Variational Description of Mott Insulators

Abstract

The Gutzwiller wave function for a strongly correlated model can, if supplemented with a longrange Jastrow factor, provide a proper variational description of Mott insulators, so far unavailable. We demonstrate this concept in the prototypical one-dimensional t − t ′ Hubbard model, where at half filling we reproduce all known phases, namely the ordinary Mott undimerized insulator with power-law spin correlations at small t ′ /t, the spin-gapped metal above a critical t ′ /t and small U , and the dimerized Mott insulator at large repulsion.PACS numbers: 71.10. Fd, 71.10.Pm, 71.27.+a, 71.30.+h Since Mott's original proposal [1] the correlationdriven metal-Mott insulator transition (MIT) has attracted rising interest, renewed by the discovery of novel strongly correlated materials. On the verge of becoming Mott insulators, many systems display very unusual properties, high-T c superconductivity being one spectacular example. While understanding Mott insulators and MITs is conceptually simple, calculations constitute a hard and long standing problem. Conventional electronic structure methods, such as Hartree-Fock (HF) or density functional theory in the local density approximation (LDA) cannot describe MITs, unless one allows for some kind of symmetry breaking. The standard example is long-range static magnetic order in the unrestricted HF, local-spin-density, or LDA+U approximations. This device works by effectively turning the MIT into a conventional metal-band insulator transition, thus masking the essence of the Mott phenomenon, where a charge gap appears quite independently of spin order. The fact that most known Mott insulators are indeed accompanied at low temperatures by some symmetry breaking, usually of magnetic type, further encourages the (wrong) surmise that it is not possible to describe any Mott insulator without a symmetry breaking.Another useful and popular approximation that may invite the same conclusion is based on the variational Gutzwiller wave function (GWF) and its various generalizations. [2,3,4,5] The GWF is the simplest way to improve a symmetry-unbroken, hence metallic, Slater determinant by partly projecting out the expensive doubleoccupancy charge configurations. In principle, were the projection complete, the GWF would indeed describe a Mott insulator devoid of symmetry breaking. Full projection however means zero band-energy gain, generally incorrect, except for infinite on-site repulsion. For finite projection, appropriate at finite repulsion, the GWF unfortunately describes a metallic state in any finite dimensional lattice, at least so long as the uncorrelated Slater determinant state is metallic. [3] To obtain an insulator, one is forced once again to Gutzwiller project an artificially symmetry-broken determinant wave function (WF). The main drawback of the GWF can be immediately recognized if one recalls Mott's original description of a correlation-driven insulator. Let us consider for simplicity the single-band Hubbard model at half-filling. First of all it is clear that the ...

Strong electronic correlation in the hydrogen chain: A variational Monte Carlo study

“…Our findings are in agreement with previous variational studies of lattice models with short-range interactions which showed that a correct description of the Mott-Hubbard insulating phase can be achieved only by combining a Gutzwiller projector and a long-range Jastrow factor. 8,30 In fact, although the single H atoms are on average neutral, charge fluctuations that give, e.g., virtual H + -H − pairs are always possible. Such charge fluctuations are in fact strongly suppressed at large interatomic distance a (and, in the Hubbard model, for large U ).…”

“…Therefore, at large a, in order to prevent an instability of the Mott-Hubbard insulator toward a metallic state driven by the quantum fluctuations, 31 the H + -H − pairs must be bound. In the context of the Hubbard model, 8,30 it has been demonstrated that such binding mechanism can be included in the variational wave function by means of an inhomogeneous Jastrow factor, analogous to the the second term in Eq. (2).…”

“…16 On the other hand, VMC can be made ergodic by tailoring the sampling and by improving the variational many-body wave function, so that it remains very effective also close to crossovers and phase transitions. 7,8 There have been dramatic theoretical advances in the quality of the variational wave function during the last decade, so that it is now possible to achieve chemical accuracy for atoms, ions, small molecules, and even periodic systems. [17][18][19][20][21] These quantitative improvements have been made possible by new stochastic optimization techniques, which can optimize variational wave functions depending on hundreds of free parameters.…”

“…Indeed, unwanted edge effects are avoided by using PBCs and a speedup of the convergence to the thermodynamic limit, i.e., the limit of infinite linear chains, is expected. 7,8 Hence an ab initio description of the low-energy physics of a properly periodic H chain is still missing. In this paper we provide an exhaustive, fully ab initio 9 variational description of periodic chains by using the same kind of variational wave function for both the weakly and the strongly correlated regimes, i.e., for both small and large interatomic distances.…”

Importance of anisotropy in the spin-liquid candidate Me3EtSb[Pd(dmit)2]2

“…For the majority of the results reported here we constrain all of these variational parameters to be real. The correlated state | BCS = J c |BCS allows us to describe a paramagnetic Mott insulator for a sufficiently singular Jastrow factor v q ∼ 1/q 2 (v q being the Fourier transform of v i,j ), 19 while a metallic state can be obtained whenever v q ∼ 1/q.…”