Department of Physics
Condensed Matter Seminar

A spin-1/2 square-lattice Heisenberg model including a particular 4-spin interaction, the "J-Q" model, undergoes a quantum phase transition from the Neel state into a valence-bond-solid (VBS) state. The model can be studied using quantum Monte Carlo simulations on large lattices without sign problems, thus allowing detailed unbiased studies. An interesting aspect of the phase transition is the nature of the VBS order-parameter fluctuations close to the critical point. The quantum fluctuations affect not only the amplitude of the order parameter, but also its "angle" characterizing the type of VBS; columnar or plaquette. These fluctuations are surprisingly strong aven rather deep inside the VBS state, reflecting a length-scale which diverges faster than the correlation length. This is in qualitative agreement with the recent theory of "deconfined" quantum critical points, which predicts emergence of U(1) symmetry in the VBS state close to the transition. I will discuss the Neel-VBS quantum phase transition, the nature of the VBS fluctuations, and attempts to extract the exponent governing the emergence of U(1) symmetry. I will also briefly mention other systems in which similar phase transitions can be studied.