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

We study the phase diagram of the extended Hubbard model on the kagome lattice at 1/3 filling. By combining a configuration interaction approach to an unrestricted Hartree-Fock, we construct an effective hamiltonian which takes the correlations back on top of the mean-field solution. We obtain a rich phase diagram with, in particular, the presence of two original phases. The first one consists of polarized droplets of metal standing on the hexagons of the lattice, and an enlarged kagome charge order, inversely polarized, on the remaining sites. The second, obeying a local ice-rule type constraint on the triangles of the kagome lattice, is driven by an antiferromagnetically coupling of spins and is constituted of disconnected 6-spin singlet rings. The nature and stability of these phases at large interactions is studied via variational wave functions and perturbation theory.Comment: 6 pages, 5 figure

Microscopic theory of the nearest-neighbor valence bond sector of the spin-1/2 kagome antiferromagnet

The spin-1/2 Heisenberg model on the kagome lattice, which is closely realized in layered Mott insulators such as ZnCu$_3$(OH)$_6$Cl$_2$, is one of the oldest and most enigmatic spin-1/2 lattice model. While the numerical evidence has accumulated in favor of a quantum spin liquid, the debate is still open as to whether it is a $Z_2$ 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-1/2 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 $Z_2$ spin liquid and a diamond valence bond crystal with a 12-site unit cell, as in the DMRG simulations of Yan, Huse and White. Furthermore, we found that, on cylinders of finite diameter $d$, there is a transition between the $Z_2$ spin liquid at small $d$ and the diamond valence bond crystal at large $d$, the prediction of the present microscopic description for the 2D lattice. These results show that, if the ground state of the spin-1/2 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.Comment: 11 pages, 14 figures. Revised and extended version. Results are untouched, implications have been clarified and better put in contex

Avoiding Stripe Order: Emergence of the Supercooled Electron Liquid

In the absence of disorder, electrons can display glassy behavior through supercooling the liquid state, avoiding the solidification into a charge ordered state. Such supercooled electron liquids are experimentally found in organic $\theta$-$MM'$ compounds. We present theoretical results that qualitatively capture the experimental findings. At intermediate temperatures, the conducting state crosses over into a weakly insulating pseudogap phase. The stripe order phase transition is first order, so that the liquid phase is metastable below $T_s$. In the supercooled liquid phase the resistivity increases further and the density of states at the Fermi level is suppressed, indicating kinetic arrest and the formation of a glassy state. Our results are obtained using classical Extended Dynamical Mean Field Theory.Comment: 4 pages, 4 figures, submitted to the proceedings of "Superstripes 2015", Journal of Superconductivity and Novel Magnetism (2015

Resonating-valence-bond physics is not always governed by the shortest tunneling loops

It is well known that the low-energy sector of quantum spin liquids and other magnetically disordered systems is governed by short-ranged resonating-valence bonds. Here we show that the standard minimal truncation to the nearest-neighbor valence-bond basis fails completely even for systems where it should work the most, according to received wisdom. This paradigm shift is demonstrated for the quantum spin-1/2 square kagome, where strong geometric frustration, similar to the kagome, prevents magnetic ordering down to zero temperature. The shortest tunneling events bear the strongest longer-range singlet fluctuations, leading to amplitudes that do not drop exponentially with the length of the loop L, and to an unexpected loop-six valence-bond crystal, which is otherwise very high in energy at the minimal truncation level. The low-energy effective description gives in addition a clear example of correlated loop processes that depend not only on the type of the loop but also on its lattice embedding, a direct manifestation of the long-range nature of the virtual singlets

