Exact equilibrium results in the interacting resonant level model

Abstract

We present exact results for the susceptibility of the interacting resonant level model in equilibrium. Detailed simulations using both the Numerical Renormalization Group and Density Matrix Renormalization Group were performed in order to compare with closed analytical expressions. By first bosonizing the model and then utilizing the integrability of the resulting boundary sine-Gordon model, one finds an analytic expression for the relevant energy scale TK with excellent agreement to the numerical results. On the other hand, direct application of the Bethe ansatz of the interacting resonant level mode does not correctly reproduce TK -however if the bare parameters in the model are renormalised, then quantities obtained via the direct Bethe ansatz such as the occupation of the resonant level as a function of the local chemical potential do match the numerical results. The case of one lead is studied in the most detail, with many results also extending to multiple leads, although there still remain open questions in this case. arXiv:1810.08246v2 [cond-mat.str-el]

Non-Hermitian quantum impurity systems in and out of equilibrium: noninteracting case

“…and the UV and IR expansions are valid when v( Γ) < 1 and v( Γ) > 1, respectively. We note that, in the scaling limit γ 1 , γ 2 , µ 1, ( 36) and (37) reproduce the known expression [24,25] in the Toulouse limit of the anisotropic Kondo model. Similar formulae can also be obtained by the same manipulations in the phase II, and presented in Appendix B. Profiles of the dot density at T = 0 as a function of µ in different phases are depicted in the panel (a) of Fig.…”

Many-body wavefunctions for quantum impurities out of equilibrium. II. Charge fluctuations

“…See Table I in Ref. [20] for a summary of the literature. While all calculations agree that α = 2 for zero coupling (or zero phase shift), there is disagreement already at the first order correction.…”

“…It can be verified that D ∂ ∂D + β ∆ ∆ ∂ ∂∆ T K = O and that T K = ∆ for U = 0. The U -dependent overall scale of T K is arbitrary (as we discuss in more detail below), and we have chosen it so that the equilibrium susceptibility at zero field takes the standard form [20…”

Efficient impurity-bath trial states from superposed Slater determinants

“…We demonstrate our ideas by studying the Interacting Resonant Level Model (IRLM) [15], the simplest quantum impurity problem in which an electronic impurity orbital interacts with a conduction band to produce Kondo correlations. In the past, the IRLM has provided an interesting test bed for studying equilibrium [16][17][18][19] and dynamical [20][21][22][23][24][25][26][27][28][29][30] features of impurity models. Our key insight is the following.…”

“…Note that the transformed Hamiltonian is completely non-local due to the term γc 0 P. In the transformed frame, the exact ground state takes the form c † −1 |Ψ , where |Ψ is the many-body ground state of Eq. (19). The CTG approach assumes a trial state c † −1 |G , in which the Gaussian state |G is the ground state of a generic quadratic parent Hamiltonian:…”