Full characterization of the quantum linear-zigzag transition in atomic chains

TL;DR

This paper provides a detailed numerical analysis of the quantum linear-zigzag transition in atomic chains, confirming its universality class as the critical Ising model and demonstrating its relevance for simulating quantum critical phenomena.

Contribution

It offers the first high-precision numerical confirmation that the quantum linear-zigzag transition belongs to the Ising universality class, using DMRG analysis.

Findings

Critical exponents match Ising model predictions

Central charge consistent with conformal field theory

Structural instabilities can simulate quantum critical phenomena

Abstract

A string of repulsively interacting particles exhibits a phase transition to a zigzag structure, by reducing the transverse trap potential or the interparticle distance. The transition is driven by transverse, short wavelength vibrational modes. Based on the emergent symmetry Z_2 it has been argued that this instability is a quantum phase transition, which can be mapped to an Ising model in transverse field. We perform an extensive Density Matrix Renormalization Group analysis of the behaviour at criticality and evaluate the critical exponents and the central charge with high precision. We thus provide strong numerical evidence confirming that the quantum linear-zigzag transition belongs to the critical Ising model universality class. These results show that structural instabilities of one-dimensional interacting atomic arrays can simulate quantum critical phenomena typical of ferromagnetic systems.