}\ensuremath{-}{S}_{y}^{2})$ restores Fermi-liquid behavior in real systems.
We explore the physics of a spin-1/2 Heisenberg chain with Kondo interaction,
Jk, to a two-dimensional electron gas. At weak
Jk the problem maps onto a Heisenberg chain locally coupled to a dissipative Ohmic bath. At the decoupled fixed point, the dissipation is a marginally relevant perturbation and drives long-range antiferromagnetic order along the chain. In the dynamical spin structure factor we observe a quadratic low-energy dispersion akin to Landau-damped Goldstone modes. At large
Jk Kondo screening dominates, and the spin correlations of the chain inherit the power law of the host metal, akin to a paramagnetic heavy Fermi liquid. In both phases we observe heavy bands near the Fermi energy in the composite-fermion spectral function. Our results, obtained from auxiliary-field quantum Monte Carlo simulations, provide a negative-sign-free realization of a quantum transition between an antiferromagnetic metal and a heavy-fermion metal. We discuss the relevance of our results in the context of scanning tunneling spectroscopy experiments of magnetic adatom chains on metallic surfaces.
In this work we consider several exactly solvable models of magnetic impurities in critical quantum antiferromagnetic spin chains and multichannel Kondo impurities. Their ground-state properties are studied, and the finite set of nonlinear integral equations which exactly describe the thermodynamics of the models is constructed. We obtain several analytical low-energy expressions for the temperature, magnetic field, and frequency dependences of important characteristics of exactly solvable disordered quantum spin models and disordered multichannel Kondo impurities with essential many-body interactions. We show that the only low-energy parameter that gets renormalized is the velocity of the low-lying excitations (or the effective crossover scale connected with each impurity); the others appear to be universal. In our study several kinds of strong disorder important for experiments were used. Some of them produce low divergences in certain characteristics of our strongly disordered critical systems (compared with finite values for the homogeneous case or a single impurity). For weak disorder, or for narrow distributions of the local Kondo temperatures, our exact results reveal the presence of Kondo screening of disordered ensembles of magnetic impurities by low-lying excitations of the host. We point out that our results qualitatively coincide with the data of experiments on real disordered quasi-one-dimensional antiferromagnetic systems and with the similar behavior of some heavy metallic alloys.