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arXiv:2207.01243

Thermal evolution of single-particle spectral function in the half-filled Hubbard model and pseudogap

Harun Al Rashid, Dheeraj Kumar Singh

Published Jul 4, 2022• 0 citations
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Abstract

In the half-filled one-orbital Hubbard model on a square lattice, we find pseduogap features in the form of two-peak structures associated with the momentum-resolved spectral function, which exists within the temperature window $T_N \lesssim T \lesssim T^*$. $T^*$ is the temperature below which there exists a well-formed dip in the density of state. Inside the window $T_N \lesssim T \lesssim T^*$, the peak-to-peak separation in the two-peak structure of the momentum-resolved spectral function rises on moving away from the point ($π/2, π/2$) along the normal state Fermi surface towards $(π, 0)$, a behavior remarkably similar to what is observed in the pseudogap phase. We unveil these features by using a parallelized cluster-based Monte-Carlo method for simulating the magnetic order parameter fields on a superlattice, which enables us to access the momentum-resolved single-particle spectral function corresponding to a lattice size of $\sim$ 240 $\times$ 240 with almost negligible finite-size effects.

DOI
10.48550/arxiv.2207.01243

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In the half-filled one-orbital Hubbard model on a square lattice, we find pseduogap features in the form of two-peak structures associated with the momentum-resolved spectral function, which exists within the temperature window TN≲T≲T∗T_N \lesssim T \lesssim T^*TN​≲T≲T∗. T∗T^*T∗ is the temperature below which there exists a well-formed dip in the density of state. Inside the window TN≲T≲T∗T_N \lesssim T \lesssim T^*TN​≲T≲T∗, the peak-to-peak separation in the two-peak structure of the momentum-resolved spectral function rises on moving away from the point (π/2,π/2π/2, π/2π/2,π/2) along the normal state Fermi surface towards (π,0)(π, 0)(π,0), a behavior remarkably similar to what is observed in the pseudogap phase. We unveil these features by using a parallelized cluster-based Monte-Carlo method for simulating the magnetic order parameter fields on a superlattice, which enables us to access the momentum-resolved single-particle spectral function corresponding to a lattice size of ∼\sim∼ 240 ×\times× 240 with almost negligible finite-size effects.
In the half-filled one-orbital Hubbard model on a square lattice, we find pseudogap-like features in the form of two-peak structures associated with the momentum-resolved spectral function. These features exist within the temperature window ${T}_{N}\ensuremath{\lesssim}T\ensuremath{\lesssim}{T}^{*}$, where TN{T}_{N}TN​ is the N\'eel temperature and T∗{T}^{*}T∗ is the temperature below which there exists a well-formed dip in the density of state. Inside the window ${T}_{N}\ensuremath{\lesssim}T\ensuremath{\lesssim}{T}^{*}$, the peak-to-peak separation in the two-peak structure of the momentum-resolved spectral function grows on moving away from the point ($\ensuremath{\pi}/2,\ensuremath{\pi}/2$) along the normal state Fermi surface toward $(\ensuremath{\pi},0)$, a behavior with remarkable similarities to what is observed in the ddd-wave state and pseudogap phase of high-Tc{T}_{c}Tc​ cuprates. We unveil these features by using a parallelized cluster-based Monte Carlo method for simulating the magnetic order parameter fields on a superlattice. The method enables us to access the momentum-resolved single-particle spectral function corresponding to a lattice size of $\ensuremath{\approx}240 \ifmmode\times\else\texttimes\fi{}$ 240 with an almost negligible finite-size effect.
