The SU(N) Heisenberg model on the square lattice: a continuous-N quantum Monte Carlo study

TL;DR

This study uses a continuous-N quantum Monte Carlo method to investigate the SU(N) Heisenberg model on a square lattice, revealing a continuous phase transition between Neel and bond-ordered phases at a specific N value.

Contribution

It introduces a singlet projector algorithm that allows continuous variation of N in the SU(N) Heisenberg model, enabling detailed analysis of phase transitions.

Findings

Identifies a continuous phase transition at N_c=4.57(5).

Determines critical exponents z=1 and beta/nu=0.81(3).

Shows the transition is between Neel-ordered and crystalline bond-ordered phases.

Abstract

A quantum phase transition is typically induced by tuning an external parameter that appears as a coupling constant in the Hamiltonian. Another route is to vary the global symmetry of the system, generalizing, e.g., SU(2) to SU(N). In that case, however, the discrete nature of the control parameter prevents one from identifying and characterizing the transition. We show how this limitation can be overcome for the SU(N) Heisenberg model with the help of a singlet projector algorithm that can treat N continuously. On the square lattice, we find a direct, continuous phase transition between Neel-ordered and crystalline bond-ordered phases at Nc=4.57(5) with critical exponents z=1 and beta/nu=0.81(3).