Quantum phase transitions in multileg spin ladders with ring exchange

Four-spin exchange interaction has been raising intriguing questions regarding the exotic phase transitions it induces in two-dimensional quantum spin systems. In this context, we investigate the effects of a cyclic four-spin exchange in the quasi-1D limit by considering a general N-leg spin ladder. We show by means of a low-energy approach that, depending on its sign, this ring exchange interaction can engender either a staggered or a uniform dimerization from the conventional phases of spin ladders. The resulting quantum phase transition is found to be described by the SU(2)_N conformal field theory. This result, as well as the fractional value of the central charge at the transition, is further confirmed by a large-scale numerical study performed by means of Exact Diagonalization and Density Matrix Renormalization Group approaches for N \le 4

Three-Component Fermi Gas in a one-dimensional Optical Lattice

We investigate the effect of the anisotropy between the s-wave scattering lengths of a three-component atomic Fermi gas loaded into a one-dimensional optical lattice. We find four different phases which support trionic instabilities made of bound states of three fermions. These phases distinguish themselves by the relative phases between the 2$k_F$ atomic density waves fluctuations of the three species. At small enough densities or strong anisotropies we give further evidences for a decoupling and the stabilization of more conventional BCS phases. Finally our results are discussed in light of a recent experiment on $^{6}$Li atoms.Comment: 4 pages, published version. Experimental discussion has been extende

Combined analytical and numerical approach to magnetization plateaux in one-dimensional spin tube antiferromagnets

In this paper, we investigate the properties of frustrated three-leg spin tubes under a magnetic field. We concentrate on two kind of geometries for these tubes, one of which is relevant for the compound $\mathrm{[(CuCl_2tachH)_3Cl]Cl_2}$. We combine an analytical path integral approach with a strong coupling approach, as well as large-scale Density Matrix Renormalization Groups (DMRG) simulations, to identify the presence of plateaux in the magnetization curve as a function of the value of spin $S$. We also investigate the issue of gapless non-magnetic excitations on some plateaux, dubbed chirality degrees of freedom for both tubes.Comment: 17 page

Competing superconducting instabilities in the one-dimensional p-band degenerate cold fermionic system

The zero-temperature phase diagram of $p$-orbital two-component fermionic system loaded into a one-dimensional optical lattice is mapped out by means of analytical and numerical techniques. It is shown that the $p$-band model away from half-filling hosts various competing superconducting phases for attractive and repulsive interactions. At quarter filling, we analyze the possible formation of incompressible Mott phases and in particular for repulsive interactions, we find the occurrence of a Mott transition with the formation of fully gapped bond-ordering waves.Comment: published versio

Quantum phase transitions in three-leg spin tubes

We investigate the properties of a three-leg quantum spin tube using several techniques such as the density matrix renormalization group method, strong coupling approaches and the non linear sigma model. For integer spins S, the model proves to exhibit a particularly rich phase diagram consisting of an ensemble of 2S phase transitions. They can be accurately identified by the behavior of a non local string order parameter associated to the breaking of a hidden symmetry in the Hamiltonian. The nature of these transitions are further elucidated within the different approaches. We carry a detailed DMRG analysis in the specific cases S = 1. The numerical data confirm the existence of two Haldane phases with broken hidden symmetry separated by a trivial singlet state. The study of the gap and of the von Neumann entropy suggest a first order phase transition but at the close proximity of a tricritical point separating a gapless and a first order transition line in the phase diagram of the quantum spin tube.Comment: 20 pages, 18 figure

Selection of factorizable ground state in a frustrated spin tube: Order by disorder and hidden ferromagnetism

The interplay between frustration and quantum fluctuation in magnetic systems is known to be the origin of many exotic states in condensed matter physics. In this paper, we consider a frustrated four-leg spin tube under a magnetic field. This system is a prototype to study the emergence of a nonmagnetic ground state factorizable into local states and the associated order parameter without quantum fluctuation, that appears in a wide variety of frustrated systems. The one-dimensional nature of the system allows us to apply various techniques: a path-integral formulation based on the notion of order by disorder, strong-coupling analysis where magnetic excitations are gapped, and density-matrix renormalization group. All methods point toward an interesting property of the ground state in the magnetization plateaus, namely, a quantized value of relative magnetizations between different sublattices (spin imbalance) and an almost perfect factorization of the ground state

Competing orders in the generalized Hund chain model at half-filling

By using a combination of several non-perturbative techniques -- a one-dimensional field theoretical approach together with numerical simulations using density matrix renormalization group -- we present an extensive study of the phase diagram of the generalized Hund model at half-filling. This model encloses the physics of various strongly correlated one-dimensional systems, such as two-leg electronic ladders, ultracold degenerate fermionic gases carrying a large hyperfine spin 3/2, other cold gases like Ytterbium 171 or alkaline-earth condensates. A particular emphasis is laid on the possibility to enumerate and exhaust the eight possible Mott insulating phases by means of a duality approach. We exhibit a one-to-one correspondence between these phases and those of the two-leg Hubbard ladder with interchain hopping. Our results obtained from a weak coupling analysis are in remarkable quantitative agreement with our numerical results carried out at moderate coupling.Comment: 26 pages, 14 figure

Entanglement of quantum spin systems: a valence-bond approach

In order to quantify entanglement between two parts of a quantum system, one of the most used estimator is the Von Neumann entropy. Unfortunately, computing this quantity for large interacting quantum spin systems remains an open issue. Faced with this difficulty, other estimators have been proposed to measure entanglement efficiently, mostly by using simulations in the valence-bond basis. We review the different proposals and try to clarify the connections between their geometric definitions and proper observables. We illustrate this analysis with new results of entanglement properties of spin 1 chains.Comment: Proceedings of StatPhys 24 satellite conference in Hanoi; submitted for a special issue of Modern Physics Letters