Continuous phase transition between Néel and valence bond solid phases in a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>J</mml:mi><mml:mtext>−</mml:mtext><mml:mi>Q</mml:mi></mml:mrow></mml:math>-like spin ladder system
Takuhiro Ogino, Ryui Kaneko, Satoshi Morita, Shunsuke Furukawa, Naoki Kawashima
Abstract
We investigate a quantum phase transition between a N\'eel phase and a valence bond solid (VBS) phase, each of which breaks a different ${\mathbb{Z}}_{2}$ symmetry, in a spin-$1/2$ two-leg XXZ ladder with a four-spin interaction. The model can be viewed as a one-dimensional variant of the celebrated $J\text{\ensuremath{-}}Q$ model on a square lattice. By means of variational uniform matrix product state calculations and an effective field theory, we determine the phase diagram of the model and present evidence that the N\'eel-VBS transition is continuous and belongs to the Gaussian universality class with the central charge $c=1$. In particular, the critical exponents $\ensuremath{\beta},\ensuremath{\eta},$ and, $\ensuremath{\nu}$ are found to satisfy the constraints expected for a Gaussian transition within numerical accuracy. These exponents do not detectably change along the phase boundary while they are in general allowed to do so for the Gaussian class.