Evidence for Columnar Order in the Fully Frustrated Transverse Field Ising Model on the Square Lattice

Using extensive classical and quantum Monte Carlo simulations, we investigate the ground-state phase diagram of the fully frustrated transverse field Ising model on the square lattice. We show that pure columnar order develops in the low-field phase above a surprisingly large length scale, below which an effective U(1) symmetry is present. The same conclusion applies to the quantum dimer model with purely kinetic energy, to which the model reduces in the zero-field limit, as well as to the stacked classical version of the model. By contrast, the 2D classical version of the model is shown to develop plaquette order. Semiclassical arguments show that the transition from plaquette to columnar order is a consequence of quantum fluctuations.

Exotic phases of quantum frustrated magnets

Julien Dorier

In this work, we study two examples of frustrated magnetic systems whose degrees of freedom are spins (or pseudo-spins) on two-dimensional lattices. The first part presents the results obtained for the quantum compass model on a square lattice. This model is a minimal model for the orbital degrees of freedom of transition metal compounds. We use exact diagonalizations, quantum Monte Carlo simulations as well as a perturbative approach in order to study the ground state degeneracy in the thermodynamic limit and the type of order in the ground state. The second part of this work is devoted to the study of the magnetic properties of SrCu2(BO3)2, which is one of the few quasi two-dimensional quantum magnets whose magnetization curve as a function of the magnetic field shows plateaus. The magnetic degrees of freedom are described by a spin 1/2 Heisenberg model on the Shastry-Sutherland lattice in the presence of an external magnetic field. In order to study the magnetic properties at zero-temperature, we use perturbative continuous unitary transformations to derive an effective Hamiltonian in which the triplets Sz = 1 are particles moving on a background of singlets. This Hamiltonian is characterized by a kinetic energy dominated by correlated hopping, which let a particle hop only if there is another particle nearby. In order to better understand the effect of the correlated hopping, we start by studying a minimal model. By using exact diagonalizations, quantum Monte Carlo and a semi-classical approximation we show that the correlated hopping can stabilize a phase characterized by a condensation of pairs of particles and strongly favor supersolid phases. Next, we determine the zero-temperature phase diagram of the effective model by using a classical approximation. A comparison to previous theoretical works and experimental measurements shows that the Shastry-Sutherland model cannot reproduce the series of magnetization plateaus measured experimentally. This suggest that the residual interactions, which were neglected, could be crucial for SrCu2(BO3)2.

EPFL2008

Supersolid phase induced by correlated hopping in spin-1/2 frustrated quantum magnets

Julien Dorier, Frédéric Mila

We show that correlated hopping of triplets, which is often the dominant source of kinetic energy in dimer-based frustrated quantum magnets, produces a remarkably strong tendency to form supersolid phases in a magnetic field. These phases are characterized by simultaneous modulation and ordering of the longitudinal and transverse magnetization, respectively. Using quantum Monte Carlo and a semiclassical approach for an effective hard-core boson model with nearest-neighbor repulsion on a square lattice, we prove, in particular, that a supersolid phase can exist even if the repulsion is not strong enough to stabilize an insulating phase at half-filling. Experimental implications for frustrated quantum antiferromagnets in a magnetic field at zero and finite temperature are discussed.

2008

Semiclassical approach to ground-state properties of hard-core bosons in two dimensions

Tommaso Coletta, Nicolas Laflorencie, Frédéric Mila

Motivated by some inconsistencies in the way quantum fluctuations are included beyond the classical treatment of hard-core bosons on a lattice in the recent literature, we revisit the large-S semiclassical approach to hard-core bosons on the square lattice at T = 0. First of all, we show that, if one stays at the purely harmonic level, the only correct way to get the 1/S correction to the density is to extract it from the derivative of the ground-state energy with respect to the chemical potential, and that to extract it from a calculation of the ground-state expectation value of the particle number operator, it is necessary to include 1/root S corrections to the harmonic ground state. Building on this alternative approach to get 1/S corrections, we provide the first semiclassical derivation of the momentum distribution, and we revisit the calculation of the condensate density. The results of these as well as other physically relevant quantities such as the superfluid density are systematically compared to quantum Monte Carlo simulations. This comparison shows that the logarithmic corrections in the dilute Bose gas limit are only captured by the semiclassical approach if the 1/S corrections are properly calculated, and that the semiclassical approach is able to reproduce the 1/k divergence of the momentum distribution at k = 0. Finally, the effect of 1/S-2 corrections is briefly discussed.

2012

Exotic phases of quantum frustrated magnets

Julien Dorier

EPFL2008