Variational wave functions for the S=1/2S=1/2 Heisenberg model on the anisotropic triangular lattice: Spin liquids and spiral orders

By using variational wave functions and quantum Monte Carlo techniques, we investigate the complete phase diagram of the Heisenberg model on the anisotropic triangular lattice, where two out of three bonds have super-exchange couplings $J$ and the third one has instead $J^\prime$. This model interpolates between the square lattice and the isotropic triangular one, for $J^\prime/J \le 1$, and between the isotropic triangular lattice and a set of decoupled chains, for $J/J^\prime \le 1$. We consider all the fully-symmetric spin liquids that can be constructed with the fermionic projective-symmetry group classification [Y. Zhou and X.-G. Wen, arXiv:cond-mat/0210662] and we compare them with the spiral magnetic orders that can be accommodated on finite clusters. Our results show that, for $J^\prime/J \le 1$, the phase diagram is dominated by magnetic orderings, even though a spin-liquid state may be possible in a small parameter window, i.e., $0.7 \lesssim J^\prime/J \lesssim 0.8$. In contrast, for $J/J^\prime \le 1$, a large spin-liquid region appears close to the limit of decoupled chains, i.e., for $J/J^\prime \lesssim 0.6$, while magnetically ordered phases with spiral order are stabilized close to the isotropic point.Comment: 11 pages, 11 figure

Emergent lattices with geometrical frustration in doped extended Hubbard models

Spontaneous charge ordering occurring in correlated systems may be considered as a possible route to generate effective lattice structures with unconventional couplings. For this purpose we investigate the phase diagram of doped extended Hubbard models on two lattices: (i) the honeycomb lattice with on-site $U$ and nearest-neighbor $V$ Coulomb interactions at $3/4$ filling ($n=3/2$) and (ii) the triangular lattice with on-site $U$, nearest-neighbor $V$, and next-nearest-neighbor $V'$ Coulomb interactions at $3/8$ filling ($n=3/4$). We consider various approaches including mean-field approximations, perturbation theory, and variational Monte Carlo. For the honeycomb case (i), charge order induces an effective triangular lattice at large values of $U/t$ and $V/t$, where $t$ is the nearest-neighbor hopping integral. The nearest-neighbor spin exchange interactions on this effective triangular lattice are antiferromagnetic in most of the phase diagram, while they become ferromagnetic when $U$ is much larger than $V$. At $U/t\sim (V/t)^3$, ferromagnetic and antiferromagnetic exchange interactions nearly cancel out, leading to a system with four-spin ring-exchange interactions. On the other hand, for the triangular case (ii) at large $U$ and finite $V'$, we find no charge order for small $V$, an effective kagome lattice for intermediate $V$, and one-dimensional charge order for large $V$. These results indicate that Coulomb interactions induce [case (i)] or enhance [case(ii)] emergent geometrical frustration of the spin degrees of freedom in the system, by forming charge order.Comment: 18 pages, 26 figure

Metal-insulator transition and strong-coupling spin liquid in the t−t′t{-}t^\prime Hubbard model

We study the phase diagram of the frustrated $t{-}t^\prime$ Hubbard model on the square lattice by using a novel variational wave function. Taking the clue from the backflow correlations that have been introduced long-time ago by Feynman and Cohen and have been used for describing various interacting systems on the continuum (like liquid $^3$He, the electron jellium, and metallic Hydrogen), we consider many-body correlations to construct a suitable approximation for the ground state of this correlated model on the lattice. In this way, a very accurate {\it ansatz} can be achieved both at weak and strong coupling. We present the evidence that an insulating and non-magnetic phase can be stabilized at strong coupling and sufficiently large frustrating ratio $t^\prime/t$.Comment: 8 pages, Proceedings of the HFM2008 Conferenc

Metal-insulator transition and strong-coupling spin liquid in the t−t′t{-}t^\prime Hubbard model

We study the phase diagram of the frustrated $t{-}t^\prime$ Hubbard model on the square lattice by using a novel variational wave function. Taking the clue from the backflow correlations that have been introduced long-time ago by Feynman and Cohen and have been used for describing various interacting systems on the continuum (like liquid $^3$He, the electron jellium, and metallic Hydrogen), we consider many-body correlations to construct a suitable approximation for the ground state of this correlated model on the lattice. In this way, a very accurate {\it ansatz} can be achieved both at weak and strong coupling. We present the evidence that an insulating and non-magnetic phase can be stabilized at strong coupling and sufficiently large frustrating ratio $t^\prime/t$.Comment: 8 pages, Proceedings of the HFM2008 Conferenc

Interaction induced Fermi-surface renormalization in the t1−t2t_1{-}t_2 Hubbard model close to the Mott-Hubbard transition