Novel chiral quantum spin liquids in Kitaev magnets

Mott insulators under sufficiently strong spin-orbit coupling can display quantum spin liquid phases with topological order and fractional excitations. Quantum magnets with pure Kitaev spin exchange interactions can host a gapped quantum spin liquid with a single Majorana edge mode propagating in the counter-clockwise direction when a small positive magnetic field is applied. Here, we show how under a sufficiently strong positive magnetic field a topological transition into a gapped quantum spin liquid with two Majorana edge modes propagating in the clockwise direction occurs. The Dzyaloshinskii-Moriya interaction is found to turn the non-chiral Kitaev's gapless quantum spin liquid into a chiral one with equal Berry phases at the two Dirac points. Thermal Hall conductance experiments can provide evidence of the novel topologically gapped quantum spin liquid states predicted.Comment: last version, 4 pages, 4 figures + Supplemental materia

Pseudogap metal induced by long-range Coulomb interactions

In correlated electron systems the metallic character of a material can be strongly suppressed near an integer concentration of conduction electrons as Coulomb interactions forbid the double occupancy of local atomic orbitals. While the Mott-Hubbard physics arising from such on-site interactions has been largely studied, several unexplained phenomena observed in correlated materials challenge this description and call for the development of new ideas. Here we explore a general route for obtaining correlated behavior that is decidedly different from the Mott-Hubbard mechanism and instead relies on the presence of unscreened, long-range Coulomb interactions. We find a previously unreported pseudogap metal phase characterized by a divergent quasiparticle mass and the opening of a Coulomb pseudogap in the electronic spectrum. The destruction of the Fermi liquid state occurs because the electrons move in a nearly frozen, disordered charge background, as collective charge rearrangements are drastically slowed down by the frustrating nature of long-range potentials on discrete lattices. The present pseudogap metal realizes an early conjecture by Efros, that a soft Coulomb gap should appear for quantum lattice electrons with strong unscreened interactions due to self-generated randomness.Comment: 4 pages + 3 pages supplementary informatio

Glassy dynamics in geometrically frustrated Coulomb liquids without disorder

We show that introducing long-range Coulomb interactions immediately lifts the massive ground state degeneracy induced by geometric frustration for electrons on quarter-filled triangular lattices in the classical limit. Important consequences include the stabilization of a stripe-ordered crystalline (global) ground state, but also the emergence of very many low-lying metastable states with amorphous "stripe-glass" spatial structures. Melting of the stripe order thus leads to a frustrated Coulomb liquid at intermediate temperatures, showing remarkably slow (viscous) dynamics, with very long relaxation times growing in Arrhenius fashion upon cooling, as typical of strong glass formers. On shorter time scales, the system falls out of equilibrium and displays the aging phenomena characteristic of supercooled liquids above the glass transition. Our results show remarkable similarity with the recent observations of charge-glass behavior in ultra-clean triangular organic materials of the $\theta$-(BEDT-TTF)$_2$ family.Comment: 5 pages,4 figure

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 compoundsJ. M. acknowledges financial support from MINECO (MAT2012-37263-C02-01). This work is supported by the French National Research Agency through Grant No. ANR-12-JS04-0003-01 SUBRISSYM

Quantum paramagnetism and magnetization plateaus in a kagome-honeycomb Heisenberg antiferromagnet

A spin-1/2 Heisenberg model on honeycomb lattice is investigated by doing triplon analysis and quantum Monte Carlo calculations. This model, inspired by Cu$_2$(pymca)$_3$(ClO$_4$), has three different antiferromagnetic exchange interactions ($J_A$, $J_B$, $J_C$) on three different sets of nearest-neighbour bonds which form a kagome superlattice. While the model is bipartite and unfrustrated, its quantum phase diagram is found to be dominated by a quantum paramagnetic phase that is best described as a spin-gapped hexagonal-singlet state. The N\'eel antiferromagnetic order survives only in a small region around $J_A=J_B=J_C$. The magnetization produced by external magnetic field is found to exhibit plateaus at 1/3 and 2/3 of the saturation value, or at 1/3 alone, or no plateaus. Notably, the plateaus exist only inside a bounded region within the hexagonal-singlet phase. This study provides a clear understanding of the spin-gapped behaviour and magnetization plateaus observed in Cu$_2$(pymca)$_3$(ClO$_4$), and also predicts the possible disappearance of 2/3 plateau under pressure.Comment: 16 pages, 14 figure