Exploring phase transitions by finite-entanglement scaling of MPS in the 1D ANNNI model

Abstract

We use the finite-entanglement scaling of infinite matrix product states (iMPS) to explore supposedly infinite order transitions. This universal method may have lower computational costs than finite-size scaling. To this end, we study possible MPS-based algorithms to find the ground states of the transverse axial next-nearest-neighbor Ising (ANNNI) model in a spin chain with first and second neighbor interactions and frustration. The ground state has four distinct phases with transitions of second order and one of supposedly infinite order, the Kosterlitz-Thouless transition. To explore phase transitions in the model, we study general quantities such as the correlation length, entanglement entropy and the second derivative of the energy with respect to the external field, and test the finite-entanglement scaling. We propose a scaling ansatz for the correlation length of a non-critical system in order to explore infinite order transitions. This method provides considerably less computational costs compared to the finite-size scaling method in [8], and quantities obtained by applying fixed boundary conditions (such as domain wall energy in [8]) are omitted. The results show good agreement with previous studies of finite-size scaling using DMRG.

References in corpus (8)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• The iTEBD algorithm beyond unitary evolution
• Scaling of entanglement support for Matrix Product States
• Strings, Projected Entangled Pair States, and variational Monte Carlo methods
• The Quantum Transverse Field Ising Model on an Infinite Tree from Matrix Product States
• Evidence for a floating phase of the transverse ANNNI model at high frustration
• Floating Phase in 1D Transverse ANNNI Model

Cited by in corpus (5)

• Study of the phase diagram of the Kitaev-Hubbard chain
• Noise-Robust Detection of Quantum Phase Transitions
• Quantum phase transition as an interplay of Kitaev and Ising interactions
• Edge modes in a frustrated quantum Ising chain
• Quantum Liang Information Flow Probe of Causality across Critical Points