Simplex solids in SU(N) Heisenberg models on the kagome and checkerboard lattices

We present a numerical study of the SU(N) Heisenberg model with the fundamental representation at each site for the kagome lattice (for N = 3) and the checkerboard lattice (for N = 4), which are the line graphs of the honeycomb and square lattices and thus belong to the class of bisimplex lattices. Using infinite projected entangled-pair states and exact diagonalizations, we show that in both cases the ground state is a simplex solid state with a twofold degeneracy, in which the N spins belonging to a simplex (i.e., a complete graph) form a singlet. Theses states can be seen as generalizations of valence bond solid states known to be stabilized in certain SU(2) spin models.

Three-sublattice order in the SU(3) Heisenberg model on the square and triangular lattice

Frédéric Mila, Karlo Penc

We present a numerical study of the SU(3) Heisenberg model of three-flavor fermions on the triangular and square lattice by means of the density-matrix renormalization group and infinite projected entangled-pair states. For the triangular lattice we confirm that the ground state has a three-sublattice order with a finite ordered moment which is compatible with the result from linear flavor wave theory (LFWT). The same type of order has recently been predicted also for the square lattice [T. A. Toth et al., Phys. Rev. Lett. 105, 265301 (2010)] from LFWT and exact diagonalization. However, for this case the ordered moment cannot be computed based on LFWT due to divergent fluctuations. Our numerical study clearly supports this three-sublattice order, with an ordered moment of m = 0.2-0.4 in the thermodynamic limit.

2012

Intermediate magnetization plateaus in the spin-1/2 Ising-Heisenberg and Heisenberg models on two-dimensional triangulated lattices

Jana Cisárová, Frédéric Alexis Michaud, Frédéric Mila

The ground state and zero-temperature magnetization process of the spin-1/2 Ising-Heisenberg model on two-dimensional triangles-in-triangles lattices are exactly calculated using eigenstates of the smallest commuting spin clusters. Our ground-state analysis of the investigated classical-quantum spin model reveals three unconventional dimerized or trimerized quantum ground states besides two classical ground states. It is demonstrated that the spin frustration is responsible for a variety of magnetization scenarios with up to three or four intermediate magnetization plateaus of either quantum or classical nature. The exact analytical results for the Ising-Heisenberg model are confronted with the corresponding results for the purely quantum Heisenberg model, which were obtained by numerical exact diagonalizations based on the Lanczos algorithm for finite-size spin clusters of 24 and 21 sites, respectively. It is shown that the zero-temperature magnetization process of both models is quite reminiscent, and hence, one may obtain some insight into the ground states of the quantum Heisenberg model from the rigorous results for the Ising-Heisenberg model even though exact ground states for the Ising-Heisenberg model do not represent true ground states for the pure quantum Heisenberg model. DOI: 10.1103/PhysRevB.87.054419

2013

A variational investigation of the SU(N) Heisenberg model in antisymmetric irreducible representations

Jérôme Dufour

Motivated by recent experimental progress in the context of ultra-cold multi-colour fermionic atoms in optical lattices, this thesis investigates the properties of the antiferromagnetic SU(N) Heisenberg models with fully antisymmetric irreducible representations labelled by a Young tableau with

m

boxes on each site of various lattices. Thanks to an intensive use of variational Monte Carlo method based on Gutzwiller projected fermionic wave functions, we aim to determine the ground state and its related properties of systems which are beyond the capabilities of other numerical methods. This typically means that we will study large lattices with many particles per site for

N>2

. The first part of this thesis will introduce the basic theoretical tools connected to the SU(N) Heisenberg model. A very short review of group theory introducing Young tableaux, will clarify the concept of fully antisymmetric irreducible representation of the SU(N) Lie algebra. Some properties of the Heisenberg model will be discussed and a mean-field solution will be given. The numerical methods used during this thesis and their limitations wil also be introduced. We will investigate the properties of 1-dimensional systems in the second part of this work. In particular, the chains have been studied for arbitrary

N

and

m

with non-abelian bosonisation leading to predictions about the nature of the ground state (gapped or critical) in most but not all cases. We have been able to verify these predictions for a representative number of cases with

N\leq10

and

m\leq N/2

, and we have shown that the opening of a gap is associated with a spontaneous dimerisation or trimerisation depending on the value of

m

and

N

. We have also investigated the marginal cases, where non-abelian bosonisation did not lead to any prediction. In these cases, variational Monte Carlo predicts that the ground state is critical with exponents that are consistent with conformal field theory. The other 1-dimensional system that has been studied is the ladder for which field-theory gives some predictions. For instance, the ground state of the SU(4) case in the fundamental irreducible representation is believed to consist of a 4-site plaquette state for any non-zero inter-leg coupling. We have confirmed the presence of this state, even if in the weak coupling regime, the optimal variational state is gapless. The study has been extended to various

N

and

m

values providing interesting results. The last part will present the results for 2-dimensional lattices. The square lattice will first be investigated. A mean-field analysis predicts a plaquette ground state for

3\leq N/m < 5

and of a chiral ground state for

N/m\geq 5

. By systematically studying the SU(3m) and SU(6m) Heisenberg model, we determined that the mean-field solution is valid even at small

m

(

m>1

for SU(3m) and

m>2

for SU(6m)). Then, for the SU(6m) Heisenberg model with

m

particles per site on a honeycomb lattice, we make the connection between the

m=1

case, for which the ground state has recently been shown to be in a plaquette singlet state, and the

m\rightarrow \infty

limit, where a mean-field approach has established that the ground state has chiral order. We were able to show that this system has a clear tendency toward the chiral order as soon as

m\geq 2

. This demonstrates that the chiral phase can be stabilised for not too large values of

m

, opening the way to its experimental realisations in other lattices. We will finally present results for the SU(3m) on the triangular lattice for which we find a plaquette state, when

m>1

EPFL2016