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

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

Bond order wave instabilities in doped frustrated antiferromagnets: "Valence bond solids" at fractional filling

We explore both analytically and numerically the properties of doped t-J models on a class of highly frustrated lattices, such as the kagome and the pyrochlore lattice. Focussing on a particular sign of the hopping integral and antiferromagnetic exchange, we find a generic symmetry breaking instability towards a twofold degenerate ground state at a fractional filling below half filling. These states show modulated bond strengths and only break lattice symmetries. They can be seen as a generalization of the well-known valence bond solid states to fractional filling.Comment: slightly shortened and reorganized versio

Numerical Contractor Renormalization Method for Quantum Spin Models

We demonstrate the utility of the numerical Contractor Renormalization (CORE) method for quantum spin systems by studying one and two dimensional model cases. Our approach consists of two steps: (i) building an effective Hamiltonian with longer ranged interactions using the CORE algorithm and (ii) solving this new model numerically on finite clusters by exact diagonalization. This approach, giving complementary information to analytical treatments of the CORE Hamiltonian, can be used as a semi-quantitative numerical method. For ladder type geometries, we explicitely check the accuracy of the effective models by increasing the range of the effective interactions. In two dimensions we consider the plaquette lattice and the kagome lattice as non-trivial test cases for the numerical CORE method. On the plaquette lattice we have an excellent description of the system in both the disordered and the ordered phases, thereby showing that the CORE method is able to resolve quantum phase transitions. On the kagome lattice we find that the previously proposed twofold degenerate S=1/2 basis can account for a large number of phenomena of the spin 1/2 kagome system. For spin 3/2 however this basis does not seem to be sufficient anymore. In general we are able to simulate system sizes which correspond to an 8x8 lattice for the plaquette lattice or a 48-site kagome lattice, which are beyond the possibilities of a standard exact diagonalization approach.Comment: 15 page

Symmetry-protected topological phases of alkaline-earth cold fermionic atoms in one dimension

We investigate the existence of symmetry-protected topological phases in one-dimensional alkaline-earth cold fermionic atoms with general half-integer nuclear spin I at half filling. In this respect, some orbital degrees of freedom are required. They can be introduced by considering either the metastable excited state of alkaline-earth atoms or the p-band of the optical lattice. Using complementary techniques, we show that SU(2) Haldane topological phases are stabilised from these orbital degrees of freedom. On top of these phases, we find the emergence of topological phases with enlarged SU(2I+1) symmetry which depend only on the nuclear spin degrees of freedom. The main physical properties of the latter phases are further studied using a matrix-product state approach. On the one hand, we find that these phases are symmetry-protected topological phases, with respect to inversion symmetry, when I=1/2,5/2,9/2,..., which is directly relevant to ytterbium and strontium cold fermions. On the other hand, for the other values of I(=half-odd integer), these topological phases are stabilised only in the presence of exact SU(2I+1)-symmetry

Numerical study of magnetization plateaux in the spin-1/2 kagome Heisenberg antiferromagnet

We clarify the existence of several magnetization plateaux for the kagome $S=1/2$ antiferromagnetic Heisenberg model in a magnetic field. Using approximate or exact localized magnon eigenstates, we are able to describe in a similar manner the plateau states that occur for magnetization per site $m=1/3$, $5/9$, and $7/9$ of the saturation value. These results are confirmed using large-scale Exact Diagonalization on lattices up to 63 sites.Comment: 8 pages; minor changes; published versio

Hidden symmetry and quantum phases in spin-3/2 cold atomic systems

Optical traps and lattices provide a new opportunity to study strongly correlated high spin systems with cold atoms. In this article, we review the recent progress on the hidden symmetry properties in the simplest high spin fermionic systems with hyperfine spin $F=3/2$, which may be realized with atoms of $^{132}$Cs, $^9$Be, $^{135}$Ba, $^{137}$Ba, and $^{201}$Hg. A {\it generic} SO(5) or isomorphically, $Sp(4)$) symmetry is proved in such systems with the s-wave scattering interactions in optical traps, or with the on-site Hubbard interactions in optical lattices. Various important features from this high symmetry are studied in the Fermi liquid theory, the mean field phase diagram, and the sign problem in quantum Monte-Carlo simulations. In the s-wave quintet Cooper pairing phase, the half-quantum vortex exhibits the global analogue of the Alice string and non-Abelian Cheshire charge properties in gauge theories. The existence of the quartetting phase, a four-fermion counterpart of the Cooper pairing phase, and its competition with other orders are studied in one dimensional spin-3/2 systems. We also show that counter-intuitively quantum fluctuations in spin-3/2 magnetic systems are even stronger than those in spin-1/2 systems

Establishing the boundaries: the hippocampal contribution to imagining scenes

When we visualize scenes, either from our own past or invented, we impose a viewpoint for our “mind's eye” and we experience the resulting image as spatially coherent from that viewpoint. The hippocampus has been implicated in this process, but its precise contribution is unknown. We tested a specific hypothesis based on the spatial firing properties of neurons in the hippocampal formation of rats, that this region supports the construction of spatially coherent mental images by representing the locations of the environmental boundaries surrounding our viewpoint. Using functional magnetic resonance imaging, we show that hippocampal activation increases parametrically with the number of enclosing boundaries in the imagined scene. In contrast, hippocampal activity is not modulated by a nonspatial manipulation of scene complexity nor to increasing difficulty of imagining the scenes in general. Our findings identify a specific computational role for the hippocampus in mental imagery and episodic recollection

Phase diagram of interacting spinless fermions on the honeycomb lattice: A comprehensive exact diagonalization study

International audienceWe investigate the phase diagram of spinless fermions with nearest and next-nearest neighbour density-density interactions on the honeycomb lattice at half-filling. Using Exact Diagonalization techniques of the full Hamiltonian and constrained subspaces, combined with a careful choice of finite-size clusters, we determine the different charge orderings that occur for large interactions. In this regime we find a two-sublattice N\'eel-like state, a charge modulated state with a tripling of the unit cell, a zig-zag phase and a novel charge ordered states with a 12 site unit cells we call N\'eel domain wall crystal, as well as a region of phase separation for attractive interactions. A sizeable region of the phase diagram is classically degenerate, but it remains unclear whether an order-by-disorder mechanism will lift the degeneracy. For intermediate repulsion we find evidence for a Kekul\'e or plaquette bond-order wave phase. We also investigate the possibility of a spontaneous Chern insulator phase (dubbed topological Mott insulator), as previously put forward by several mean-field studies. Although we are unable to detect convincing evidence for this phase based on energy spectra and order parameters, we find an enhancement of current-current correlations with the expected spatial structure compared to the non-interacting situation. While for the studied t−V1−V2 model the phase transition to the putative topological Mott insulator is preempted by the phase transitions to the various ordered states, our findings might hint at the possibility for a topological Mott insulator in an enlarged Hamiltonian parameter space, where the competing phases are suppressed