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Journal of Experimental and Theoretical Physics

Nematic order of spin structures of clusters in the hubbard model

M. Ya. Ovchinnikova

Published Jul 1, 2011• 1 citation
Publisher

Abstract

The possibility of interpreting the normal pseudogap state of cuprates as a result of the formation of spin and charge structures is investigated for solutions of the Hubbard model of a finite 2D cluster based on the mean field method. The iterative self-consistency procedure reduces the initial uncorrelated spin distributions to stable structures. The Fourier components of the charge and spin distributions in such structures have peaks for characteristic incommensurate quasi-momenta depending on the doping. It is shown that for any doping, the density of states of the system has a sharp minimum (pseudogap) at the Fermi level. This emergence of the gap just at the Fermi level is a property typical of not only the superconducting state, but also the normal state of spin glasses. The characteristics of the Fermi surface averaged over the implemented structures and the properties of quasiparticles in the nodal and antinodal regions of the quasi-momentum are considered.

DOI
10.1134/s1063776111060197

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arXiv:cond-mat/9810393•Oct 29, 1998•0 citations
The possibility of interpreting the normal pseudogap state of cuprates as a result of the formation of spin and charge structures is investigated for solutions of the Hubbard model of a finite 2D cluster based on the mean field method. The iterative self-consistency procedure reduces the initial uncorrelated spin distributions to stable structures. The Fourier components of the charge and spin distributions in such structures have peaks for characteristic incommensurate quasi-momenta depending on the doping. It is shown that for any doping, the density of states of the system has a sharp minimum (pseudogap) at the Fermi level. This emergence of the gap just at the Fermi level is a property typical of not only the superconducting state, but also the normal state of spin glasses. The characteristics of the Fermi surface averaged over the implemented structures and the properties of quasiparticles in the nodal and antinodal regions of the quasi-momentum are considered.
Cluster dynamical mean field methods are used to calculate the normal and anomalous components of the electron self-energy of the two-dimensional Hubbard model. Issues associated with the analytical continuation of the normal and anomalous parts of the gap function are discussed. Methods of minimizing the uncertainties associated with the pseudogap-related pole in the self-energy are discussed. From these the evolution of the superconducting gap and the momentum-dependent electron spectral function across the phase diagram are determined. In the pseudogap regime, decreasing the temperature into the superconducting state leads to a decrease in the energy gap and the formation of a ``peak-dip-hump'' structure in the electronic density of states. The peak feature disperses very weakly. The calculated spectral functions are in good qualitative agreement with published data. The mathematical origin of the behavior is found to be the effect of the superconductivity on the pole structure giving rise to the normal state pseudogap. In particular the ``hump'' feature is found to arise from a zero crossing of the real part of the electron self-energy rather than from an onset of scattering. The effect of superconductivity on the zone diagonal spectra is presented.
The cluster perturbation theory is presented in the 2D Hubbard model constructed using X operators in the Hubbard-I approximation. The short-range magnetic order is taken into account by dividing the entire lattice into individual 2 × 2 clusters and solving the eigenvalue problem in an individual cluster using exact diagonalization taking into account all excited levels. The case of half-filling taking into account jumps between nearest neighbors is considered. As a result of numerical solution, a shadow zone is discovered in the quasiparticle spectrum. It is also found that a gap in the density of states in the quasiparticle spectrum at zero temperature exists for indefinitely small values of Coulomb repulsion parameter U and increases with this parameter. It is found that the presence of this gap in the spectrum is due to the formation of a short-range antiferromagnetic order. An analysis of the temperature evolution of the density of states shows that the metal-insulator transition occurs continuously. The existence of two characteristic energy scales at finite temperatures is demonstrated, the larger scale is associated with the formation of a pseudogap in the vicinity of the Fermi level, and the smaller scale is associated with the metal-insulator transition temperature. A peak in the density of states at the Fermi level, which is predicted in the dynamic mean field theory in the vicinity of the metal-insulator transition, is not observed.
