Probing universal critical scaling with scan density matrix renormalization group

We explore the universal signatures of quantum phase transitions that can be extracted with the density matrix renormalization group (DMRG) algorithm applied to quantum chains with a gradient. We present high-quality data collapses for the order parameter and for the entanglement entropy for three minimal models: transverse-field Ising, three-state Potts, and Ashkin-Teller. Furthermore, we show that scan-DMRG successfully captures the universal critical scaling when applied across the magnetic Wess-Zumino-Witten and nonmagnetic Ising transitions in the frustrated Haldane chain. In addition, we report a universal scaling of the lowest excitation energy as a function of a gradient rate. Finally, we argue that the scan-DMRG approach has significantly lower computational cost compare to the conventional DMRG protocols to study quantum phase transitions.