For many-particle systems defined on lattices we investigate the global structure of effective Hamiltonians and observables obtained by means of a suitable basis transformation. We study transformations which lead to effective Hamiltonians conserving the number of excitations. The same transformation must be used to obtain effective observables.The analysis of the structure shows that effective operators give rise to a simple and intuitive perspective on the initial problem. The systematic calculation of n-particle irreducible quantities becomes possible constituting a significant progress. Details how to implement the approach perturbatively for a large class of systems are presented.

We determine analytically the phase diagram of the toric code model in a parallel magnetic field which displays three distinct regions. Our study relies on two high-order perturbative expansions in the strong-and weak-field limit, as well as a large-spin analysis. Calculations in the topological phase establish a quasiparticle picture for the anyonic excitations. We obtain two second-order transition lines that merge with a first-order line giving rise to a multicritical point as recently suggested by numerical simulations. We compute the values of the corresponding critical fields and exponents that drive the closure of the gap. We also give the one-particle dispersions of the anyonic quasiparticles inside the topological phase.

The magnetization process of the orthogonal-dimer antiferromagnet SrCu2(BO3)2 is investigated in high magnetic fields of up to 118 T. A 1/2 plateau is clearly observed in the field range 84 to 108 T in addition to 1/8, 1/4, and 1/3 plateaus at lower fields. Using a combination of state-of-the-art numerical simulations, the main features of the high-field magnetization, a 1/2 plateau of width 24 T, a 1/3 plateau of width 34 T, and no 2/5 plateau, are shown to agree quantitatively with the Shastry-Sutherland model if the ratio of inter- to intradimer exchange interactions J'/J=0.63. It is further predicted that the intermediate phase between the 1/3 and 1/2 plateaus is not uniform but consists of a 1/3 supersolid followed by a 2/5 supersolid and possibly a domain-wall phase, with a reentrance into the 1/3 supersolid above the 1/2 plateau.

Spectral densities are computed in unprecedented detail for quantum antiferromagnetic spin 1/2 two-leg ladders. These results were obtained due to a major methodical advance achieved by optimally chosen unitary transformations. The approach is based on dressed integer excitations. Considerable weight is found at high energies in the two-particle sector. Precursors of fractional spinon physics occur supporting the conclusion that there is no necessity to resort to fractional excitations in order to describe features at higher energies.

We show that the spin liquid phase of the half-filled Hubbard model on the triangular lattice can be described by a pure spin model. This is based on a high-order strong coupling expansion (up to order 12) using perturbative continuous unitary transformations. The resulting spin model is consistent with a transition from three-sublattice long-range magnetic order to an insulating spin liquid phase, and with a jump of the double occupancy at the transition. Exact diagonalizations of both models show that the effective spin model is quantitatively accurate well into the spin liquid phase, and a comparison with the Gutzwiller projected Fermi sea suggests a gapless spectrum and a spinon Fermi surface. PACS numbers: 75.10.Jm, 75.10.Kt, 05.30.Rt Although the Hubbard model has been one of the central paradigms in the field of strongly correlated systems for about five decades, new aspects of its extremely rich phase diagram are regularly unveiled. Even at half-filling, the popular wisdom according to which the model has only two phases, a metallic one at weak coupling and an insulating one at strong coupling separated by a first order transition [1], has been recently challenged. This goes back to the work of Morita et al.[2] on the triangular lattice which revealed the presence of a non-magnetic insulating phase close to the metal-insulator transition using path integral renormalization group. Further evidence in favour of a phase transition inside the insulating phase has been reported using a variety of theoretical tools [3][4][5][6]. More recently, an intermediate spin liquid (SL) phase has also been identified on the honeycomb lattice using Quantum Monte Carlo simulations [7].The precise nature of the SL phase of the Hubbard model on the triangular lattice is of direct experimental relevance for the 2D organic salt κ-(BEDT-TTF) 2 Cu 2 (CN) 3 [8]. As such, it has already attracted a lot of attention, but fundamental questions such as the appropriate low-energy effective theory remain unanswered. Since the phase is insulating, an effective model where charge fluctuations are treated as virtual excitations should be possible. One step forward in this direction has been taken by Motrunich [9], who proposed to describe the SL phase with 4-spin interactions. However, whether a description in terms of a pure spin model is possible is far from obvious, in particular since there seems to be a jump in the double occupancy at the transition from the three-sublattice Néel phase to the SL [2,6].In this Letter, we show that the correct low-energy theory of both insulating phases, and in particular of the SL phase, is indeed a pure spin model. This has been achieved by deriving an effective spin model to very high order about the strong coupling limit using perturbative continuous unitary transformations (PCUTs), and by showing that it gives a qualitative and quantitative account of the transition from the three-sublattice magnetic order to the SL state. This description gives deep insight into the nature of the SL phase and ...