Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1503.08291

Exact-Diagonalization Analysis of Composite Excitations in the t-J Model

Takashi Otaki, Yuta Yahagi, Hiroaki Matsueda

Published Mar 28, 2015• 0 citations
arXivHTMLPDF

Abstract

We examine spectral properties of doped holes dressed with surrounding spin cloud in the t-J model. These composite-hole excitations well characterize prominent band structures in the angle-resolved photoemission spectrum. In one-dimensional (1D) case at half-filling, we identify the composite operators that separately pick up the spinon and holon branches, respectively. After hole doping, we find that the composite hole excitations with string-like spins tend to be localized at k=π/2 in the momentum space. This means that such composite excitations should be actual electronic excitations, since the spinon and holon branches merge together at this momentum. In 2D case, we find that the composite excitations with more non-local spin fluctuation have stronger intensity near the Fermi level. The composite band structure along diagonal (0,0)-(π,π) direction in 2D has some similarity to that in 1D, and such non-local spin fluctuation plays an important role on the formation of the pseudogap in high-Tc cuprates.

DOI
10.48550/arxiv.1503.08291

Related papers

Spectral Properties of Composite Excitations in the t–J Model

Takashi Otaki, Yuta Yahagi, Hiroaki Matsueda

In quantum many-body systems, the equation of motion for a simple fermionic operator does not close, and higher-order processes induce composite operators dressed with several types of nonlocal quantum fluctuation. We systematically examine the spectral properties of these composite excitations in the t–J model in one spatial dimension by both numerical and theoretical approaches. Of particular interest, with the help of the Bethe ansatz for the large-U Hubbard model, is the classification of which composite excitations are due to the string excitation, which is usually hidden in the single-particle spectrum, as well as the spinon and holon branches. We examine how the mixing between the spinon and string excitations is prohibited in terms of the composite operator method. Owing to the dimensionality independent nature of the present approach, we discuss the implications of the mixing in close connection with the pseudogap in high-Tc cuprates.

Journal of the Physical Society of Japan•Jul 26, 2017•2 citations

Photoemission spectra of the t - J model in one and two dimensions: Similarities and differences

R. Eder, Y. Ohta

We present an exact diagonalization study of the single-particle spectral function in the one-dimensional (1D) and two-dimensional (2D) $t$-$J$ model. By studying the scaling properties with $J$ and $t$ we find a simple building pattern in 1D and show that every spectral feature can be uniquely assigned by a spinon and holon momentum. We find two types of low-energy excitations: A band with energy scale $J$ and high spectral weight disperses upwards in the interior part of the Brillouin zone and reaches ${E}_{F}$ at ${k}_{F},$ and a band with energy scale $t$ and low spectral weight disperses downwards in the outer part of the zone, touching ${E}_{F}$ at ${3k}_{F}.$ An analogous analysis of the 2D case at half-filling shows that the $t$ band exists also in this case, but is diffuse and never reaches the Fermi energy. For the doped case in 2D the picture is more reminiscent of 1D; in particular, the ``main band'' with a dispersion $\ensuremath{\propto}J$ and the ``shadow band'' with energy scale $t$ can be identified also in this case. This leads us to propose that the shadow bands discovered by Aebi et al. in Bi2212 are the 2D analog of the ${3k}_{F}$ singularity in 1D systems and unrelated to antiferromagnetic spin fluctuations.

arXiv:cond-mat/9702221•Physical review. B, Condensed matter•Aug 1, 1997•25 citations

Spin bags in the dopedt-Jmodel

R. Eder, Y. Ohta

We present a nonperturbative method for deriving a quasiparticle description of the low-energy excitations in the t-J model for strongly correlated electrons. Using the exact diagonalization technique we evaluated exactly the spectral functions of composite operators, which describe an electron or hole dressed by antiferromagnetic spin fluctuations as expected in the string or spin bag picture. For hole doping up to 1/8, use of the composite operators leads to a drastic simplification of the single-particle spectral function: at half-filling it takes free-particle form, for the doped case it resembles a system of weakly interacting fermions corresponding to the doped holes. We conclude that for all doping levels studied, the elementary electronic excitations next to the Fermi level are adequately described by the antiferromagnetic spin-fluctuation picture.

arXiv:cond-mat/9406098•Physical review. B, Condensed matter•Oct 1, 1994•20 citations

Angle-resolved photoemission spectra of the stripe phase in the two-dimensional t−J model

