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

TL;DR

This work investigates a dimensionally mismatched Kondo lattice realized as a sign-problem-free U(1) lattice gauge theory, with a 1D spin chain coupled to 2D Dirac electrons. Using determinant quantum Monte Carlo and analytic continuation, the authors identify two symmetry-equivalent phases: a Kondo-coherent 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, consistent with an orbital-selective Mott transition. The study shows that the heavy-fermion Luttinger volume counts both composite and conduction electrons in the metallic phase, but only conduction electrons in the KB phase, providing a nonperturbative transport fingerprint of gauge-mediated Kondo breakdown. By computing the composite-fermion spectral function, dynamical spin structure factor, and optical conductivity, the work demonstrates how gauge fluctuations drive the transition and produce measurable signatures in transport and spectroscopic observables, advancing understanding of heavy-fermion criticality in lattice gauge settings.

Abstract

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.

Figures (10)

• Figure 1: Color map of the composite-fermion zero-frequency density of states $N_{\Psi}(\omega = 0)$ as a function of Kondo coupling $h$ and temperature $T$. Bright colors at small $h$ indicate a Kondo-coherent phase with large $N_{\Psi}$, while dark colors at large $h$ correspond to a Kondo breakdown(KB) phase with strongly suppressed composite quasi-particles.
• Figure 2: Composite-fermion spectral function $A_{\Psi}(k,\omega)$ at $\beta = 5$ for three representative values of the parameters $h$. For small $h$ (top panel), a clear hybridization low-energy band with substantial composite-fermion weight are visible, signalling the formation of heavy quasiparticles in the Kondo-coherent phase. Upon increasing $h$ (middle and bottom panels), the hybridization gradually disappears and the spectrum evolves into two separated, predominantly incoherent bands, indicating the destruction of the heavy quasiparticle band and the localization of the $f$ electrons characteristic of Kondo breakdown.
• Figure 3: Dynamical spin structure factor of the $f$ chain, $S_f(q,\omega)$, at $\beta = 5$ for three values of the parameter $h$. For small $h$ (top panel), the spin response is broad and continuum-like, consistent with itinerant magnetic correlations mediated by hybridized quasiparticles in the Kondo-coherent phase. As $h$ increases (middle and bottom panels), a well-defined dispersive mode emerges and closely follows the spectrum of an isolated one-dimensional Heisenberg chain, demonstrating the recovery of local-moment behavior and corroborating the interpretation of $f$-electron Mott localization in the Kondo-breakdown phase.
• Figure 4: Frequency dependence of the real part of the optical conductivity $\sigma'(\omega)$ of the composite-fermion chain at inverse temperature $\beta = 5$ for several values of the parameter $h$. For small $h$, the spectrum is dominated by a pronounced Drude-like peak at $\omega \approx 0$, indicating metallic transport carried by itinerant composite quasiparticles in the Kondo-coherent phase. Upon increasing $h$, the low-frequency weight and thus the Drude component are strongly suppressed, while spectral weight is transferred to a broad finite-frequency hump, signalling the onset of Mott-insulating behavior in the $f$ sector. This evolution of $\sigma'(\omega)$ with $h$ provides dynamical evidence for an orbital-selective Mott transition, while the Dirac $c$ electrons remain itinerant.
• Figure S1: Band structure of the one-dimensional tight-binding model for two sets of parameters. The dispersions are obtained by diagonalizing the Bloch Hamiltonian, and the color scale encodes the $f$-electron component of the $i$-th band at momentum $k$, quantified by $|U_{L+1,i}(k)|^{2}$; brighter (yellow) points correspond to states with larger $f$-electron weight. Left: $V = 1.0$, $J = 1.0$, $t = 1.0$. Right: $V = 0.5$, $J = 0.5$, $t = 1.0$.