We study a family of frustrated anti-ferromagnetic spin-$S$ systems with a fully dimerized ground state. This state can be exactly obtained without the need to include any additional three-body interaction in the model. The simplest members of the fa
mily can be used as a building block to generate more complex geometries like spin tubes with a fully dimerized ground state. After present some numerical results about the phase diagram of these systems, we show that the ground state is robust against the inclusion of weak disorder in the couplings as well as several kinds of perturbations, allowing to study some other interesting models as a perturbative expansion of the exact one. A discussion on how to determine the dimerization region in terms of quantum information estimators is also presented. Finally, we explore the relation of these results with a the case of the a 4-leg spin tube which recently was proposed as the model for the description of the compound Cu$_2$Cl$_4$D$_8$C$_4$SO$_2$, delimiting the region of the parameter space where this model presents dimerization in its ground state.
The phase diagram of a frustrated spin-$S$ zig-zag ladder is studied through different numerical and analytical methods. We show that for arbitrary $S$, there is a family of Hamiltonians for which a fully-dimerized state is an exact ground state, bei
ng the Majumdar-Ghosh point a particular member of the family. We show that the system presents a transition between a dimerized phase to a Neel-like phase for $S=1/2$, and spiral phases can appear for large $S$. The phase diagram is characterized by means of a generalization of the usual Mean Field Approximation (MFA). The novelty in the present implementation is to consider the strongest coupled sites as the unit cell. The gap and the excitation spectrum is analyzed through the Random Phase Approximation (RPA). Also, a perturbative treatment to obtain the critical points is discussed. Comparisons of the results with numerical methods like DMRG are also presented.
Quantum Dimer Models (QDM) arise as low energy effective models for frustrated magnets. Some of these models have proven successful in generating a scenario for exotic spin liquid phases with deconfined spinons. Doping, i.e. the introduction of mobil
e holes, has been considered within the QDM framework and partially studied. A fundamental issue is the possible existence of a superconducting phase in such systems and its properties. For this purpose, the question of the statistics of the mobile holes (or holons) shall be addressed first. Such issues are studied in details in this paper for generic doped QDM defined on the most common two-dimensional lattices (square, triangular, honeycomb, kagome,...) and involving general resonant loops. We prove a general statistical transmutation symmetry of such doped QDM by using composite operators of dimers and holes. This exact transformation enables to define duality equivalence classes (or families) of doped QDM, and provides the analytic framework to analyze dynamical statistical transmutations. We discuss various possible superconducting phases of the system. In particular, the possibility of an exotic superconducting phase originating from the condensation of (bosonic) charge-e holons is examined. A numerical evidence of such a superconducting phase is presented in the case of the triangular lattice, by introducing a novel gauge-invariant holon Greens function. We also make the connection with a Bose-Hubbard model on the kagome lattice which gives rise, as an effective model in the limit of strong interactions, to a doped QDM on the triangular lattice.
We investigate the magnetic properties of quasi-one-dimensional quantum spin-S antiferromagnets. We use a combination of analytical and numerical techniques to study the presence of plateaux in the magnetization curve. The analytical technique consis
ts in a path integral formulation in terms of coherent states. This technique can be extended to the presence of doping and has the advantage of a much better control for large spins than the usual bosonization technique. We discuss the appearance of doping-dependent plateaux in the magnetization curves for spin-S chains and ladders. The analytical results are complemented by a density matrix renormalization group (DMRG) study for a trimerized spin-1/2 and anisotropic spin-3/2 doped chains.
We describe a new mechanism leading to the formation of rational magnetization plateau phases, which is mainly due to the anharmonic spin-phonon coupling. This anharmonicity produces plateaux in the magnetization curve at unexpected values of the mag
netization without explicit magnetic frustration in the Hamiltonian and without an explicit breaking of the translational symmetry. These plateau phases are accompanied by magneto-elastic deformations which are not present in the harmonic case.
In the present paper we extend the method to detect Pomeranchuk instabilities in lattice systems developed in previous works to study more general situations. The main result presented here is the extension of the method to include finite temperature
effects, which allows to compute critical temperatures as a function of interaction strengths and density of carriers. Furthermore, it can be applied to multiband problems which would be relevant to study systems with spin/color degrees of freedom. Altogether, the present extended version provides a potentially powerful technique to investigate microscopic realistic models relevant to e.g. the Fermi liquid to nematic transition extensively studied in connection with different materials such as cuprates, ruthenates, etc.
In the present paper we study the phase diagram of the Heisenberg model on the honeycomb lattice with antiferromagnetic interactions up to third neighbors along the line $J_2=J_3$ that include the point $J_2=J_3=J_1/2$, corresponding to the highly fr
ustrated point where the classical ground state has macroscopic degeneracy. Using the Linear Spin-Wave, Schwinger boson technique followed by a mean field decoupling and exact diagonalization for small systems we find an intermediate phase with a spin gap and short range Neel correlations in the strong quantum limit (S=1/2). All techniques provide consistent results which allow us to predict the existence of a quantum disordered phase, which may have been observed in recent high-field ESR measurements in manganites.
The two-dimensional Hubbard model on the square lattice is studied in the presence of lattice distortions in the adiabatic approximation. The self energy is computed within perturbation theory up to second order, which provides a way for studying the
quasiparticle dispersion. We compute numerically the second order contribution to the self-energy using a standard Fast Fourier Transform Algorithm for finite system sizes. The stability of the lattice distortions is investigated and a schematic phase diagram is drawn. The Fermi surface is analyzed for densities near to half filling, the presence of lattice distortion change some spectral properties of the model and gives an anisotropic interacting FS. The spectral function is calculated along several lines in momentum space and the renormalized quasiparticle dispersion is obtained. The behavior of the density of states is shown for different values of the intrasite repulsion U in the different phases.
We develop a procedure for detecting Fermi liquid instabilities by extending the analysis of Pomeranchuk to two-dimensional lattice systems. The method is very general and straightforward to apply, thus providing a powerful tool for the search of exo
tic phases. We test it by applying it to a lattice electron model with interactions leading to $s$ and d-wave instabilities.