R. Eder, Y. Ohta

The two-dimensional $t\ensuremath{-}J$ model with and without ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$ hopping-terms is studied by exact diagonalization on a $5\ifmmode\times\else\texttimes\fi{}4$ cluster, which realizes a hole stripe in y direction in a spin-Peierls phase. Next nearest hopping terms with a sign appropriate for hole-doped cuprates enhance the stripe formation. The dispersion of the quasiparticle peaks in the single-particle spectrum is in good agreement with bond operator theory for hole motion in the spin-Peierls phase, particularly so for realistic values of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}.$ The resulting spectral weight distribution and Fermi surface agree well with experimental angle-resolved photoemission spectra on ${\mathrm{La}}_{1.28}{\mathrm{Nd}}_{0.6}{\mathrm{Sr}}_{0.12}{\mathrm{CuO}}_{4}.$

Physical Review B•Mar 18, 2004•7 citations

NUMERICAL STUDY OF THE ELECTRONIC STATES IN HOLE- AND ELECTRON-DOPED HIGH-TC CUPRATES

Takami Tohyama

We examine the electronic states in the hole- and electron-doped cuprates by using the t-t′-t″-J model. Numerically exact diagonalization method is employed for a 20-site square lattice under twisted boundary conditions. The density of states in the underdoped region clearly shows a pseudogap behavior near the Fermi level in both hole and electron dopings. In hole doping, the edge of the pseudogap in the occupied side exhibits a large weight that comes from a flat band near k=(π,0). In contrast, the weight near the gap edge in electron doping is larger for the unoccupied side than for the occupied side.

International Journal of Modern Physics B•Jan 30, 2005•0 citations

Doped carrier formulation and mean-field theory of the tt′t″J model

Tiago C. Ribeiro, Xiao-Gang Wen

In the generalized-$tJ$ model the effect of a large local Coulomb repulsion is accounted for by restricting the Hilbert space to states with at most one electron per site. In this case the electronic system can be viewed in terms of holes hopping in a lattice of correlated spins, where holes are the carriers doped into the half-filled Mott insulator. To explicitly capture the interplay between the hole dynamics and local spin correlations we derive a formulation of the generalized-$tJ$ model where doped carrier operators are used instead of the original electron operators. This ``doped carrier'' formulation provides a starting point to address doped spin systems, and we use it to develop a fully fermionic, mean-field description of doped Mott insulators. This mean-field approach reveals a mechanism for superconductivity---namely, spinon-dopon mixing---and we apply it to the $t{t}^{\ensuremath{'}}{t}^{\ensuremath{''}}J$ model as of interest to high-temperature superconductors. In particular, we use model parameters borrowed from band calculations and from fitting angle-resolved photoemission spectroscopy data to obtain a mean-field phase diagram that reproduces semiquantitatively that of hole- and electron-doped cuprates. The mean-field approach hereby presented accounts for the local antiferromagnetic and $d$-wave superconducting correlations which, we show, provide a rational for the role of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$ in strengthening superconductivity as expected by experiments and other theoretical approaches. As we discuss how $t$, ${t}^{\ensuremath{'}}$, and ${t}^{\ensuremath{''}}$ affect the phase diagram, we also comment on possible scenarios to understand the differences between as-grown and oxygen-reduced electron-doped samples.

