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

Physical review. B, Condensed matter

Dynamics of a small density of holes in a two-dimensional quantum antiferromagnet

Bumsoo Kyung, Sergei I. Mukhin

Published Feb 1, 1997• 16 citations
Publisher

Abstract

The hole dynamics in a quantum antiferromagnetic background for a small doping concentration is studied within the t-J model description. The noncrossing approximation for the hole self-energy is used. The correct quasiparticle pole structure (without artificial broadening) in the spectral density function is employed. Dyson's equation for the hole Green's function is solved numerically by introducing a lattice in momentum space. The evolution of the density of states and the momentum-distribution function for holes is investigated as a function of hole-magnon coupling constant t at fixed J. The momentum distribution function shows a sharp drop at the Fermi surface for several different hole-magnon coupling constants. This indicates the validity of the Fermi liquid description for the t-J model in the low doping concentration. The volume (surface) enclosed by the Fermi surface (curve) is found to be invariant for all the coupling strengths we have studied. The incoherent spectrum below the chemical potential in the density of states becomes more significant for stronger interaction constants. These features numerically verify Luttinger's theorem for a small density of doped holes in the t-J model. The optical conductivity is computed using the lowest-order diagrams. As the hole-magnon coupling constant t increases, absorption becomes stronger at \ensuremath{\omega}\ensuremath{\simeq}2J, the characteristic frequency for spin waves. This feature may be associated with the experimentally observed midinfrared absorption band in underdoped cuprates.

DOI
10.1103/physrevb.55.3886

Related papers

Spectral properties of thet-Jmodel in the presence of hole-phonon interaction

Bumsoo Kyung, Sergei I. Mukhin, Vladimir N. Kostur +1 more

We examine the effects of electron-phonon interaction on the dynamics of the charge carriers doped in two-dimensional (2D) Heisenberg antiferromagnet. The t-J model Hamiltonian with a Fr\"ohlich term which couples the holes to a dispersionless (optical) phonon mode is considered for low doping concentration. The evolution of the spectral density function, the density of states, and the momentum distribution function of the holes with an increase of the hole-phonon coupling constant g is studied numerically. As the coupling to a phonon mode increases the quasiparticle spectral weight decreases and a ``phonon satellite'' feature close to the quasiparticle peak becomes more pronounced. Furthermore, strong electron-phonon coupling smears the multimagnon resonances (``string states'') in the incoherent part of the spectral function. The jump in the momentum distribution function at the Fermi surface is reduced without changing the hole pocket volume, thereby providing a numerical verification of Luttinger theorem for this strongly interacting system. The vertex corrections due to electron-phonon interaction are negligible in spite of the fact that the ratio of the phonon frequency to the effective bandwidth is not small. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9609186•Physical review. B, Condensed matter•Nov 1, 1996•18 citations

RENORMALIZATION OF ELEMENTARY EXCITATIONS OF THE t-J MODELWITH DOPING

Alexei Sherman, Michael Schreiber

Hole and magnon spectral functions of the 2D ¢-J model are self-consistently calculated from a set of Dyson's equations for the hole concentrations z < 0.3.For J < ¢, itis shown that near z = 0.05 the hole spectrum changes drastically, acquiring features of a weakly correlated spectrum.This change is accompanied by the entering of the chemical potential u into a sharp maximum of the density of states.With z increasing the maximum moves together with u upto z =~0.15 and then lags behind.This concentration is also distinctive in that the Fermi surface becomes a simply connected surface and the overdamped magnons which appear near z = 0.02 occupy the widest region in k space.Besides, a limiting frequency of usual magnons passes through a minimum here.Significant deviations from the normal Fermi liquid, which partly resemble the marginal Fermi liquid, are observed for x > 0.05.

Proceedings of the Estonian Academy of Sciences Physics Mathematics•Feb 14, 1995•0 citations

