arXiv:cond-mat/9607140 · Physical review. B, Condensed matter

Spectral properties of the planar t-J model

Janez Jaklič, Peter Prelovšek

Published Mar 15, 1997• 26 citations

Abstract

The single-particle spectral functions A(k,\ensuremath{\omega}) and self-energies \ensuremath{\Sigma}(k,\ensuremath{\omega}) are calculated within the t-J model using the finite-temperature Lanczos method for small systems. A remarkable asymmetry between the electron and hole part is found. The hole (photoemission) spectra are overdamped, with Im\ensuremath{\Sigma}\ensuremath{\propto}\ensuremath{\omega} in a wide energy range, consistent with the marginal Fermi liquid scenario, and in good agreement with experiments on cuprates. In contrast, the quasiparticles in the electron part of the spectrum show weak damping.

DOI: 10.1103/physrevb.55.r7307

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arXiv:cond-mat/9607140 · Physical review. B, Condensed matter

Spectral properties of the planar t-J model

Janez Jaklič, Peter Prelovšek

Published Mar 15, 1997• 26 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.55.r7307

Related papers

One-electron self-energies and spectral functions for the t−J model in the large- N limit

Matías Bejas, A. Greco, A. Foussats

Using a recently developed perturbative approach, which considers Hubbard operators as fundamental excitations, we have performed electronic self-energy and spectral function calculations for the $t\text{\ensuremath{-}}J$ model on the square lattice. We have found that the spectral functions along the Fermi surface are isotropic, even close to the critical doping where the $d$ density wave phase occurs. Fermi liquid behavior with scattering rate $\ensuremath{\sim}{\ensuremath{\omega}}^{2}$ and a finite quasiparticle weight $Z$ was obtained. $Z$ decreases with decreasing doping taking low values for low doping. Results are compared with others obtained by analytical and numerical methods like the slave-boson and Lanczos diagonalization approaches, finding agreement. We discuss our results in the light of recent angle-resolved photoemission spectroscopy experiments in cuprates.Using a recently developed perturbative approach, which considers Hubbard operators as fundamental excitations, we have performed electronic self-energy and spectral function calculations for the $t\text{\ensuremath{-}}J$ model on the square lattice. We have found that the spectral functions along the Fermi surface are isotropic, even close to the critical doping where the $d$ density wave phase occurs. Fermi liquid behavior with scattering rate $\ensuremath{\sim}{\ensuremath{\omega}}^{2}$ and a finite quasiparticle weight $Z$ was obtained. $Z$ decreases with decreasing doping taking low values for low doping. Results are compared with others obtained by analytical and numerical methods like the slave-boson and Lanczos diagonalization approaches, finding agreement. We discuss our results in the light of recent angle-resolved photoemission spectroscopy experiments in cuprates.

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Recent angle-resolved photoemission experiments in hole doped cuprates reported new and interesting high energy features which may be useful for understanding the electronic properties of these materials. Using a perturbative approach, which allows the calculation of dynamical properties in the $t-J$ model, one-electron spectral properties were calculated. A strongly renormalized quasiparticle band near the Fermi surface and incoherent spectra at high energy were obtained. Among different current experimental interpretations, the obtained results are closer to the interpretation given by Pan {\it et al.}\cite{pan}. The self-energy shows large high energy contributions which are responsible for the incoherent structures showed by the spectral functions and the reduction of the quasiparticle weight and bandwidth. According to the calculation, collective charge fluctuations are the main source for the self-energy renormalizations. For testing if the obtained self-energy is compatible with transport measurement the resistivity versus temperature was estimated.Recent angle-resolved photoemission experiments in hole doped cuprates reported new and interesting high energy features which may be useful for understanding the electronic properties of these materials. Using a perturbative approach, which allows the calculation of dynamical properties in the $t-J$ model, one-electron spectral properties were calculated. A strongly renormalized quasiparticle band near the Fermi surface and incoherent spectra at high energy were obtained. Among different current experimental interpretations, the obtained results are closer to the interpretation given by Pan {\it et al.}\cite{pan}. The self-energy shows large high energy contributions which are responsible for the incoherent structures showed by the spectral functions and the reduction of the quasiparticle weight and bandwidth. According to the calculation, collective charge fluctuations are the main source for the self-energy renormalizations. For testing if the obtained self-energy is compatible with transport measurement the resistivity versus temperature was estimated.

