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Motivated by the recent discovery of an intermediate quantum critical phasebetween the antiferromagnetic order and the Fermi liquid in the frustratedKondo lattice CePdAl, we study here a Kondo-Heisenberg chain with frustrated$J_1$-$J_2$ XXZ interactions among local spins using the density matrixrenormalization group method. Our simulations reveal a global phase diagramwith rich ground states including the antiferromagnetic order, thevalence-bond-solid and bond-order-wave orders, the pair density wave state, theuniform superconducting state, and the Luttinger liquid state. We show thatboth the pair density wave and uniform superconductivity belong to the familyof Luther-Emery liquids and may arise from pair instability of an intermediatequantum critical phase with medium Fermi volume in the presence of strongquantum fluctuations, while the Luttinger liquid has a large Fermi volume. Thissuggests a deep connection between the pair density wave, the unconventionalsuperconductivity, and the non-Fermi liquid quantum critical phase.

Pair density wave, unconventional superconductivity, and non-Fermi liquid quantum critical phase in frustrated Kondo lattice