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

TL;DR

This paper introduces a finite-entanglement scaling method using iMPS to efficiently explore phase transitions, including infinite order ones, in the 1D ANNNI model, reducing computational costs compared to traditional finite-size scaling.

Contribution

It develops a universal finite-entanglement scaling approach for studying phase transitions, especially infinite order transitions, in the ANNNI model with lower computational costs.

Findings

Successfully identified phase transitions including the Kosterlitz-Thouless transition.

Demonstrated good agreement with previous finite-size scaling results.

Proposed a new scaling ansatz for correlation length in non-critical systems.

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.