SU(N) Heisenberg model with multi-column representations

Abstract

The $\mathrm{SU}(N)$ symmetric antiferromagnetic Heisenberg model with multi-column representations on the two-dimensional square lattice is investigated by quantum Monte Carlo simulations. For the representation of Young diagram with two columns, we confirm that a valence-bond solid order appears as soon as the Néel order disappears at $N=10$ indicating no intermediate phase. In the case of the representation with three columns, there is no evidence for both of the Néel and the valence-bond solid ordering for $N\ge 15$. This is actually consistent with the large-$N$ theory, which predicts that the VBS state immediately follows the Néel state, because the expected spontaneous order is too weak to be detected.

5 pages, 5 figures

References in corpus (8)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Fate of CP(N-1) fixed points with q-monopoles
• Possibility of Deconfined Criticality in SU(N) Heisenberg Models at Small N
• Néel and Spin-Peierls ground states of two-dimensional SU(N) quantum antiferromagnets
• Ground States of the SU(N) Heisenberg Model

Cited by in corpus (8)

• Phase diagram and dynamics of the SU($\mathbf{N}$) symmetric Kondo lattice model
• Structure of Spin Correlations in High Temperature SU($N$) Quantum Magnets
• Spin-$S$ designer hamiltonians and the square lattice $S=1$ Haldane nematic
• Resummation-based updates for Stochastic Series Expansion Quantum Monte Carlo
• Critical exponents of nonlinear sigma model on Grassmann manifold $U(N)/U(m)U(N-m)$ by $1/N$ expansion
• Transition from band insulator to Mott insulator and formation of local moment in half-filled ionic SU($N$) Hubbard model
• Nematic Antiferromagnetism and Deconfined Criticality from the Interplay between Electron-Phonon and Electron-Electron Interactions
• Competition between Neel, Haldane nematic, plaquette valence bond solid, and $(\pi ,\pi )$ valence bond solid phases in SU(N) analogs of $S=1$ square-lattice antiferromagnets