Extended Ashkin-Teller transition in two coupled frustrated Haldane chains

We report an extremely rich ground-state phase diagram of two spin-1 Haldane chains frustrated with a three-site exchange and coupled by the antiferromagnetic Heisenberg interaction on a zigzag ladder. A particular feature of the phase diagram is the extended quantum phase transition in the Ashkin-Teller universality class that separates the plaquette phase, which spontaneously breaks translation symmetry, and the uniform disordered phase. The former is connected to the Haldane phase, stabilized by large interchain coupling, via the topological Gaussian transition. Upon decreasing the interchain interactions, this intermediate disorder phase vanishes, giving place to a dimerized phase separated from the plaquette phase on one side via a nonmagnetic Ising transition and from the Haldane phase on the other side by a topological weak first-order transition. Finally, in the limit of two decoupled chains, we recover a quantum critical point that corresponds to two copies of the Wess-Zumino-Witten <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>SU</a:mi> <a:msub> <a:mrow> <a:mo>(</a:mo> <a:mn>2</a:mn> <a:mo>)</a:mo> </a:mrow> <a:mn>2</a:mn> </a:msub> </a:mrow> </a:math> criticality with a total central charge <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>c</b:mi> <b:mo>=</b:mo> <b:mn>3</b:mn> </b:mrow> </b:math> .