arXiv:cond-mat/0601174•Physical Review B•Oct 17, 2006•42 citations
We examine spectral properties of doped holes dressed with surrounding spin cloud in the t-J model. These composite-hole excitations well characterize prominent band structures in the angle-resolved photoemission spectrum. In one-dimensional (1D) case at half-filling, we identify the composite operators that separately pick up the spinon and holon branches, respectively. After hole doping, we find that the composite hole excitations with string-like spins tend to be localized at k=π/2 in the momentum space. This means that such composite excitations should be actual electronic excitations, since the spinon and holon branches merge together at this momentum. In 2D case, we find that the composite excitations with more non-local spin fluctuation have stronger intensity near the Fermi level. The composite band structure along diagonal (0,0)-(π,π) direction in 2D has some similarity to that in 1D, and such non-local spin fluctuation plays an important role on the formation of the pseudogap in high-Tc cuprates.
In quantum many-body systems, the equation of motion for a simple fermionic operator does not close, and higher-order processes induce composite operators dressed with several types of nonlocal quantum fluctuation. We systematically examine the spectral properties of these composite excitations in the t–J model in one spatial dimension by both numerical and theoretical approaches. Of particular interest, with the help of the Bethe ansatz for the large-U Hubbard model, is the classification of which composite excitations are due to the string excitation, which is usually hidden in the single-particle spectrum, as well as the spinon and holon branches. We examine how the mixing between the spinon and string excitations is prohibited in terms of the composite operator method. Owing to the dimensionality independent nature of the present approach, we discuss the implications of the mixing in close connection with the pseudogap in high-Tc cuprates.
We present an exact diagonalization study of the single-particle spectral function in the one-dimensional (1D) and two-dimensional (2D) ttt-JJJ model. By studying the scaling properties with JJJ and ttt we find a simple building pattern in 1D and show that every spectral feature can be uniquely assigned by a spinon and holon momentum. We find two types of low-energy excitations: A band with energy scale JJJ and high spectral weight disperses upwards in the interior part of the Brillouin zone and reaches EF{E}_{F}EF​ at kF,{k}_{F},kF​, and a band with energy scale ttt and low spectral weight disperses downwards in the outer part of the zone, touching EF{E}_{F}EF​ at 3kF.{3k}_{F}.3kF​. An analogous analysis of the 2D case at half-filling shows that the ttt band exists also in this case, but is diffuse and never reaches the Fermi energy. For the doped case in 2D the picture is more reminiscent of 1D; in particular, the ``main band'' with a dispersion $\ensuremath{\propto}J$ and the ``shadow band'' with energy scale ttt can be identified also in this case. This leads us to propose that the shadow bands discovered by Aebi et al. in Bi2212 are the 2D analog of the 3kF{3k}_{F}3kF​ singularity in 1D systems and unrelated to antiferromagnetic spin fluctuations.
We present a nonperturbative method for deriving a quasiparticle description of the low-energy excitations in the t-J model for strongly correlated electrons. Using the exact diagonalization technique we evaluated exactly the spectral functions of composite operators, which describe an electron or hole dressed by antiferromagnetic spin fluctuations as expected in the string or spin bag picture. For hole doping up to 1/8, use of the composite operators leads to a drastic simplification of the single-particle spectral function: at half-filling it takes free-particle form, for the doped case it resembles a system of weakly interacting fermions corresponding to the doped holes. We conclude that for all doping levels studied, the elementary electronic excitations next to the Fermi level are adequately described by the antiferromagnetic spin-fluctuation picture.
The two-dimensional $t\ensuremath{-}J$ model with and without ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$ hopping-terms is studied by exact diagonalization on a $5\ifmmode\times\else\texttimes\fi{}4$ cluster, which realizes a hole stripe in y direction in a spin-Peierls phase. Next nearest hopping terms with a sign appropriate for hole-doped cuprates enhance the stripe formation. The dispersion of the quasiparticle peaks in the single-particle spectrum is in good agreement with bond operator theory for hole motion in the spin-Peierls phase, particularly so for realistic values of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}.$ The resulting spectral weight distribution and Fermi surface agree well with experimental angle-resolved photoemission spectra on La1.28Nd0.6Sr0.12CuO4.{\mathrm{La}}_{1.28}{\mathrm{Nd}}_{0.6}{\mathrm{Sr}}_{0.12}{\mathrm{CuO}}_{4}.La1.28​Nd0.6​Sr0.12​CuO4​.
We examine the electronic states in the hole- and electron-doped cuprates by using the t-t′-t″-J model. Numerically exact diagonalization method is employed for a 20-site square lattice under twisted boundary conditions. The density of states in the underdoped region clearly shows a pseudogap behavior near the Fermi level in both hole and electron dopings. In hole doping, the edge of the pseudogap in the occupied side exhibits a large weight that comes from a flat band near k=(π,0). In contrast, the weight near the gap edge in electron doping is larger for the unoccupied side than for the occupied side.
In the generalized-tJtJtJ model the effect of a large local Coulomb repulsion is accounted for by restricting the Hilbert space to states with at most one electron per site. In this case the electronic system can be viewed in terms of holes hopping in a lattice of correlated spins, where holes are the carriers doped into the half-filled Mott insulator. To explicitly capture the interplay between the hole dynamics and local spin correlations we derive a formulation of the generalized-tJtJtJ model where doped carrier operators are used instead of the original electron operators. This ``doped carrier'' formulation provides a starting point to address doped spin systems, and we use it to develop a fully fermionic, mean-field description of doped Mott insulators. This mean-field approach reveals a mechanism for superconductivity---namely, spinon-dopon mixing---and we apply it to the $t{t}^{\ensuremath{'}}{t}^{\ensuremath{''}}J$ model as of interest to high-temperature superconductors. In particular, we use model parameters borrowed from band calculations and from fitting angle-resolved photoemission spectroscopy data to obtain a mean-field phase diagram that reproduces semiquantitatively that of hole- and electron-doped cuprates. The mean-field approach hereby presented accounts for the local antiferromagnetic and ddd-wave superconducting correlations which, we show, provide a rational for the role of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$ in strengthening superconductivity as expected by experiments and other theoretical approaches. As we discuss how ttt, ${t}^{\ensuremath{'}}$, and ${t}^{\ensuremath{''}}$ affect the phase diagram, we also comment on possible scenarios to understand the differences between as-grown and oxygen-reduced electron-doped samples.