We consider the easy-plane limit of bipartite $\mathrm{SU}(N$ ) Heisenberg Hamiltonians, which have a fundamental representation on one sublattice and the conjugate to fundamental on the other sublattice. For $N=2$ the easy plane limit of the SU(2) Heisenberg model is the well-known quantum $XY$ model of a lattice superfluid. We introduce a logical method to generalize the quantum $XY$ model to arbitrary $N$ , which keeps the Hamiltonian sign-free. We show that these quantum Hamiltonians have a world-line representation as the statistical mechanics of certain tightly packed loop models of $N$ colors in which neighboring loops are disallowed from having the same color. In this loop representation we design an efficient Monte Carlo cluster algorithm for our model. We present extensive numerical results for these models on the two dimensional square lattice, where we find the nearest neighbor model has superfluid order for $N\ensuremath{\le}5$ and valence-bond order for $N>5$ . By introducing $\mathrm{SU}(N$ ) easy-plane symmetric four-spin couplings we are able to tune across the superfluid-VBS phase boundary for all $N\ensuremath{\le}5$. We present clear evidence that this quantum phase transition is first order for $N=2$ and $N=5$ , suggesting that easy-plane deconfined criticality runs away generically to a first-order transition for small $N$ .We consider the easy-plane limit of bipartite $\mathrm{SU}(N$) Heisenberg Hamiltonians, which have a fundamental representation on one sublattice and the conjugate to fundamental on the other sublattice. For $N=2$ the easy plane limit of the SU(2) Heisenberg model is the well-known quantum $XY$ model of a lattice superfluid. We introduce a logical method to generalize the quantum $XY$ model to arbitrary $N$, which keeps the Hamiltonian sign-free. We show that these quantum Hamiltonians have a world-line representation as the statistical mechanics of certain tightly packed loop models of $N$ colors in which neighboring loops are disallowed from having the same color. In this loop representation we design an efficient Monte Carlo cluster algorithm for our model. We present extensive numerical results for these models on the two dimensional square lattice, where we find the nearest neighbor model has superfluid order for $N\ensuremath{\le}5$ and valence-bond order for $N>5$. By introducing $\mathrm{SU}(N$) easy-plane symmetric four-spin couplings we are able to tune across the superfluid-VBS phase boundary for all $N\ensuremath{\le}5$. We present clear evidence that this quantum phase transition is first order for $N=2$ and $N=5$, suggesting that easy-plane deconfined criticality runs away generically to a first-order transition for small $N$.

arXiv:1512.05082Physical review. B./Physical review. BFeb 3, 201621 citations

Logarithmic singularities in the susceptibility of the antiferromagnetic SU(N) Heisenberg model

P. Schlottmann

We consider the integrable SU(N)-invariant Heisenberg model in one dimension with degrees of freedom in the symmetric rank-m tensor representation. It is shown that for antiferromagnetic coupling the zero-temperature susceptibility to an arbitrary field breaking the SU(N) invariance of the internal degrees of freedom has logarithmic singularities as the field tends to zero. The logarithms arise from the interference of the two ``Fermi points'' of the spin-wave spectrum and do not depend on the level splitting scheme. These properties hold for a variety of models, e.g., the SU(N)-invariant Heisenberg chain of spin S=(N-1)/2, the Babujian-Takhtajan model, the N-component fermion gas interacting in one dimension by a repulsive \ensuremath{\delta}-function potential, the N-component supersymmetric t-J model in one dimension, the Gross-Neveu model, and the SU(N) generalization of the Hubbard chain.We consider the integrable SU(N)-invariant Heisenberg model in one dimension with degrees of freedom in the symmetric rank-m tensor representation. It is shown that for antiferromagnetic coupling the zero-temperature susceptibility to an arbitrary field breaking the SU(N) invariance of the internal degrees of freedom has logarithmic singularities as the field tends to zero. The logarithms arise from the interference of the two ``Fermi points'' of the spin-wave spectrum and do not depend on the level splitting scheme. These properties hold for a variety of models, e.g., the SU(N)-invariant Heisenberg chain of spin S=(N-1)/2, the Babujian-Takhtajan model, the N-component fermion gas interacting in one dimension by a repulsive \ensuremath{\delta}-function potential, the N-component supersymmetric t-J model in one dimension, the Gross-Neveu model, and the SU(N) generalization of the Hubbard chain.

Physical review. B, Condensed matterMar 1, 199220 citations

We consider the easy-plane limit of bipartite

\mathrm{SU}(N

) Heisenberg Hamiltonians, which have a fundamental representation on one sublattice and the conjugate to fundamental on the other sublattice. For

N=2

the easy plane limit of the SU(2) Heisenberg model is the well-known quantum

XY

model of a lattice superfluid. We introduce a logical method to generalize the quantum

XY

model to arbitrary

N

, which keeps the Hamiltonian sign-free. We show that these quantum Hamiltonians have a world-line representation as the statistical mechanics of certain tightly packed loop models of

N

colors in which neighboring loops are disallowed from having the same color. In this loop representation we design an efficient Monte Carlo cluster algorithm for our model. We present extensive numerical results for these models on the two dimensional square lattice, where we find the nearest neighbor model has superfluid order for $N\ensuremath{\le}5$ and valence-bond order for

N>5

. By introducing

\mathrm{SU}(N

) easy-plane symmetric four-spin couplings we are able to tune across the superfluid-VBS phase boundary for all $N\ensuremath{\le}5$. We present clear evidence that this quantum phase transition is first order for

N=2

and

N=5

, suggesting that easy-plane deconfined criticality runs away generically to a first-order transition for small

N