Quantum Monte Carlo studies of U(1) lattice gauge models of Kondo breakdown

In the local-moment regime, heavy fermions are most economically described by a compact U(1) gauge theory. With this formulation of the Kondo lattice, we study a spin chain coupled to two-dimensional Dirac conduction electrons. The spin chain is described by fermionic partons carrying spin and U(1) gauge charge. The heavy-fermion quasiparticle is a bound state of a U(1) matter field carrying unit electric and U(1) gauge charge, and the fermionic parton. Using sign-problem-free determinant quantum Monte Carlo simulations, we identify two symmetry-equivalent regimes: a heavy-fermion metal with a sharp composite-fermion resonance and robust low-frequency transport, and a Kondo-breakdown metal with an incoherent resonance and vanishing low-frequency transport. For any finite lattice extent in the direction perpendicular to the chain, the Luttinger volume of the heavy-fermion phase counts both composite and conduction electrons, while in the Kondo-breakdown phase it counts only the conduction electrons. The evolution of the composite-fermion spectrum, dynamical spin structure factor, and optical conductivity provides a nonperturbative demonstration of gauge-mediated Kondo breakdown and establishes transport fingerprints of an orbital-selective Mott transition in the context of U(1) gauge theories of heavy fermions.

💡 Research Summary

The authors present a sign‑problem‑free determinant quantum Monte‑Carlo (DQMC) study of a lattice‑gauge formulation of a Kondo lattice in which a one‑dimensional spin‑½ chain is antiferromagnetically coupled to two‑dimensional Dirac conduction electrons. By representing the local moments with fermionic partons (f‑fermions) subject to a compact U(1) gauge constraint, and introducing a matter field z that carries both electric and gauge charge, they construct a gauge‑invariant composite fermion operator Ψ = z† f. Ψ carries electric charge and spin but no gauge charge, and therefore plays the role of the heavy‑fermion quasiparticle in this model. The Hamiltonian includes hopping of the Dirac c‑electrons on a π‑flux square lattice, a Kondo‑like hybridization V between c and Ψ, and dynamical gauge fields (U, E) controlled by a single parameter h that tunes the strength of gauge and matter‑field fluctuations.

Using the ALF implementation of DQMC, the authors simulate lattices up to 20 × 20 sites for the conduction electrons and a chain of equal length for the f‑fermions, at inverse temperatures β ≤ 10. Imaginary‑time correlation functions are analytically continued with stochastic analytic continuation to obtain real‑frequency spectra. The key observables are the composite‑fermion Green’s function GΨ, the zero‑frequency density of states NΨ≈β GΨ(β/2), the momentum‑resolved spectral function AΨ(k,ω), the dynamical spin structure factor S(q,ω) of the f‑chain, and the optical conductivity σ′(ω) derived from the current–current correlator of Ψ.

The results reveal two symmetry‑equivalent phases separated by a continuous transition at a critical h_c ≈ 1.2. For h < h_c the system is in a Kondo‑coherent heavy‑fermion metal: NΨ is large, AΨ shows a sharp low‑energy hybridized band with substantial Ψ weight, S(q,ω) is broad and continuum‑like reflecting itinerant magnetic correlations, and σ′(ω) exhibits a pronounced Drude peak indicating metallic transport carried by coherent composite quasiparticles. For h > h_c the composite quasiparticle is destroyed: NΨ collapses, AΨ splits into two incoherent bands, S(q,ω) develops a well‑defined dispersive mode identical to that of an isolated 1D Heisenberg chain, and σ′(ω) loses its low‑frequency weight, with spectral weight shifted to a finite‑frequency hump. This behavior constitutes a non‑perturbative demonstration of a gauge‑mediated Kondo breakdown, i.e., an orbital‑selective Mott transition in which the f‑sector becomes insulating while the Dirac c‑electrons remain metallic.

A crucial consequence is the change of the Luttinger volume across the transition. In the heavy‑fermion phase the Luttinger count includes both conduction electrons and the localized spin degrees of freedom (large Fermi surface), whereas in the Kondo‑breakdown phase only the conduction electrons contribute (small Fermi surface). This aligns with the FL* picture where local moments decouple from the Fermi sea, and the violation of the conventional Luttinger theorem is tied to topological degeneracy of the emergent gauge sector.

The study showcases that a compact U(1) lattice‑gauge formulation enables direct computation of transport properties of the composite fermion, something not accessible in earlier DQMC work on conventional Kondo lattice models. The authors argue that the approach opens the door to larger‑scale simulations (e.g., using Hybrid Monte‑Carlo for gauge fields) and to investigations of critical behavior in both Kondo‑breakdown and magnetic ordering transitions in dimensionally mismatched Kondo systems. Overall, the paper provides a controlled, sign‑problem‑free numerical demonstration of Kondo breakdown, identifies clear spectroscopic and transport fingerprints of an orbital‑selective Mott transition, and establishes a versatile framework for future studies of gauge‑theoretic heavy‑fermion physics.