Spatially homogeneous ground state of the two-dimensional Hubbard model

Becca, Federico; Capone, Massimo; Sorella, Sandro

doi:10.1103/physrevb.62.12700

Cited by 60 publications

(63 citation statements)

References 33 publications

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“…37, the evaluation of phase separation is strongly affected by the accuracy of the states that are used to compute the energy, phase separation being more favorable for less accurate variational wave functions. In fact, at the pure VMC level, we find that phase separation dominates the low-doping regime of the phase diagram for a wide range of interaction strengths U , as shown below.…”

Section: A the Half-filled Casementioning

confidence: 99%

“…However, determining the presence of phase separation in the Hubbard model is a difficult task, due to its strong dependence on the accuracy of the states that are used to compute the energy. In particular, it has been shown that phase separation is more favorable for less accurate variational states 37 . The formation of stripes in the Hubbard model, possibly favored with respect to a homogeneous superconducting state, has been also considered 38 .…”

Section: Introductionmentioning

confidence: 99%

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Hidden Mott transition and large- U superconductivity in the two-dimensional Hubbard model

2016

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We consider the one-band Hubbard model on the square lattice by using variational and Green's function Monte Carlo methods, where the variational states contain Jastrow and backflow correlations on top of an uncorrelated wave function that includes BCS pairing and magnetic order. At half filling, where the ground state is antiferromagnetically ordered for any value of the on-site interaction U , we can identify a hidden critical point UMott, above which a finite BCS pairing is stabilized in the wave function. The existence of this point is reminiscent of the Mott transition in the paramagnetic sector and determines a separation between a Slater insulator (at small values of U ), where magnetism induces a potential energy gain, and a Mott insulator (at large values of U ), where magnetic correlations drive a kinetic energy gain. Most importantly, the existence of UMott has crucial consequences when doping the system: We observe a tendency to phase separation into a hole-rich and a hole-poor region only when doping the Slater insulator, while the system is uniform by doping the Mott insulator. Superconducting correlations are clearly observed above UMott, leading to the characteristic dome structure in doping. Furthermore, we show that the energy gain due to the presence of a finite BCS pairing above UMott shifts from the potential to the kinetic sector by increasing the value of the Coulomb repulsion.

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Section: A the Half-filled Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hidden Mott transition and large- U superconductivity in the two-dimensional Hubbard model

2016

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“…Alternatively, the constraint can be implemented exactly at T = 0 using the variational Monte Carlo (VMC) method. Previous variational studies [3][4][5][6] have focussed primarily on the energetics of competing states.In this letter, we revisit projected wavefunctions of the form proposed by Anderson in 1987 [1]. We compute physically interesting correlations using VMC and show that projection leads to loss of coherence.…”

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confidence: 99%

Projected Wave Functions and High Temperature Superconductivity

2001

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We study the Hubbard model with parameters relevant to the cuprates, using variational Monte Carlo with projected d-wave states. For doping 0 < x < ∼ 0.35 we obtain a superconductor whose order parameter tracks the observed nonmonotonic Tc(x). The variational parameter ∆var(x) scales with the (π, 0) "hump" and T * seen in photoemission. Projection leads to incoherence in the spectral function and from the singular behavior of its moments we obtain the nodal quasiparticle weight Z ∼ x though the Fermi velocity remains finite as x → 0. The Drude weight D low and superfluid density are consistent with experiment and D low ∼ Z.PACS numbers: 74.20.-z, 74.20.Fg, 74.25.-q, 74.72.-h (March 20, 2018) Strong correlations are essential to understand d-wave high temperature superconductivity in doped Mott insulators [1]. The no-double occupancy constraint arising from strong correlations has been treated within two complementary approaches. Within the gauge theory approach [2], which is valid at all temperatures, the constraint necessitates the inclusion of strong gauge fluctuations. Alternatively, the constraint can be implemented exactly at T = 0 using the variational Monte Carlo (VMC) method. Previous variational studies [3][4][5][6] have focussed primarily on the energetics of competing states.In this letter, we revisit projected wavefunctions of the form proposed by Anderson in 1987 [1]. We compute physically interesting correlations using VMC and show that projection leads to loss of coherence. We obtain information about low energy excitations from the singular behavior of moments of the occupied spectral function. Remarkably, our results for various observables are in semi-quantitative agreement with experiments on the cuprates. We also make qualitative predictions for the doping (x) dependence of correlation functions in projected states (for x ≪ 1) from general arguments which are largely independent of the detailed form of the wavefunction and the Hamiltonian. We use the Hubbard Hamiltonian H = K + H int . The kinetic energy K = k,σ ǫ(k)c † kσ c kσ with ǫ(k) = −2t (cos k x + cos k y ) + 4t ′ cos k x cos k y the dispersion on a square lattice with nearest (t) and next-near (t ′ ) hopping. The on-site repulsion is H int = U r n ↑ (r)n ↓ (r) with n σ (r) = c † σ (r)c σ (r). We work in the strongly correlated regime where J = 4t 2 /U, t ′ < ∼ t ≪ U near half filling: n = 1 − x with the hole doping x ≪ 1. We choose t ′ = t/4, t = 300meV and U = 12t, so that J = 100meV consistent with neutron data on cuprates.We describe the ground state by the wavefunctionHere|0 is the Nelectron d-wave BCS wave function withThe two variational parameters(1) eliminates all configurations with double occupancy, as appropriate for U → ∞.The unitary transformation exp(iS) includes double occupancy perturbatively in t/U [7]. The transformation exp(−iS)H exp(iS) is well known to lead to the tJ Hamiltonian [7]. We emphasize that our approach effectively transforms all operators, and not only H. Using Ψ 0 |Q|Ψ 0 = Ψ BCS |PQP|Ψ BCS withQ ...

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“…Theoretically, the general tendency towards phase separation in cuprates and cuprate-related models is extensively discussed in the literature [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30], but any conclusion about the actual presence or absence of phase separation suffers from uncertainties associated with the gross simplifications in the models. The important advantage of the phase separation measure introduced in this work is that it is directly applicable to real materials.…”

Section: Introductionmentioning

confidence: 99%

Phase separation in the vicinity of quantum-critical doping concentration: Implications for high-temperature superconductors

Fine

Egami

2008

Phys. Rev. B

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A general quantitative measure of the tendency towards phase separation is introduced for systems exhibiting phase transitions or crossovers controlled by charge carrier concentration. This measure is devised for the situations when the quantitative knowledge of various contributions to free energy is incomplete, and is applied to evaluate the chances of electronic phase separation associated with the onset of antiferromagnetic correlations in high-temperature cuprate superconductors. The experimental phenomenology of lanthanum-and yittrium-based cuprates was used as input to this analysis. It is also pointed out that Coulomb repulsion between charge carriers separated by the distances of 1-3 lattice periods strengthens the tendency towards phase separation by accelerating the decay of antiferromagnetic correlations with doping. Overall, the present analysis indicates that cuprates are realistically close to the threshold of phase separation -nanoscale limited or even macroscopic with charge density varying between adjacent crystal planes.

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Spatially homogeneous ground state of the two-dimensional Hubbard model

Cited by 60 publications

References 33 publications

Hidden Mott transition and large- U superconductivity in the two-dimensional Hubbard model

Hidden Mott transition and large- U superconductivity in the two-dimensional Hubbard model

Projected Wave Functions and High Temperature Superconductivity

Phase separation in the vicinity of quantum-critical doping concentration: Implications for high-temperature superconductors

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