We study the electronic structure within a system of phase-decoupled one-dimensional superconductors coexisting with stripe spin and charge-density-wave order. This system has a nodal Fermi surface (Fermi arc) in the form of a hole pocket and an antinodal pseudogap. The spectral function in the antinodes is approximately particle-hole symmetric contrary to the gapped regions just outside the pocket. We find that states at the Fermi energy are extended whereas states near the pseudogap energy have localization lengths as short as the interstripe spacing. We consider pairing which has either local ddd-wave or sss-wave symmetry and find similar results in both cases, consistent with the pseudogap being an effect of local pair correlations. We suggest that this state is a stripe-ordered caricature of the pseudogap phase in underdoped cuprates with coexisting spin-, charge-, and pair-density-wave correlations. Lastly, we also model a superconducting state which (1) evolves smoothly from the pseudogap state, (2) has a signature subgap peak in the density of states, and (3) has the coherent pair density concentrated to the nodal region.
We investigate the doped two-dimensional Hubbard model at finite temperature using controlled diagrammatic Monte Carlo calculations allowing for the computation of spectral properties in the infinite-size limit and, crucially, with arbitrary momentum resolution. We show that three distinct regimes are found as a function of doping and interaction strength, corresponding to a weakly correlated metal with properties close to those of the non-interacting system, a correlated metal with strong interaction effects including a reshaping of the Fermi surface, and a pseudogap regime at low doping in which quasiparticle excitations are selectively destroyed near the antinodal regions of momentum space. We study the physical mechanism leading to the pseudogap and show that it forms both at weak coupling when the magnetic correlation length is large and at strong coupling when it is shorter. In both cases, we show that spin-fluctuation theory can be modified in order to account for the behavior of the non-local component of the self-energy. We discuss the fate of the pseudogap as temperature goes to zero and show that, remarkably, this regime extrapolates precisely to the ordered stripe phase found by ground-state methods. This handshake between finite temperature and ground-state results significantly advances the elaboration of a comprehensive picture of the physics of the doped Hubbard model.
Cluster dynamical mean-field calculations based on 2-, 4-, 8-, and 16-site clusters are used to analyze the doping-driven metal-insulator transition in the two-dimensional Hubbard model. Comparison of results obtained on different clusters enables a determination of those aspects of the physics that are common to all clusters and permits identification of artifacts associated with particular cluster geometries. A modest particle-hole asymmetry in the underlying band structure is shown to lead to qualitatively different behavior on the hole-doped side than on the electron-doped side. For particle-hole asymmetry of the sign and magnitude appropriate to high-Tc{T}_{c}Tc​ cuprates, the approach to the insulator from the hole-doping side is found to proceed in two stages from a high-doping region where the properties are those of a Fermi liquid with moderately renormalized parameters and very weak momentum dependence. As doping is reduced the system first enters an intermediate doping regime where the Fermi-liquid renormalizations are larger and the electron self-energy varies significantly around the Fermi surface and then passes to a small doping regime characterized by a gap on some parts of the Fermi surface but gapless behavior in other parts. On the electron-doped side the partially gapped regime does not occur, and the momentum dependence of the electron self-energy is less pronounced. Implications for the high-Tc{T}_{c}Tc​ cuprates and for the use of cluster dynamical mean-field methods in wider classes of problems are discussed.
We have studied the pseudogap formation in the single-particle spectra of the half-filling two-dimensional Hubbard model. Using a Green's function with the one-loop self-energy correction of the spin and charge fluctuations, we have numerically calculated the self-energy, the spectral function, and the density of states in the weak-coupling regime at finite temperature. Pseudogap formations have been observed in both the density of states and the spectral function at the Fermi level. The pseudogap in the spectral function is explained by the non-Fermi-liquid-like nature of the self-energy. The anomalous behavior in the self-energy is caused by both the strong antiferromagnetic spin fluctuation and the nesting condition on the non-interacting Fermi surface. In the present approximation, we find a logarithmic singularity in the integrand of the imaginary part of the self-energy. Concerning the energy dependence of the spectral function and the self-energy, two theorems are proved. They give a necessary condition in the self-energy to produce the pseudogap at the Fermi level. The pseudogap in the spectral function is highly momentum dependent on the Fermi surface. It opens initially in the (±π,0)(\pm π,0)(±π,0), (0,±π)(0,\pm π)(0,±π) regions as the normal state pseudogap observed in the high-TcT_cTc​ superconductors and if the interaction is increased, it spreads to other Fermi surface sectors. The anisotropy of the pseudogap is produced by the low-energy enhancement of the spin excitation around Q=(π,π){\bf Q}=(π,π)Q=(π,π) and the flatness of the band dispersion around the saddle point.