We study the Kondo chain in the regime of high spin concentration where the low energy physics is dominated by the Ruderman-Kittel-Kasuya-Yosida interaction. As has been recently shown (Tsvelik and Yevtushenko 2015 Phys. Rev. Lett. 115 216402), this model has two phases with drastically different transport properties depending on the anisotropy of the exchange interaction. In particular, the helical symmetry of the fermions is spontaneously broken when the anisotropy is of the easy plane type. This leads to a parametrical suppression of the localization effects. In the present paper we substantially extend the previous theory, in particular, by analyzing a competition of forward-and backward-scattering, including into the theory short range electron interactions and calculating spin correlation functions. We discuss applicability of our theory and possible experiments which could support the theoretical findings.where t is the hopping matrix element, ( †) c i annihilates (creates) an electron at site i, S i is a local spin of magnitude s, s a is a Pauli matrix, and M constitutes a subset of all lattice sites. J denotes the interaction strength between the impurities and the electrons. We distinguish J z and ≕ =Ĵ , and K s =1), we see that the backward scattering terms flow faster in the RG-flow from high to low energies than forward scattering ones, i.e. the terms~J b can dominate.Let us assume that an impurity scatters anisotropically in spin space ( ¹Ĵ J z ), but there is no difference between the electrons' directions ( = J J 4.1. EA anisotropy, Ĵ J z Let us consider Ĵ J z a y t F=^^-v a J J J J s , i ,2 6) in the last inequality. This severly affects the charge transport, which is mediated by α. Breaking the  2 symmetryWe have demonstrated that for Ĵ J z , all fermionic modes have approximately the same gap~J z . Approaching the SU(2) symmtric point, the massm shrinks until it would reach zero at =Ĵ J z . In terms of the EA picture, some fermions (two helical modes) become light and their contribution encompasses large fluctuations on top of their ground state energy. We explicitely assumed that the fluctuations around the ground state are small. Therefore, our approach is no longer valid for  -m 0. For now, let us consider the other limit Ĵ J z . We will see that this parameter regime behaves in a way qualitatively different to Ĵ J z . The order parameter distinguishing the phases is discussed in section 6. The vanishing of the gap for Ĵ J z , the spontaneous symmetry breaking for Ĵ J z and the presence of an order parameter all strongly suggest the presence of a quantum phase transition, although its theoretical description is missing. EP anisotropy, Ĵ J zLet us put for simplicity  J 0

It has been argued that the 0.7 anomaly in quantum point contacts (QPCs) is due to an enhanced density of states at the top of the QPC-barrier (van Hove ridge), which strongly enhances the effects of interactions. Here, we analyze their effect on dynamical quantities. We find that they pin the van Hove ridge to the chemical potential when the QPC is subopen; cause a temperature dependence for the linear conductance that qualitatively agrees with experiment; strongly enhance the magnitude of the dynamical spin susceptibility; and significantly lengthen the QPC traversal time. We conclude that electrons traverse the QPC via a slowly fluctuating spin structure of finite spatial extent.Quantum point contacts are narrow, one-dimensional (1D) constrictions usually patterned in a two-dimensional electron system (2DES) by applying voltages to local gates. As QPCs are the ultimate building blocks for controlling nanoscale electron transport, much effort has been devoted to understand their behavior at a fundamental level. Nevertheless, in spite of a quarter of a century of intensive research into the subject, some aspects of their behavior still remain puzzling.When a QPC is opened up by sweeping the gate voltage, V g , that controls its width, its linear conductance famously rises in integer steps of the conductance quantum,. This conductance quantization is well understood [3] and constitutes one of the foundations of mesoscopic physics. However, during the first conductance step, where the dimensionless conductance g = G/G Q changes from 0 to 1 ("closed" to "open" QPC), an unexpected shoulder is generically observed near g 0.7. More generally, the conductance shows anomalous behavior as function of temperature (T ), magnetic field (B) and source-drain voltage (V sd ) throughout the regime 0.5 g 0.9, where the QPC is "subopen". The source of this behavior, collectively known as the "0.7-anomaly", has been controversially discussed [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] ever since it was first systematically described in 1996 [4]. Though no consensus has yet been reached regarding its detailed microscopic origin [10,22], general agreement exists that it involves electron spin dynamics and geometrically-enhanced interaction effects.In this paper we further explore the van Hove ridge scenario, proposed in [22]. It asserts that the 0.7 anomaly is a direct consequence of a "van Hove ridge", i. e. a smeared van Hove peak in the energy-resolved local density of states (LDOS) A i (ω) at the bottom of the lowest 1D subband of the QPC. Its shape follows that of the QPC barrier [22,23] and in the subopen regime, where the barrier top lies just below the chemical potential µ, it causes the LDOS at µ to be strongly enhanced. This reflects the fact that electrons slow down while crossing the QPC barrier (since the semiclassical velocity of an electron with energy ω at position i is inversely proportional to the LDOS, A i (ω) ∼ v −1 ). The slow electrons experience strongly enhanced mutual interactions...

We present a Keldysh-based derivation of a formula, previously obtained by Oguri using the Matsubara formalisum, for the linear conductance through a central, interacting region coupled to non-interacting fermionic leads. Our starting point is the well-known Meir-Wingreen formula for the current, whose derivative w.r.t. to the source-drain voltage yields the conductance. We perform this derivative analytically, by exploiting an exact flow equation from the functional renormalization group, which expresses the flow w.r.t. voltage of the self-energy in terms of the two-particle vertex. This yields a Keldysh-based formulation of Oguri's formula for the linear conductance, which facilitates applying it in the context of approximation schemes formulated in the Keldysh formalism. (Generalizing our approach to the non-linear conductance is straightforward, but not pursued here.) -We illustrate our linear conductance formula within the context of a model that has previously been shown to capture the essential physics of a quantum point contact in the regime of the 0.7 anomaly. The model involves a tight-binding chain with a one-dimensional potential barrier and onsite interactions, which we treat using second order perturbation theory. We show that numerical costs can be reduced significantly by using a non-uniform lattice spacing, chosen such that the occurence of artificial bound states close to the upper band edge is avoided.

We combine two recently established methods, the extended Coupled-Ladder Approximation (eCLA) [Phys. Rev. B 95, 035122 (2017)] and a dynamic Keldysh functional Renormalization Group (fRG) approach for inhomogeneous systems [Phys. Rev. Lett. 119, 196401 (2017)] to tackle the problem of finite-ranged interactions in quantum point contacts (QPCs) at finite temperature. Working in the Keldysh formalism, we develop an eCLA framework, proceeding from a static to a fully dynamic description. Finally, we apply our new Keldysh eCLA method to a QPC model with finite-ranged interactions and show evidence that an interaction range comparable to the length of the QPC might be an essential ingredient for the development of a pronounced 0.7-shoulder in the linear conductance. We also discuss problems arising from a violation of a Ward identity in second-order fRG.