Only 3% hole doping by Li is sufficient to suppress the long-range 3-dimensional (3D) antiferromagnetic order in La2CuO4. The spin dynamics of such a 2D spin liquid state at T ≪ J was investigated with measurements of the dynamic magnetic structure factor S(ω, q), using cold neutron spectroscopy, for single crystalline La2Cu0.94Li0.06O4. S(ω, q) peaks sharply at (π, π) and crosses over around 50 K from ω/T scaling to a novel low temperature regime characterized by a constant energy scale. The possible connection to a crossover from the quantum critical to the quantum disordered regime of the 2D antiferromagnetic spin liquid is discussed.The experimental investigation of the spin dynamics of doped Heisenberg antiferromagnets on a square lattice is essential to understanding cuprate superconductors, as well as to current research on quantum phase transitions [1]. For the structurally simplest laminar cuprate, La 2 CuO 4 , the 3-dimensional (3D) antiferromagnetic Néel order due to weak interlayer magnetic interaction can be suppressed by 2-3% hole doping using Sr, Ba or Li, thus allowing experimental investigation of the quantum spin dynamics of a 2-dimensional (2D) spin liquid in a wide temperature range, 0At the critical doping concentration, y c , of La 2 CuO 4 and at T = 0, namely at the quantum critical point, spin dynamics is described by classical critical dynamics in 2+1 dimensions [2]. At a finite temperature, the extra dimension in imaginary time is reduced to a finite thickness ofhc/k B T , where c is the spin wave velocity. As a consequence of this long wavelength cutoff, spin dynamics follows the quantum criticalhω/k B T scaling [3]. This has been experimentally observed in Ba and Sr doped La 2 CuO 4 in previous inelastic neutron scattering studies [4,5,6]. At T = 0 and above the critical doping concentration y > y c , zero-point quantum fluctuations set another long wavelength cutoff. Therefore, for y > y c , when the thermal cutoff length,hc/k B T , reaches the quantum cutoff during cooling, a crossover in spin dynamics from the quantum critical (QC) regime, where the energy scale is k B T , to the quantum disordered (QD) regime, where the energy scale is fixed at infrared by the quantum cutoff, occurs [2,3]. This crossover, however, has not been explicitly investigated experimentally. Here, we report a cold neutron inelastic scattering study on spin dynamics in Li doped La 2 CuO 4 from 150 K to 1.5 K. A crossover from the ω/T scaling to a new low temperature regime, which features an infrared energy cutoff, is directly observed.The critical doping concentration, y c , for Li doped La 2 CuO 4 is 3% [7,8]. In this study, a y=6% single crystal, La 2 Cu 0.94 Li 0.06 O 4 , weighing 2.1 g, was grown in CuO flux, using isotopically enriched 7 Li (98.4%) to reduce neutron absorption of natural Li. The crystal has orthorhombic Cmca symmetry with lattice parameters a = 5.351Å, b = 13.15Å and c = 5.386Å at 295 K. Using this orthorhombic unit cell to label reciprocal q space, the (π, π) point in the square latt...