Non-hermitian tricriticality in the Blume-Capel model with imaginary field

TL;DR

This paper investigates a non-Hermitian quantum spin chain model, revealing a new tricritical point associated with a non-unitary conformal field theory, expanding understanding of phase transitions in non-Hermitian systems.

Contribution

It identifies a novel tricritical point in a non-Hermitian spin model linked to a specific non-unitary conformal field theory, demonstrating complex phase behavior.

Findings

First ground-state level crossing leads to a Yang-Lee type transition.

Discovery of a line of tricriticality with three degenerate energy levels.

Spectrum analysis suggests universality class of ${ m M}_{2,7}$-conformal theory.

Abstract

Using finite-size-scaling methods, we study the quantum chain version of the spin-$1$-Blume-Capel model coupled to an imaginary field. The aim is to realize higher order non-unitary conformal field theories in a simple Ising-type spin model. We find that the first ground-state level crossing in the high-temperature phase leads to a second-order phase transition of the Yang-Lee universality class (central charge $c=-22/5$). The Yang-Lee transition region ends at a line of a new type of tricriticality, where the {\em three} lowest energy levels become degenerate. The analysis of the spectrum at two points on this line gives good evidence that this line belongs to the universality class of the ${\cal M}_{2,7}$-conformal theory with $c=-68/7$.