Nonlinear Sigma Model Analysis of the AFM Phase Transition of the Kondo Lattice

We have studied the antiferromagnetic quantum phase transition of a 2D Kondo-Heisenberg square lattice using the non-linear sigma model. A renormalization group analysis of the competing Kondo -- RKKY interaction was carried out to 1-loop order in the $\epsilon$ expansion, and a new quantum critical point is found, dominated by Kondo fluctuations. In addition, the spin-wave velocity scales logarithmically near the new QCP, i.e breakdown of hydrodynamic behavior. The results allow us to propose a new phase diagram near the AFM fixed point of this 2D Kondo lattice model.Comment: 4 pages, 4 figure

A Gell-Mann & Low Theorem Perspective on Quantum Computing: New Paradigm for Designing Quantum Algorithm

The Gell-Mann & Low theorem is a cornerstone of Quantum Field Theory (QFT) and condensed matter physics, and many-body perturbation theory is a foundational tool for treating interactions. However, their integration into quantum algorithms remains a largely unexplored area of research, with current quantum simulation algorithms predominantly operating in the Schr\"odinger picture, leaving the potential of the interaction picture largely untapped. Our Variational Interaction-Picture S-matrix Ansatz (VIPSA) now fills this gap, specifically in the context of the Fermi-Hubbard model -- a canonical paradigm in condensed matter physics which is intricately connected to phenomena such as high-temperature superconductivity and Mott insulator transitions. This work offers a new conceptual perspective for variational quantum computing based upon the Gell-Mann & Low theorem. We achieve this by employing an innovative mathematical technique to explicitly unfold the normalized S-matrix, thereby enabling the systematic reconstruction of the Dyson series on a quantum computer, order by order. This method stands in contrast to the conventional reliance on Trotter expansion for adiabatic time evolution, marking a conceptual shift towards more sophisticated quantum algorithmic design. We leverage the strengths of the recently developed ADAPT-VQE algorithm, tailoring it to reconstruct perturbative terms effectively. Our simulations indicate that this method not only successfully recovers the Dyson series but also exhibits robust and stable convergence. We believe that our approach shows great promise in generalizing to more complex scenarios without increasing algorithmic complexity.Comment: 12 pages, 10 figure

Local Quantum Criticality of an Iron-Pnictide Tetrahedron

Motivated by the close correlation between transition temperature (T-c) and the tetrahedral bond angle of the As-Fe-As layer observed in the iron-based superconductors, we study the interplay between spin and orbital physics of an isolated iron-arsenide tetrahedron embedded in a metallic environment. Whereas the spin-Kondo effect is suppressed to low temperatures by Hund's coupling, the orbital degrees of freedom are expected to quantum mechanically quench at high temperatures, giving rise to an overscreened, non-Fermi liquid ground state. Translated into a dense environment, this critical state may play an important role in the superconductivity of these materials

Generalized Schrieffer-Wolff transformation of the two-impurity Kondo model

We have carried out a generalized Schrieffer-Wolff transformation of an Anderson two-impurity Hamiltonian to study the low-energy spin interactions of the system. The 2nd-order expansion yields the standard Kondo Hamiltonian for two impurities with additional scattering terms. At 4th order, we get the well-known RKKY interaction. In addition, we also find an antiferromagnetic superexchange coupling, and a previously undiscovered correlated Kondo coupling between the two impurities