Dilute magnetic moments in an exactly solvable interacting host

Abstract

Despite concerted efforts, the problem of dilute local moments embedded in a correlated conduction electron host such as Nd1−xCexCuO2 persists due to lack of analytically controllable models. Here, we address the question: how do local moments couple to correlated but integrable hosts? We describe the conduction electrons by the model of Hatsugai-Kohmoto (HK) which has undergone a recent resurgence arising from its exact solvability, existence of Luttinger surfaces, and connections to Sachdev-Ye-Kitaev (SYK) thermodynamics. We derive an exact low energy "Kondo-HK" Hamiltonian and show the existence of additional spin-exchange coupling that is relevant in the renormalization group (RG) sense. This term is ferromagnetic and does not vanish at low energies yielding an algebraic enhancement of the Kondo temperature. "Poor man's" scaling of couplings exhibits an exotic step-like RG flow between UV-IR fixed points attributed to severely restricted scattering phase space. This phenomenon is analogous to the flow of central charge in Zamolodchikov's diagonal resonance scattering in integrable quantum field theories.

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

“…63,64 It is noted that the former one has already been explored by poorman's scaling approach and deviation from usual Kondo impurity in FL is noticeable. 10 Due to the perturbative nature of poorman's scaling, the ground-state of Kondo impurity in HK model has not been established and it seems that the state-of-art numerical renormalization group, which is very successful on Kondo impurity in non-interacting environment, 65 cannot be utilized without nontrivial modification. To explore the ground-state, it will be helpful to follow the classic variational wave-function calculation of Yosida as the first step.…”

“…the Hatsugai-Kohmoto (HK) model, [1][2][3] has been hotly studied. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] In contrast with celebrated and more familiar Sachdev-Ye-Kitaev, Kitaev's toric code and honeycomb model with either quenched disorder or local Z 2 gauge symmetry, [22][23][24][25][26][27][28][29] the original HK model has translation invariance with topologically trivial nature, but surprisingly, it provides a strictly exact playground for non-Fermi liquid (NFL) and featureless Mott insulator in any spatial dimension, which is rare in statistical mechanics and condensed matter physics.…”

Symmetry constraints and spectral crossing in a Mott insulator with Green's function zeros

“…1(a), bottom panel) [23]. We focus on local in momentum interactions analogous to those appearing in the Hatsugai-Kohmoto (HK) model [21,[24][25][26][27][28][29][30][31][32][33]. This form of interaction can be solved exactly [see the Supplementary Material (SM), Sec.…”

Solvable Periodic Anderson Model with Infinite-Range Hatsugai-Kohmoto Interaction: Ground-states and beyond

“…[1][2][3][4][5][6][7][8][9][10] Among them, an infinite-range interaction model without any quenched disorder or local gauge structure called Hatsugai-Kohmoto (HK) model has been revisited. [11][12][13][14][15][16][17][18][19][20][21][22][23] The original HK model provides a strictly exact example for non-Fermi liquid and featureless Mott insulator in any spatial dimension, which is rare in statistical mechanics and condensed matter physics. The solvability of HK model results from its locality in momentum space and one can diagonalize HK Hamiltonian (only 4 × 4-matrix) for each momentum.…”

“…The current studies have mainly focused on an interesting extension of HK model, i.e. the superconducting instability from the intrinsic non-Fermi liquid state in HK model, 16 (note however a study on Kondo impurity in HK model 20 ) and unexpected properties (compared with standard Bardeen-Cooper-Schrieffer (BCS) model 24 ) have been discovered, e.g. the emergence of topological s-wave pairing, twostage superconductivity, tricritical point and absence of Hebel-Slichter peak.…”