SU($\mathbf{N}$) Kondo-Heisenberg chain: Phase diagram, Ising criticality, and the coexistence of heavy quasiparticles and valence bond solid order

Abstract

We map out the ground state phase diagram of a one-dimensional SU($N$) Kondo-Heisenberg lattice model at half filling and in the fully antisymmetric self-adjoint representation as a function of $\frac{1}{N}$ and Kondo coupling $J_k/t$. On the basis of auxiliary field quantum Monte Carlo (QMC) simulations with even $N$ up to 8, we show that the enlarged SU($N\ge 4$) symmetry realizes a quantum phase transition separating a valence bond solid (VBS) phase occupying a weak coupling part of the phase diagram and the Kondo insulator (KI) state dominating in the strong $J_k/t$ limit. Along the phase boundary, we always observe critical exponents that belong to a two-dimensional classical Ising universality class. We next trace the evolution of the composite fermion and spin spectral functions across the phase boundary and conclude that VBS order triggers a bond order wave state of conduction electrons, both coexisting with Kondo screening. Upon further reducing $J_k/t$ we observe that composite quasiparticles lose their spectral weight indicating that VBS order gradually liberates localized $f$ spins from forming Kondo singlets with conduction electron spins. We contrast the QMC results with a static large-$N$ approximation, and we show that in the limit of infinite degeneracy $N\to \infty$ the order-disorder transition becomes of first order and is accompanied by a full decoupling of conduction electrons and localized $f$ spins. We complete our analysis by considering the limit of a vanishing Heisenberg coupling $J_h=0$, and we provide evidence that the enlarged SU($N$) symmetry and low dimensionality of the RKKY exchange interaction are not sufficient to induce VBS order in the conventional SU($N$) Kondo chain which hosts solely a KI phase.

26 pages, 23 figures; comment on the validity of the large-N approach in the finite N case added

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Cited by in corpus (1)

• Lieb-Schultz-Mattis constraints for the insulating phases of the one-dimensional SU($N$) Kondo lattice model