Dynamical properties of a single hole in an antiferromagnet

Didier Poilblanc, Timothy A. L. Ziman, Heinz J. Schulz +1 more

A finite-size scaling analysis of the spectral function and of the optical conductivity of a single hole moving in an antiferromagnetic background is performed. It is shown that both the low-energy quasiparticle peak and the broad higher-energy structure are robust with increasing cluster size from 4\ifmmode\times\else\texttimes\fi{}4 to \ensuremath{\surd}26 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}26 sites. In the absence of spin fluctuations, for most static or dynamical quantities saturation occurs when the size exceeds a characteristic size ${\mathit{N}}_{\mathit{c}}$(${\mathit{J}}_{\mathit{z}}$). Typically, 16- and 26-site clusters give reliable results for ${\mathit{J}}_{\mathit{z}}$>0.75 and ${\mathit{J}}_{\mathit{z}}$>0.3, respectively. The hole optical mass is shown to be very large (>20) in agreement with the small bandwidth. Due to the energy gap to flip a spin in the vicinity of a hole, a small gap \ensuremath{\propto}${\mathit{J}}_{\mathit{z}}$ separates the low-energy \ensuremath{\delta} function from the rest of the spectrum in the dynamical correlation functions. On the other hand, with ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ this gap seems to disappear with increasing system size as one would expect since the spin waves are gapless in the thermodynamic limit. The large momentum dependence of the quasiparticle weight in the isotropic case is inconsistent with a string picture but agrees well with the self-consistent Born approximation.An accurate estimation of the higher-energy part of the spectral functions of the t-J model can be made for momenta close to (0,0) or (\ensuremath{\pi},\ensuremath{\pi}); it consists of a broad featureless band. For momenta close to the Fermi surface, no evidence for excited string states is found. This may be either because the string scenario breaks down or because exact calculations at momenta near (\ensuremath{\pi}/2,\ensuremath{\pi}/2) are limited by the differing geometries of the finite clusters. In the Ising limit, the spectral function also depends crucially on the momentum, but a feature resembling a string excitation is seen for momenta close to (0,0). Our data on the finite-frequency optical conductivity of a single hole in the t-J model reveal that the total spectral weight at finite frequency has a strong size dependence and decreases with increasing size (for J not too small). This suggests that the optical mass and the optical absorption of the t-J model may have been overestimated in the past.

arXiv:cond-mat/9212010•Physical review. B, Condensed matter•Jun 1, 1993•54 citations

Transient carrier dynamics in a Mott insulator with antiferromagnetic order

Eiki Iyoda, Sumio Ishihara

We study transient dynamics of hole carriers injected into a Mott insulator with antiferromagnetic long-range order. This ``dynamical hole doping'' contrasts with chemical hole doping. The theoretical framework for the transient carrier dynamics is presented based on the two-dimensional $t$-$J$ model. The time dependencies of the optical conductivity spectra, as well as the one-particle excitation spectra, are calculated based on the Keldysh Green's function formalism at zero temperature combined with the self-consistent Born approximation. In the early stage after dynamical hole doping, the Drude component appears, and then incoherent components originating from hole-magnon scattering start to grow. Fast oscillatory behavior owing to coherent magnon and slow relaxation dynamics are confirmed in the spectra. The time profiles are interpreted as doped bare holes being dressed by magnon clouds and relaxed into spin polaron quasiparticle states. The characteristic relaxation times for Drude and incoherent peaks strongly depend on the momentum of the dynamically doped hole and the exchange constant. Implications for recent pump-probe experiments are discussed.

arXiv:1312.1077•Physical Review B•Mar 27, 2014•26 citations

Dynamical properties of a hole in a Heisenberg antiferromagnet

Zhiping Liu, Efstratios Manousakis

The t-J model in the large-t/J and low-doping limit is approximated by an effective Hamiltonian that treats spin degrees of freedom within the linear-spin-wave approximation and the hole-hopping term with a hole-spin interaction vertex that is linear in the spin-wave operators. The Dyson's equation for the single-hole Green's function is solved numerically on finite- but sufficiently large-size square lattices. Our calculation is based on an approximate equation for the hole motion that has been obtained using a self-consistent perturbation approach where crossing diagrams are neglected. We have studied the contribution of vertex corrections and found that the leading two-loop crossing diagram is exactly zero. Thus, the leading nonzero contribution to the proper self-energy from crossing diagrams is a three-loop correction. In two dimensions, it is possible to solve Dyson's equation numerically including these three-loop corrections. The results demonstrate that the contribution of such vertex corrections is indeed small. Our solution for the hole spectral function, obtained by neglecting such small contributions from vertex corrections, shows that most features describing the hole motion are in close agreement with the results of the exact diagonalization on the ${4}^{2}$ lattice in the region of J/t\ensuremath{\le}0.2. The results obtained on sufficiently large-size lattices suggest that certain important features of the spectral function remain while others change due to finite-size effects. In particular, we find well-defined peaks above the lowest-energy peak that survive in the thermodynamic limit. We analyze these higher-energy peaks of the spectral functions and find that they can be understood as ``string'' excitations, which are created by the hole moving in a nearly linear potential.

