Arnaud Ralko

Zero-temperature properties of the quantum dimer model on the triangular lattice

Using exact diagonalizations and Greens function Monte Carlo simulations, we have studied the zero-temperature properties of the quantum dimer model on the triangular lattice on clusters with up to 588 sites. A detailed comparison of the properties in different topological sectors as a function of the cluster size and for different cluster shapes has allowed us to identify different phases, to show explicitly the presence of topological degeneracy in a phase close to the Rokhsar-Kivelson point, and to understand finite-size effects inside this phase. The nature of the various phases has been further investigated by calculating dimer-dimer correlation functions. The present results confirm and complement the phase diagram proposed by Moessner and Sondhi on the basis of finite-temperature simulations [Phys. Rev. Lett. 86, 1881 (2001)].

Dynamics of the quantum dimer model on the triangular lattice: Soft modes and local resonating valence-bond correlations.

We report on an exhaustive investigation of the dynamical dimer-dimer correlations in imaginary time for the quantum dimer model on the triangular lattice using the Green’s function Monte Carlo method. We show in particular that soft modes develop upon reducing the dimer-dimer repulsion, indicating the presence of a second-order phase transition into an ordered phase with broken translational symmetry. We further investigate the nature of this ordered phase, for which a 12-site unit cell has been previously proposed, with the surprising result that significant Bragg peaks are only present at two of the three high-symmetry points consistent with this unit cell. We attribute the absence of a detectable peak to its small magnitude due to the nearly uniform internal structure of the 12-site crystal cell.

Doping quantum dimer models on the square lattice

A family of models is proposed to describe the motion of holes in a fluctuating quantum dimer background on the square lattice. Following Castelnovo et al. [Ann. Phys. (NY) 318, 316 (2005)], a generalized Rokhsar-Kivelson Hamiltonian at **finite doping** which can be mapped on a **doped** interacting classical dimer model is constructed. A simple physical extension of this model is also considered. Using numerical computations and simple considerations based on the above exact mapping, we determine the phase diagram of the model showing a number of quantum phases typical of a doped Mott insulator. The two-hole correlation function generically exhibits short-range or long-range algebraic correlations in the solid (columnar) and liquid (critical) phases of the model, respectively. Evidence for an extended region of a doped VBS phase exhibiting holon pairing but **no** phase separation is given. In contrast, we show that hole deconfinement occurs in the staggered dimer phase.

Geometrical frustration effects on charge-driven quantum phase transitions

by geometrical frustration. A comparison with the spinless model indicates that renormalization eects in the homogeneous metallic phase close to charge ordering are mainly due to charge rather than spin correlations. Spin degeneracy is, however, essential to describe the dependence of the system on geometrical frustration. Based on nite temperature Lanczos diagonalization we nd that the eective Fermi temperature scale, T , of the homogeneous metal vanishes at the quantum phase transition to the ordered metallic phase driven by the Coulomb repulsion. Above this temperature scale ’bad’ metallic behavior is found which is robust against geometrical frustration in general. Quantum critical phenomena are not found whenever nesting of the Fermi surface is strong, possibly indicating a rst order transition instead. ’Reentrant’ behavior in the phase diagram is encountered whenever the 2kF -CDW instability competes with the Coulomb driven three-fold charge order transition. The relevance of our results to the family of quarter-lled materials: -(BEDT-TTF)2X is discussed.

Phase separation and flux quantization in the doped quantum dimer model on square and triangular lattices.

The doped two-dimensional quantum dimer model is investigated by numerical techniques on the square and triangular lattices, with significantly different results. On the square lattice, at small enough doping, there is always a phase separation between an insulating valence-bond solid and a uniform superfluid phase, whereas on the triangular lattice, doping leads directly to a uniform superfluid in a large portion of the resonating-valence-bond (RVB) phase. Under an applied Aharonov-Bohm flux, the superfluid exhibits quantization in terms of half-flux quanta, consistent with Q=2e elementary charge quanta in transport properties.

