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SciPost Physics

Effect of next-nearest neighbor hopping on the single-particle excitations at finite temperature

Harun Al Rashid, Dheeraj Kumar Singh

Published Apr 22, 2024• 5 citations
Publisher

Abstract

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.

DOI
10.21468/scipostphys.16.4.107

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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 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 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 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.
The attractive Hubbard model plays a paradigmatic role in the study of superconductivity (superfluidity) and has become directly realizable in ultracold atom experiments on optical lattices. However, the critical temperatures, TcT_cTc​'s, remain lower than the lowest temperatures currently achievable in experiments. Here, we explore a possible route to enhance TcT_cTc​ by introducing an additional next-nearest-neighbor (NNN) hopping, t′t^\primet′, in a two-dimensional square lattice. We perform sign-problem-free determinant quantum Monte Carlo simulations to compute response functions such as pairing correlation functions, superfluid density, and uniform spin susceptibility. Our results show that a judicious choice of t′t^\primet′ can increase TcTcTc by up to 50%50\%50% compared to the case with only nearest-neighbor hopping. In contrast, the preformed pairs temperature scale, named pairing temperature, TpT_pTp​, decreases with increasing ∣t′/t∣|t^{\prime}/t|∣t′/t∣, which should represent a reduction of the pseudogap region, favoring a more BCS-like behavior at intermediate coupling. We further analyze the interacting density of states to characterize the transition from a pseudogap regime to a fully gapped superconducting state. These findings suggest that NNN hopping could be a viable route to increase TcT_cTc​ to values closer to experimentally accessible temperature scales.
The effect of doping in the two-dimensional Hubbard model is studied within finite temperature exact diagonalization combined with cluster dynamical mean field theory. By employing a mixed basis involving cluster sites and bath molecular orbitals for the projection of the lattice Green's function onto 2x2 clusters, a considerably more accurate description of the low frequency properties of the self-energy is achieved than in a pure site picture. The transition from Fermi-liquid to non-Fermi-liquid behavior for decreasing hole doping is studied as a function of Coulomb energy, next-nearest neighbor hopping, and temperature. In particular, the self-energy component Sigma_X associated with X=(pi,0) is shown to exhibit an onset of non-Fermi-liquid behavior as the hole doping decreases below a critical value delta_c. The imaginary part of Sigma_X(omega) then develops a collective mode above E_F, which exhibits a distinct dispersion with doping. Accordingly, the real part of Sigma_X(omega) has a positive slope above E_F, giving rise to an increasing particle-hole asymmetry as the system approaches the Mott transition. This behavior is consistent with the removal of spectral weight from electron states close to E_F and the opening of a pseudogap which increases with decreasing doping. The phase diagram reveals that delta_c = 0.15 ... 0.20 for various system parameters. For electron doping, the collective mode of Sigma_X(omega) and the concomitant pseudogap are located below the Fermi energy which is consistent the removal of spectral weight from hole states just below E_F. The critical doping which marks the onset of non-Fermi-liquid behavior, is systematically smaller than for hole doping.
Using the dynamical cluster approximation and quantum Monte Carlo simulations we calculate the single-particle spectra of the Hubbard model with next-nearest neighbor hopping . In the underdoped region, we find that the pseudogap along the zone diagonal in the electron doped systems is due to long-range antiferromagnetic correlations. The physics in the proximity of (0, pi) is dramatically influenced by t' and determined by the short range correlations. The effect t' of on the low-energy angle-resolved photoemission spectroscopy spectra is weak except close to the zone edge. The short range correlations are sufficient to yield a pseudogap signal in the magnetic susceptibility and produce a concomitant gap in the single-particle spectra near (pi, pi/2), but not necessarily at a location in the proximity of the Fermi surface.