Physical review. B, Condensed matter•Feb 1, 1992•274 citations

Hole spectral functions in lightly doped quantum antiferromagnets

Satyaki Kar, Efstratios Manousakis

We study the hole and magnon spectral functions as a function of hole doping in the two-dimensional $t\ensuremath{-}J$ and $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{'}\ensuremath{'}}\ensuremath{-}J$ models working within the limits of spin-wave theory by linearizing the hole-spin-deviation interaction and by adapting the noncrossing approximation. We find that the staggered magnetization decreases rather rapidly with doping and it goes to zero at a few percent of hole concentration in both $t\ensuremath{-}J$ and $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{'}\ensuremath{'}}\ensuremath{-}J$ models. Furthermore, our results show that the residue of the quasiparticle peak at $\stackrel{P\vec}{G}=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2)$ decreases very rapidly with doping. We also find pockets centered at $\stackrel{P\vec}{G}$, (i) with an elliptical shape with large eccentricity along the antinodal direction in the case of the $t\ensuremath{-}J$ model and (ii) with an almost circular shape in the case of the $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{'}\ensuremath{'}}\ensuremath{-}J$ model. Last, we show that the spectral intensity distribution in the doped antiferromagnet has a waterfall-like pattern along the nodal direction of the Brillouin zone, a feature that is also seen in angle-resolved photoemission spectroscopy measurements.