In the half-filled one-orbital Hubbard model on a square lattice, we study the effect of next-nearest neighbor hopping on the single-particle spectral function at finite temperature using an exact-diagonalization + Monte-Carlo based approach to the simulation process. We find that the pseudogap-like dip, existing in the density of states in between the Néel temperature TNT_NTN​ and a relatively higher temperature T∗T^*T∗, is accompanied with a significant asymmetry in the hole- and particle-excitation energy along the high-symmetry directions as well as along the normal-state Fermi surface. On moving from (π/2,π/2π/2, π/2π/2,π/2) toward (π,0)(π, 0)(π,0) along the normal state Fermi surface, the hole-excitation energy increases, a behavior remarkably similar to what is observed in the ddd-wave state and pseudogap phase of high-TcT_cTc​ cuprates, whereas the particle-excitation energy decreases. The quasiparticle peak height is the largest near (π/2,π/2π/2, π/2π/2,π/2) whereas it is the smallest near (π,0)(π, 0)(π,0). These spectral features survive beyond TNT_NTN​. The temperature window TN≲T≲T∗T_N \lesssim T \lesssim T^*TN​≲T≲T∗ shrinks with an increase in the next-nearest neighbor hopping, which indicates that the next-nearest neighbor hopping may not be supportive to the pseudogap-like features.
In the half-filled one-orbital Hubbard model on a square lattice, we study the effect of next-nearest neighbor hopping on the single-particle spectral function at finite temperature using an exact-diagonalization + Monte-Carlo based approach to the simulation process. We find that the pseudogap-like dip, existing in the density of states in between the Néel temperature T_N T N and a relatively higher temperature scale T^* T * , is accompanied with a significant asymmetry in the hole- and particle-excitation energy along the high-symmetry directions as well as along the normal-state Fermi surface. On moving from ( \pi/2, \pi/2 π / 2 , π / 2 ) toward (\pi, 0) ( π , 0 ) along the normal state Fermi surface, the hole-excitation energy increases, a behavior remarkably similar to what is observed in the d d -wave state and pseudogap phase of high- T_c T c cuprates, whereas the particle-excitation energy decreases. The quasiparticle peak height is the largest near ( \pi/2, \pi/2 π / 2 , π / 2 ) whereas it is the smallest near (\pi, 0) ( π , 0 ) . These spectral features survive beyond T_N T N . The temperature window T_N ≲ T ≲ T^* T N ≲ T ≲ T * shrinks with an increase in the next-nearest neighbor hopping, which indicates that the next-nearest neighbor hopping may not be supportive to the pseudogap-like features.
In this study, the metal-insulator transition in the square-lattice Hubbard model at half-filling is revisited in relation to the DOS and spectral functions by means of the ladder dual fermion approximation (LDFA). For this purpose, a new expression of the two-body Green's function in the form of resolvents is proposed, which provides tractable and efficient means to calculate the local vertex function with the Lanczos exact diagonalization (ED) method. This makes it possible to use the Lanczos ED method as a solver of the effective impurity Anderson model for LDFA, opening up the way to access low temperatures for these perturbative extensions of the dynamical mean-field theory and to obtain accurate DOS and spectral functions on the real frequency axis by a new variant of the maximum entropy method. It is found that for $U\ensuremath{\le}3.5t$, as temperature decreases, the pseudogap formation due to antiferromagnetic correlations in the quasiparticle peak of the spectral function occurs at the XXX point $[\mathbit{k}=(\ensuremath{\pi},0)]$, spreads through the Fermi surface and ends at the M2{M}_{2}M2​ point $[\mathbit{k}=(\ensuremath{\pi}/2,\ensuremath{\pi}/2)]$. The almost simultaneous creation of the pseudogap and the loss of the Fermi liquid feature is consistent with that expected in the Slater regime. Although the pseudogap still appears in the quasi-particle-like single peak for $U\ensuremath{\ge}4.0t$, the Fermi-liquid feature is partially lost on the Fermi surface already at higher temperatures as expected in the Mott-Heisenberg regime, in which local spins are preformed at high temperatures. A sharp crossover from a pseudogap phase to a Mott insulator at finite ${U}^{*}\ensuremath{\approx}4.7t$ is found to occur below the temperature of the pseudogap formation similar to a previous study with the nonlinear $\ensuremath{\sigma}$ model approach.
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.
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 temperatures. 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 self-energy imaginary part. The pseudogap in the spectral function is highly momentum dependent on the Fermi surface. This anisotropy of the pseudogap is produced by the flatness of the band dispersion around the saddle point rather than the nesting condition on the Fermi level.