Hierarchical Data Format version 5 (HDF5) file contains both experimental and simulation data which reproduce figures and support findings of the study in the paper, “Realizing discontinuous quantum phase transitions in a strongly correlated driven optical lattice” (DOI: 10.1038/s41567-021-01476-w). See the paper for more details. Contact details: uws20@cam.ac.uk. --- Figures in the Main text --- Fig1 Schematic of the shaken lattice Fig1d-e: X: momentum in the y direction; Y: momentum in the x direction; Data: optical density (OD). (d) and (e) are the Mott insulator and the superfluid, respectively. Fig2 Simulated phase diagram of the shaken lattice Fid2a: X: shaking amplitude; Y: shaking frequency; Data: band-edge population; FirstOrderLine: shaking frequency (the second column) vs shaking amplitude (the first column). Fig2b: correlation length vs shaking frequency for the shaking amplitude A=1.5, 2.0, 3.0, 4.0 and 5.0nm. The first and second columns are shaking frequency and correlation length, respectively. Fig3 Sweeps across phase transitions and metastability Fig3a-d: X: shaking amplitude; Y: shaking frequency; Data: band-edge population. (a) and (b) are experimental and simulated band-edge populations following the direct sweeps, while (c) and (d) are experimental and simulated band-edge populations following the indirect sweeps. Fig4 Dynamics of phase transitions Fig4a-b: X: sweep duration; Y: momentum in the y direction; Data: momentum distributions in the y direction. (a) and (b) are the experiment and the theory, respectively. Fig4c: amplitudeExp: shaking amplitude (in the experimental curve); amplitudeTheo: shaking amplitude (in the theoretical curve); slopeExp: initial growth rate (in the experimental curve); slopeErrExp: error bars (in the experimental curve); slopeTheo: initial growth rate (in the theoretical curve). Fig4d: amplitude: shaking amplitude; slope: initial growth rate; slopeErr: error bars; dephasingLine: dephasing rate. --- Extended Data Figures in Methods --- FigM1 Single-particle correlations FigM1a: lowerCorr, lowerFit are one-body correlation (the second column) as a function of separation (the first column) in the lower band and its fit, respectively; upperCorr, upperFit are one-body correlation (the second column) vs separation (the first column) in the upper band and its fit, respectively. FigM1b-c: lowerCorrlen, lowerLutt are correlation length and Luttinger parameter (second columns) as a function of shaking frequency (first columns) in the lower band; upperCorrlen, upperLutt are correlation length and Luttinger parameter (second columns) as a function of shaking frequency (first columns) in the upper band. (b) and (c) are the shaking amplitude A=2.6 and 4nm, respectively. FigM2 Entanglement and central charge FigM2a: Von Neumann entanglement entropy (the second column) for the shaking frequency f=17.98,18.001,18.002,18.004 and 18.1kHz as a function of bipartition site (the first column); and their fits. FigM2b-f: CFT charge (the second column) vs shaking frequency (the first column) for the shaking amplitude A=2.6, 2.8, 3, 3.6 and 3.9nm. FigM3 Frequency modulation of lattice laser FigM3a: A: shaking amplitude; Al: modulation depth; t: time. FigM3b: f: shaking frequency; t: time. FigM3c: fl-fc: change of the laser frequency; s: displacement of the lattice; t: time. FigM4 Measured band-edge population after different sweep durations for different shaking amplitudes FigMa-b: forward and backward sweeps for different shaking amplitudes. The first and second columns for each dataset are sweep duration and band-edge population, respectively. FigM5 The band-edge population FigM5b-f: X: shaking amplitude; Y: Shaking frequency; Data: band-edge population. (b-f) are phase diagrams measured with the box size=0.1, 0.2, 0.4, 0.6 and 0.8 k0, respectively. --- Figures in Supplementary Information --- FigS1 Micromotion FigS1a_part1: X: momentum in the y direction; Y: momentum in the x direction; Data: optical density. Time-of-flight images are labeled in sequential order. FigS1a_part2: center of mass (the second column) vs sweep duration (the first column). FigS1b: fft: Fourier transform (the second column) vs frequency (the first column); vogitFit: a fit by a Voigt profile (the second column) vs frequency (the first column). FigS2 Dephasing of superfluid correlations FigS2: amplitude: shaking amplitude; slope: dephrasing rate; slopeErr: error bars; dephasingLine: average dephrasing rate. FigS3 Phase boundaries FigS3a: the first and second columns are shaking amplitude and frequency, respectively. A1, A2 and A3 are phase boundaries. FigS3b: phase boundaries (A1, A2 and A3) with lower error bars (A1ErrNeg, A2ErrNeg and A3ErrNeg) and upper error bars (A1ErrPos, A2ErrPos and A3ErrPos) as a function of inverse system size (invSysSize). FigS3c: difference between A1 and A3 (width) with lower error bars (widthErrNeg) and upper error bars (widthErrPos) as a function of inverse system size (invSysSize). FigS4 Evolution of ground state across phase transitions FigS4a: band populations in the upper and lower bands. The first and second columns are shaking frequency and band population, respectively. FigS4b: nearest-neighbor correlation (the second column) as a function of shaking frequency (the first column). FigS4c: band-edge population (the second column) as a function of shaking frequency (the first column). FigS4d: correlation lengths in the upper and lower bands. The first and second columns are shaking frequency and correlation length, respectively. FigS4e: number fluctuations in the upper and lower bands. The first and second columns are shaking frequency and number fluctuation, respectively. FigS4f: density correlation lengths in the upper and lower bands. The first and second columns are shaking frequency and density correlation length, respectively. FigS5 Simulation of an experimental sweep FigS5a: band population as a function of time in two-band and three-band models. The first and seconds column are time and band population, respectively. FigS5b: band-edge population in two-band and three-band models. The first and second columns are time and population, respectively. FigS5c: band energies (second columns in E1, E2 and E3) and occupations (second columns in N1, N2 and N3) as a function of quasimomentum (first columns). FigS5d: final quasimomentum occupations in two-band and three-band models. The first and second columns are quasimomentum and occupation, respectively. FigS5e-f: X: momentum in the y direction; Y: time; Data: normalized momentum distributions. (e) and (f) are the two-band and the three-band models. FigS6 Three-band vs two-band simulations FigS6a: third-band population (the second column) vs sweep duration (the first column) for shaking amplitude A=2.5, 5.8 and 9.6nm. FigS6b: band-edge populations in two-band and three-band models (second columns) vs sweep duration (first columns). FigS6c: heating in two-band and three-band models vs sweep duration (first columns).