arXiv:1106.6332•Physical Review B•Nov 9, 2011•7 citations
The hole dynamics in a quantum antiferromagnetic background for a small doping concentration is studied within the t-J model description. The noncrossing approximation for the hole self-energy is used. The correct quasiparticle pole structure (without artificial broadening) in the spectral density function is employed. Dyson's equation for the hole Green's function is solved numerically by introducing a lattice in momentum space. The evolution of the density of states and the momentum-distribution function for holes is investigated as a function of hole-magnon coupling constant t at fixed J. The momentum distribution function shows a sharp drop at the Fermi surface for several different hole-magnon coupling constants. This indicates the validity of the Fermi liquid description for the t-J model in the low doping concentration. The volume (surface) enclosed by the Fermi surface (curve) is found to be invariant for all the coupling strengths we have studied. The incoherent spectrum below the chemical potential in the density of states becomes more significant for stronger interaction constants. These features numerically verify Luttinger's theorem for a small density of doped holes in the t-J model. The optical conductivity is computed using the lowest-order diagrams. As the hole-magnon coupling constant t increases, absorption becomes stronger at \ensuremath{\omega}\ensuremath{\simeq}2J, the characteristic frequency for spin waves. This feature may be associated with the experimentally observed midinfrared absorption band in underdoped cuprates.
We examine the effects of electron-phonon interaction on the dynamics of the charge carriers doped in two-dimensional (2D) Heisenberg antiferromagnet. The t-J model Hamiltonian with a Fr\"ohlich term which couples the holes to a dispersionless (optical) phonon mode is considered for low doping concentration. The evolution of the spectral density function, the density of states, and the momentum distribution function of the holes with an increase of the hole-phonon coupling constant g is studied numerically. As the coupling to a phonon mode increases the quasiparticle spectral weight decreases and a ``phonon satellite'' feature close to the quasiparticle peak becomes more pronounced. Furthermore, strong electron-phonon coupling smears the multimagnon resonances (``string states'') in the incoherent part of the spectral function. The jump in the momentum distribution function at the Fermi surface is reduced without changing the hole pocket volume, thereby providing a numerical verification of Luttinger theorem for this strongly interacting system. The vertex corrections due to electron-phonon interaction are negligible in spite of the fact that the ratio of the phonon frequency to the effective bandwidth is not small. \textcopyright{} 1996 The American Physical Society.
Hole and magnon spectral functions of the 2D ¢-J model are self-consistently calculated from a set of Dyson's equations for the hole concentrations z < 0.3.For J < ¢, itis shown that near z = 0.05 the hole spectrum changes drastically, acquiring features of a weakly correlated spectrum.This change is accompanied by the entering of the chemical potential u into a sharp maximum of the density of states.With z increasing the maximum moves together with u upto z =~0.15 and then lags behind.This concentration is also distinctive in that the Fermi surface becomes a simply connected surface and the overdamped magnons which appear near z = 0.02 occupy the widest region in k space.Besides, a limiting frequency of usual magnons passes through a minimum here.Significant deviations from the normal Fermi liquid, which partly resemble the marginal Fermi liquid, are observed for x > 0.05.
A finite-size scaling analysis of the spectral function and of the optical conductivity of a single hole moving in an antiferromagnetic background is performed. It is shown that both the low-energy quasiparticle peak and the broad higher-energy structure are robust with increasing cluster size from 4\ifmmode\times\else\texttimes\fi{}4 to \ensuremath{\surd}26 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}26 sites. In the absence of spin fluctuations, for most static or dynamical quantities saturation occurs when the size exceeds a characteristic size Nc{\mathit{N}}_{\mathit{c}}Nc​(Jz{\mathit{J}}_{\mathit{z}}Jz​). Typically, 16- and 26-site clusters give reliable results for Jz{\mathit{J}}_{\mathit{z}}Jz​>0.75 and Jz{\mathit{J}}_{\mathit{z}}Jz​>0.3, respectively. The hole optical mass is shown to be very large (>20) in agreement with the small bandwidth. Due to the energy gap to flip a spin in the vicinity of a hole, a small gap \ensuremath{\propto}Jz{\mathit{J}}_{\mathit{z}}Jz​ separates the low-energy \ensuremath{\delta} function from the rest of the spectrum in the dynamical correlation functions. On the other hand, with ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ this gap seems to disappear with increasing system size as one would expect since the spin waves are gapless in the thermodynamic limit. The large momentum dependence of the quasiparticle weight in the isotropic case is inconsistent with a string picture but agrees well with the self-consistent Born approximation.An accurate estimation of the higher-energy part of the spectral functions of the t-J model can be made for momenta close to (0,0) or (\ensuremath{\pi},\ensuremath{\pi}); it consists of a broad featureless band. For momenta close to the Fermi surface, no evidence for excited string states is found. This may be either because the string scenario breaks down or because exact calculations at momenta near (\ensuremath{\pi}/2,\ensuremath{\pi}/2) are limited by the differing geometries of the finite clusters. In the Ising limit, the spectral function also depends crucially on the momentum, but a feature resembling a string excitation is seen for momenta close to (0,0). Our data on the finite-frequency optical conductivity of a single hole in the t-J model reveal that the total spectral weight at finite frequency has a strong size dependence and decreases with increasing size (for J not too small). This suggests that the optical mass and the optical absorption of the t-J model may have been overestimated in the past.
We study transient dynamics of hole carriers injected into a Mott insulator with antiferromagnetic long-range order. This ``dynamical hole doping'' contrasts with chemical hole doping. The theoretical framework for the transient carrier dynamics is presented based on the two-dimensional ttt-JJJ model. The time dependencies of the optical conductivity spectra, as well as the one-particle excitation spectra, are calculated based on the Keldysh Green's function formalism at zero temperature combined with the self-consistent Born approximation. In the early stage after dynamical hole doping, the Drude component appears, and then incoherent components originating from hole-magnon scattering start to grow. Fast oscillatory behavior owing to coherent magnon and slow relaxation dynamics are confirmed in the spectra. The time profiles are interpreted as doped bare holes being dressed by magnon clouds and relaxed into spin polaron quasiparticle states. The characteristic relaxation times for Drude and incoherent peaks strongly depend on the momentum of the dynamically doped hole and the exchange constant. Implications for recent pump-probe experiments are discussed.
The t-J model in the large-t/J and low-doping limit is approximated by an effective Hamiltonian that treats spin degrees of freedom within the linear-spin-wave approximation and the hole-hopping term with a hole-spin interaction vertex that is linear in the spin-wave operators. The Dyson's equation for the single-hole Green's function is solved numerically on finite- but sufficiently large-size square lattices. Our calculation is based on an approximate equation for the hole motion that has been obtained using a self-consistent perturbation approach where crossing diagrams are neglected. We have studied the contribution of vertex corrections and found that the leading two-loop crossing diagram is exactly zero. Thus, the leading nonzero contribution to the proper self-energy from crossing diagrams is a three-loop correction. In two dimensions, it is possible to solve Dyson's equation numerically including these three-loop corrections. The results demonstrate that the contribution of such vertex corrections is indeed small. Our solution for the hole spectral function, obtained by neglecting such small contributions from vertex corrections, shows that most features describing the hole motion are in close agreement with the results of the exact diagonalization on the 42{4}^{2}42 lattice in the region of J/t\ensuremath{\le}0.2. The results obtained on sufficiently large-size lattices suggest that certain important features of the spectral function remain while others change due to finite-size effects. In particular, we find well-defined peaks above the lowest-energy peak that survive in the thermodynamic limit. We analyze these higher-energy peaks of the spectral functions and find that they can be understood as ``string'' excitations, which are created by the hole moving in a nearly linear potential.
We study the hole and magnon spectral functions as a function of hole doping in the two-dimensional $t\ensuremath{-}J$ and $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{'}\ensuremath{'}}\ensuremath{-}J$ models working within the limits of spin-wave theory by linearizing the hole-spin-deviation interaction and by adapting the noncrossing approximation. We find that the staggered magnetization decreases rather rapidly with doping and it goes to zero at a few percent of hole concentration in both $t\ensuremath{-}J$ and $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{'}\ensuremath{'}}\ensuremath{-}J$ models. Furthermore, our results show that the residue of the quasiparticle peak at $\stackrel{P\vec}{G}=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2)$ decreases very rapidly with doping. We also find pockets centered at $\stackrel{P\vec}{G}$, (i) with an elliptical shape with large eccentricity along the antinodal direction in the case of the $t\ensuremath{-}J$ model and (ii) with an almost circular shape in the case of the $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{'}\ensuremath{'}}\ensuremath{-}J$ model. Last, we show that the spectral intensity distribution in the doped antiferromagnet has a waterfall-like pattern along the nodal direction of the Brillouin zone, a feature that is also seen in angle-resolved photoemission spectroscopy measurements.