On $c=1$ critical phases in anisotropic spin-1 chains

TL;DR

This paper investigates c=1 critical phases in anisotropic spin-1 chains using analytical and numerical methods, confirming a Gaussian model description and clarifying the universality class of the multicritical point.

Contribution

It provides a detailed analysis of c=1 phases in spin-1 chains, demonstrating the adequacy of a Gaussian model and correcting previous assumptions about the multicritical point's universality class.

Findings

Quantitative agreement with theoretical predictions.

Gaussian model accurately describes low-energy physics.

Multicritical point differs from Takhtajan-Babujian universality class.

Abstract

Quantum spin-1 chains may develop massless phases in presence of Ising-like and single-ion anisotropies. We have studied c=1 critical phases by means of both analytical techniques, including a mapping of the lattice Hamiltonian onto an O(2) nonlinear sigma model, and a multi-target DMRG algorithm which allows for accurate calculation of excited states. We find excellent quantitative agreement with the theoretical predictions and conclude that a pure Gaussian model, without any orbifold construction, describes correctly the low-energy physics of these critical phases. This combined analysis indicates that the multicritical point at large single-ion anisotropy does not belong to the same universality class as the Takhtajan-Babujian Hamiltonian as claimed in the past. A link between string-order correlation functions and twisting vertex operators, along the c=1 line that ends at this point, is also suggested.