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Register a new userDual parquet scheme for the two-dimensional Hubbard model: modelling low-energy physics of high-$T_c$ cuprates with high momentum resolution
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Added by
Grigory Astretsov Mr
Publication date
2019
fields
Physics
and research's language is
English
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We present a new method to treat the two-dimensional (2D) Hubbard model for parameter regimes which are relevant for the physics of the high-$T_c$ superconducting cuprates. Unlike previous attempts to attack this problem, our new approach takes into account all fluctuations in different channels on equal footing and is able to treat reasonable large lattice sizes up to 32x32. This is achieved by the following three-step procedure: (i) We transform the original problem to a new representation (dual fermions) in which all purely local correlation effects from the dynamical mean field theory are already considered in the bare propagator and bare interaction of the new problem. (ii) The strong $1/(i u)^2$ decay of the bare propagator allows us to integrate out all higher Matsubara frequencies besides the lowest using low order diagrams. The new effective action depends only on the two lowest Matsubara frequencies which allows us to, (iii) apply the two-particle self-consistent parquet formalism, which takes into account the competition between different low-energy bosonic modes in an unbiased way, on much finer momentum grids than usual. In this way, we were able to map out the phase diagram of the 2D Hubbard model as a function of temperature and doping. Consistently with the experimental evidence for hole-doped cuprates and previous dynamical cluster approximation calculations, we find an antiferromagnetic region at low-doping and a superconducting dome at higher doping. Our results also support the role of the van Hove singularity as an important ingredient for the high value of $T_c$ at optimal doping. At small doping, the destruction of antiferromagnetism is accompanied by an increase of charge fluctuations supporting the scenario of a phase separated state driven by quantum critical fluctuations.
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Recent excperiments (ARPES, Raman) suggest the presence of two distinct energy gaps in high-Tc superconductors (HTSC), exhibiting different doping dependences. Results of a variational cluster approach to the superconducting state of the two-dimensional Hubbard model are presented which show that this model qualitatively describes this gap dichotomy: One gap (antinodal) increases with less doping, a behavior long considered as reflecting the general gap behavior of the HTSC. On the other hand, the near-nodal gap does even slightly decrease with underdoping. An explanation of this unexpected behavior is given which emphasizes the crucial role of spin fluctuations in the pairing mechanism.
We use quantum Monte Carlo methods and single-mode approximation to study the magnon dispersion in the 2D half-filled Hubbard and phonon-coupled Heisenberg models. We find that in the Hubbard model with $U/t< 8$, high-energy magnon dispersion is similar to those observed in inelastic neutron scattering experiments in ${La}_2{CuO}_4$. On the other hand, our studies of a 2D Heisenberg model coupled to dynamic optical bond phonons, fails to reproduce the experimental dispersion. These results can be interpreted as evidence for intermediate $U/t$ and charge fluctuations in the cuprate materials.
We study the competition between stripe states with different periods and a uniform $d$-wave superconducting state in the extended 2D Hubbard model at 1/8 hole doping using infinite projected entangled-pair states (iPEPS). With increasing strength of negative next-nearest neighbor hopping $t$, the preferred period of the stripe decreases. For the values of $t$ predicted for cuprate high-T$_c$ superconductors, we find stripes with a period 4 in the charge order, in agreement with experiments. Superconductivity in the period 4 stripe is suppressed at $1/8$ doping. Only at larger doping, $0.18 lesssim delta < 0.25$, the period 4 stripe exhibits coexisting $d$-wave superconducting order. The uniform $d$-wave state is only favored for sufficiently large positive $t$.
A major pathway towards understanding complex systems is given by exactly solvable reference systems that contain the essential physics of the system. For the $t-t-U$ Hubbard model, the four-site plaquette is known to have a quantum critical point in the $U-mu$ space where states with electron occupations $N=2, 3, 4$ per plaquette are degenerate [Phys. Rev. B {bf 94}, 125133 (2016)]. We show that such a critical point in the lattice causes an instability in the particle-particle singlet d-wave channel and manifests some of the essential elements of the cuprate superconductivity. For this purpose we design an efficient superperturbation theory -- based on the dual fermion approach -- with the critical plaquette as the reference system. Thus, the perturbation theory already contains the relevant d-wave fluctuations from the beginning via the two-particle correlations of the plaquette. We find that d-wave superconductivity remains a leading instability channel under reasonably broad range of parameters. The next-nearest-neighbour hopping $t$ is shown to play a crucial role in a formation of strongly bound electronic bipolarons whose coherence at lower temperature results in superconductivity. The physics of the pseudogap within the developed picture is also discussed.
The role of charge order in the phase diagram of high temperature cuprate superconductors has been recently re-emphasized by the experimental discovery of an incipient bi-directional charge density wave (CDW) phase in a class of underdoped cuprates. In a subset of the experiments, the CDW has been found to be accompanied by a d-wave intra-unit-cell form factor, indicating modulation of charge density on the oxygen orbitals sandwiched between neighboring Cu atoms on the CuO planes (the so-called bond-density wave (BDW) phase). Here we take a mean field Q_1=(2pi/3,0) and Q_2=(0,2pi/3) bi-directional BDW phase with a d-wave form factor, which closely resembles the experimentally observed charge ordered states in underdoped cuprates, and calculate the Fermi surface topology and the resulting quasiparticle Nernst coefficient as a function of temperature and doping. We establish that, in the appropriate doping ranges where the low temperature phase (in the absence of superconductivity) is a BDW, the Fermi surface consists of an electron and a hole pocket, resulting in a low temperature negative Nernst coefficient as observed in experiments.
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