The J1-J2 model: First order phase transition versus deconfinement of spinons

TL;DR

This paper investigates the nature of the phase transition in the 2D J1-J2 antiferromagnetic Heisenberg model, providing evidence that it is a first order transition and analyzing the likely valence bond solid pattern.

Contribution

It offers a new method to detect first order phase transitions and clarifies the nature of the transition and VBS pattern in the J1-J2 model.

Findings

Transition is most likely first order based on series expansion and spin-wave theory.

Columnar dimerization pattern is the most probable VBS state.

Proposed method for detecting first order transitions is highly sensitive.

Abstract

We revisit the phase transition from the N\'eel ordered to a valence bond solid (VBS) state in the two-dimensional $J_1-J_2$ antiferromagnetic Heisenberg model. In the first part we address the question whether or not this transition could be an example of a second order phase transition due to a deconfinement of spinons. We give arguments based on series expansion and spin-wave theory that this is not the case and the transition is most likely first order. The method proposed here to detect first order phase transitions seems to be very sensitive and might be useful in other models as well. In the second part we analyze possible VBS patterns in the magnetically disordered phase based on numerical data for different susceptibilities, obtained in the ordered phase, which test the breaking of lattice symmetries. We conclude that a columnar dimerization pattern is the most likely candidate.