Probing universal critical scaling with scan-DMRG

Abstract

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, 3-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 non-magnetic 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.

11 pages, 12 figures

References in corpus (11)

• The density-matrix renormalization group in the age of matrix product states
• Universal adiabatic dynamics across a quantum critical point
• Connecting distant ends of one-dimensional critical systems by a sine-square deformation
• Front dynamics and entanglement in the XXZ chain with a gradient
• Phase Transition in Space: How Far Does a Symmetry Bend Before It Breaks?
• MERA for Spin Chains with Continuously Varying Criticality
• Lifshitz point at commensurate melting of 1D Rydberg atoms
• Spontaneous dimerization, critical lines, and short-range correlations in a frustrated spin-1 chain
• Comment on "Frustration and Multicriticality in the Antiferromagnetic Spin-1 Chain"
• Adiabatic dynamics of an inhomogeneous quantum phase transition: the case of z > 1 dynamical exponent
• Gradient critical phenomena in the Ising quantum chain: surface behaviour