We investigate the nature of the interaction-driven Mott-Hubbard transition of the half-filled $t_1{-}t_2$ Hubbard model in one dimension, using a full-fledged variational Monte Carlo approach including a distance-dependent Jastrow factor and backflow correlations. We present data for the evolution of the magnetic properties across the Mott-Hubbard transition and on the commensurate to incommensurate transition in the insulating state. Analyzing renormalized excitation spectra, we find that the Fermi surface renormalizes to perfect nesting right at the Mott-Hubbard transition in the insulating state, with a first-order reorganization when crossing into the conducting state.Comment: 6 pages and 7 figure

Mott correlated states in the underdoped two-dimensional Hubbard model: variational Monte Carlo versus a dynamical cluster approximation

We investigate the properties of the frustrated underdoped Hubbard model on the square lattice using two complementary approaches, the dynamical cluster extension of dynamical mean field theory, and variational Monte Carlo simulations of Gutzwiller-Jastrow wavefunctions with backflow corrections. We compare and discuss data for the energy and the double occupancies, as obtained from both approaches. At small dopings, we observe a rapid crossover from a weakly correlated metal at low interaction strength U to a non-Fermi liquid correlated state with strong local spin correlations. Furthermore, we investigate the stability of the correlated state against phase separation. We observe phase separation only for large values of U or very large frustration. No phase separation is present for the parameter range relevant for the cuprates.Comment: 8 pages, 8 figure

Spin-liquid and magnetic phases in the anisotropic triangular lattice: the case of κ\kappa-(ET)2_2X

The two-dimensional Hubbard model on the anisotropic triangular lattice, with two different hopping amplitudes $t$ and $t^\prime$, is relevant to describe the low-energy physics of $\kappa$-(ET)$_2$X, a family of organic salts. The ground-state properties of this model are studied by using Monte Carlo techniques, on the basis of a recent definition of backflow correlations for strongly-correlated lattice systems. The results show that there is no magnetic order for reasonably large values of the electron-electron interaction $U$ and frustrating ratio $t^\prime/t = 0.85$, suitable to describe the non-magnetic compound with X=Cu$_2$(CN)$_3$. On the contrary, N\'eel order takes place for weaker frustrations, i.e., $t^\prime/t \sim 0.4 \div 0.6$, suitable for materials with X=Cu$_2$(SCN)$_2$, Cu[N(CN)$_2$]Cl, or Cu[N(CN)$_2$]Br.Comment: 7 pages, Physical Review B 80, 064419 (2009

Spontaneous symmetry breaking in correlated wave functions

We show that Jastrow-Slater wave functions, in which a density-density Jastrow factor is applied onto an uncorrelated fermionic state, may possess long-range order even when all symmetries are preserved in the wave function. This fact is mainly related to the presence of a sufficiently strong Jastrow term (also including the case of full Gutzwiller projection, suitable for describing spin models). Selected examples are reported, including the spawning of N\'eel order and dimerization in spin systems, and the stabilization of charge and orbital order in itinerant electronic systems.Comment: 13 pages, 11 figure

Tunnelling matrix elements with antiferromagnetic Gutzwiller wave functions

We use a generalized Gutzwiller Approximation (GA) elaborated to evaluate matrix elements with partially projected wave functions and formerly applied to homogeneous systems. In the present paper we consider projected single-particle (hole) excitations for electronic systems with antiferromagnetic (AFM) order and obtain the corresponding tunnelling probabilities. The accuracy and the reliability of our analytical approximation is tested using the Variational Monte Carlo (VMC). Possible comparisons with experimental results are also discussed.Comment: 16 pages, 10 figure

Superconductivity, charge-density waves, antiferromagnetism, and phase separation in the Hubbard-Holstein model

By using variational wave functions and quantum Monte Carlo techniques, we investigate the interplay between electron-electron and electron-phonon interactions in the two-dimensional Hubbard-Holstein model. Here, the ground-state phase diagram is triggered by several energy scales, i.e., the electron hopping t, the on-site electron-electron interaction U, the phonon energy omega(0), and the electron-phonon coupling g. At half filling, the ground state is an antiferromagnetic insulator for U >= 2g(2)/omega(0), while it is a charge-density-wave (or bipolaronic) insulator for U <= 2g(2) omega(0). In addition to these phases, we find a superconducting phase that intrudes between them. For omega(0)/t = 1, superconductivity emerges when both U/t and 2g(2)/t omega(0) are small; then, by increasing the value of the phonon energy omega(0), it extends along the transition line between antiferromagnetic and charge-density-wave insulators. Away from half filling, phase separation occurs when doping the charge-density-wave insulator, while a uniform (superconducting) ground state is found when doping the superconducting phase. In the analysis of finite-size effects, it is extremely important to average over twisted boundary conditions, especially in the weak-coupling limit and in the doped case