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arXiv:1406.0910 · Physical Review B

Spectral properties near the Mott transition in the two-dimensional Hubbard model with next-nearest-neighbor hopping

Masanori Kohno

Published Jul 10, 2014• 36 citations
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Abstract

The single-particle spectral properties near the Mott transition in the two-dimensional Hubbard model with next-nearest-neighbor hopping are investigated by using cluster perturbation theory. Complicated spectral features of this model are simply interpreted, by considering how the next-nearest-neighbor hopping shifts the spectral weights of the two-dimensional Hubbard model. Various anomalous features observed in hole-doped and electron-doped cuprate high-temperature superconductors are explained in a unified manner as properties near the Mott transition in a two-dimensional system whose spectral weights are shifted by next-nearest-neighbor hopping.

DOI
10.1103/physrevb.90.035111

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The single-particle spectral properties near the Mott transition in the two-dimensional Hubbard model with next-nearest-neighbor hopping are investigated by using cluster perturbation theory. Complicated spectral features of this model are simply interpreted, by considering how the next-nearest-neighbor hopping shifts the spectral weights of the two-dimensional Hubbard model. Various anomalous features observed in hole-doped and electron-doped cuprate high-temperature superconductors are explained in a unified manner as properties near the Mott transition in a two-dimensional system whose spectral weights are shifted by next-nearest-neighbor hopping.
The single-particle spectral properties of the two-dimensional $t\text{\ensuremath{-}}J$ model in the parameter regime relevant to cuprate high-temperature superconductors are investigated using cluster perturbation theory. Various anomalous features observed in cuprate high-temperature superconductors are collectively explained in terms of the dominant modes near the Mott transition in this model. Although the behavior of the dominant modes in the low-energy regime is similar to that in the two-dimensional Hubbard model, significant differences appear near the Mott transition for the high-energy electron removal excitations which can be considered to primarily originate from holon modes in one dimension. The overall spectral features are confirmed to remain almost unchanged as the cluster size is increased from $4\ifmmode\times\else\texttimes\fi{}4$ to $6\ifmmode\times\else\texttimes\fi{}6$ sites by using a combined method of the non-Abelian dynamical density-matrix renormalization group method and cluster perturbation theory.
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.
The single-particle spectral properties near the Mott transition in the one-dimensional Hubbard model are investigated by using the dynamical density-matrix renormalization group method and the Bethe ansatz. The pseudogap, hole-pocket behavior, spectral-weight transfer, and upper Hubbard band are explained in terms of spinons, holons, antiholons, and doublons. The Mott transition is characterized by the emergence of a gapless mode whose dispersion relation extends up to the order of hopping t (spin exchange J) in the weak (strong) interaction regime caused by infinitesimal doping.
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.