The emergence of resonating valence bond physics in spin-orbital models

We discuss how orbital degeneracy, which is usually removed by a cooperative Jahn–Teller distortion, could under appropriate circumstances lead rather to a resonating valence bond spin–orbital liquid. The key points are: (i) the tendency to form spin–orbital dimers, a tendency already identified in several cases; (ii) mapping onto quantum dimer models, which have been shown to possess resonating valence bond phases on the triangular lattice. How this programme can be implemented is explained in some detail starting from a microscopic model of LiNiO2. (Some figures in this article are in colour only in the electronic version)

Microscopic theory of the nearest-neighbor valence bond sector of the spin-12 kagome antiferromagnet

© 2018 American Physical Society. The spin-12 Heisenberg model on the kagome lattice, which is closely realized in layered Mott insulators such as ZnCu3(OH)6Cl2, is one of the oldest and most enigmatic spin-12 lattice models. While the numerical evidence has accumulated in favor of a quantum spin liquid, the debate is still open as to whether it is a Z2 spin liquid with very short-range correlations (some kind of resonating valence bond spin liquid), or an algebraic spin liquid with power-law correlations. To address this issue, we have pushed the program started by Rokhsar and Kivelson in their derivation of the effective quantum dimer model description of Heisenberg models to unprecedented accuracy for the spin-12 kagome, by including all the most important virtual singlet contributions on top of the orthogonalization of the nearest-neighbor valence bond singlet basis. Quite remarkably, the resulting picture is a competition between a Z2 spin liquid and a diamond valence bond crystal with a 12-site unit cell, as in the density-matrix renormalization group simulations of Yan et al. Furthermore, we found that, on cylinders of finite diameter d, there is a transition between the Z2 spin liquid at small d and the diamond valence bond crystal at large d, the prediction of the present microscopic description for the two-dimensional lattice. These results show that, if the ground state of the spin-12 kagome antiferromagnet can be described by nearest-neighbor singlet dimers, it is a diamond valence bond crystal, and, a contrario, that, if the system is a quantum spin liquid, it has to involve long-range singlets, consistent with the algebraic spin liquid scenario.

Phase diagram of the 1/3-filled extended Hubbard model on the Kagome lattice

Institut Ne´el, UPR2940, Universite´ Grenoble Alpes et CNRS, Grenoble, FR-38042 France(Dated: March 4, 2014)We study the phase diagram of the extended Hubbard model on the kagome latticeat 1/3 filling. By combininga configuration interaction approach to an unrestricted Har tree-Fock, we construct an effective hamiltonianwhich takes the correlations back on top of the mean-field solution. We obtain a rich phase diagram with, inparticular, the presence of two original phases. The first on e consists of polarized droplets of metal standingon the hexagons of the lattice, and an enlarged kagome charge order, inversely polarized, on the remainingsites. The second, obeying a local ice-ruletype constraint on the triangles of the kagome lattice, is driven by anantiferromagnetically coupling of spins and is constituted of disconnected 6-spin singlet rings. The nature andstability of these phases at large interactions is studied via variational wave functions and perturbation theory.I. INTRODUCTION

Emergent heavy fermion behavior at the Wigner-Mott transition.

We study charge ordering driven by Coulomb interactions on triangular lattices relevant to the Wigner-Mott transition in two dimensions. Dynamical mean-field theory reveals the pinball liquid phase, a charge ordered metallic phase containing quasilocalized (pins) coexisting with itinerant (balls) electrons. Based on an effective periodic Anderson model for this phase, we find an antiferromagnetic Kondo coupling between pins and balls and strong quasiparticle renormalization. Non-Fermi liquid behavior can occur in such charge ordered systems due to the spin-flip scattering of itinerant electrons off the pins in analogy with heavy fermion compounds.

Quantum melting of valence-bond crystal insulators and novel supersolid phase at commensurate density.

Bosonic and fermionic Hubbard models on the checkerboard lattice are studied numerically for infinite on-site repulsion. At particle density n=1/4 and strong nearest-neighbor repulsion, insulating Valence-Bond crystals (VBC) of resonating particle pairs are stabilized. Their melting into superfluid or metallic phases under increasing hopping is investigated at T=0 K. We identify a novel and unconventional commensurate VBC supersolid region, precursor to the melting of the bosonic crystal. Hardcore bosons (spins) are compared to fermions (electrons), as well as positive to negative (frustrating) hoppings.