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Spectral functions within the generalized $t\ensuremath{-}J$ model as relevant to cuprates are analyzed using the method of equations of motion for projected fermion operators. In the evaluation of the self-energy a decoupling of spin and single-particle fluctuations is performed. It is shown that in an undoped antiferromagnet the method reproduces the self-consistent Born approximation. For finite doping with short-range antiferromagnetic order the approximation evolves into a paramagnon contribution which retains a large incoherent contribution in the hole part of the spectral function as well as the hole-pocket-like Fermi surface at low doping. On the other hand, the contribution of longer-range spin fluctuations, with the coupling mostly determined predominantly by J and next-neighbor hopping ${t}^{\ensuremath{'}},$ is essential for the emergence of the pseudogap. The latter shows, at low doping in the effective truncation of the large Fermi surface, a reduced electron density of states and at the same time a quasiparticle density of states at the Fermi level.Spectral functions within the generalized $t\ensuremath{-}J$ model as relevant to cuprates are analyzed using the method of equations of motion for projected fermion operators. In the evaluation of the self-energy a decoupling of spin and single-particle fluctuations is performed. It is shown that in an undoped antiferromagnet the method reproduces the self-consistent Born approximation. For finite doping with short-range antiferromagnetic order the approximation evolves into a paramagnon contribution which retains a large incoherent contribution in the hole part of the spectral function as well as the hole-pocket-like Fermi surface at low doping. On the other hand, the contribution of longer-range spin fluctuations, with the coupling mostly determined predominantly by J and next-neighbor hopping ${t}^{\ensuremath{'}},$ is essential for the emergence of the pseudogap. The latter shows, at low doping in the effective truncation of the large Fermi surface, a reduced electron density of states and at the same time a quasiparticle density of states at the Fermi level.

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Several thermodynamic quantities within the planar $t\ensuremath{-}J$ model are calculated using the $T>0$ Lanczos method on clusters of up to 26 sites. The hole density ${c}_{h}(\ensuremath{\mu},T)$ shows a non-Fermi-liquid behavior as a function of $T$ and suggests a transition from small to large Fermi surfaces at ${c}_{h}\ensuremath{\sim}0.15$. The specific heat reveals a maximum at the exchange energy scale up to ${c}_{h}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.2$ , where it becomes almost $T$ independent for $T\ensuremath{\gtrsim}0.15t$. At constant $T$ the entropy has maximum for ${c}_{h}\ensuremath{\sim}0.15$ with large values at low $T$ , consistent with experiments on cuprates. In the underdoped regime the spin susceptibility ${\ensuremath{\chi}}_{0}(T)$ exhibits a maximum at finite ${T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}T}^{*}$ , with ${T}^{*}$ decreasing with doping and disappearing for ${c}_{h}>0.15$ .Several thermodynamic quantities within the planar $t\ensuremath{-}J$ model are calculated using the $T>0$ Lanczos method on clusters of up to 26 sites. The hole density ${c}_{h}(\ensuremath{\mu},T)$ shows a non-Fermi-liquid behavior as a function of $T$ and suggests a transition from small to large Fermi surfaces at ${c}_{h}\ensuremath{\sim}0.15$. The specific heat reveals a maximum at the exchange energy scale up to ${c}_{h}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.2$, where it becomes almost $T$ independent for $T\ensuremath{\gtrsim}0.15t$. At constant $T$ the entropy has maximum for ${c}_{h}\ensuremath{\sim}0.15$ with large values at low $T$, consistent with experiments on cuprates. In the underdoped regime the spin susceptibility ${\ensuremath{\chi}}_{0}(T)$ exhibits a maximum at finite ${T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}T}^{*}$, with ${T}^{*}$ decreasing with doping and disappearing for ${c}_{h}>0.15$.

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Igor Sega, P. Prelovek

The single-hole states are studied by the exact diagonalization method in two models for strongly correlated systems: the single-band effective (t-J) model and the Kondo-lattice model. The coherent mass ${\mathit{m}}^{\mathrm{*}}$ of the quasiparticle and the frequency-dependent conductivity \ensuremath{\sigma}(\ensuremath{\omega}) are calculated for clusters with 4\ifmmode\times\else\texttimes\fi{}4 and 8\ifmmode\times\else\texttimes\fi{}4 sites. In particular, \ensuremath{\sigma}(\ensuremath{\omega}) shows an isolated quasiparticle peak of weak intensity at small \ensuremath{\omega} and a broad but structured incoherent part at higher \ensuremath{\omega}.The single-hole states are studied by the exact diagonalization method in two models for strongly correlated systems: the single-band effective (t-J) model and the Kondo-lattice model. The coherent mass ${\mathit{m}}^{\mathrm{*}}$ of the quasiparticle and the frequency-dependent conductivity \ensuremath{\sigma}(\ensuremath{\omega}) are calculated for clusters with 4\ifmmode\times\else\texttimes\fi{}4 and 8\ifmmode\times\else\texttimes\fi{}4 sites. In particular, \ensuremath{\sigma}(\ensuremath{\omega}) shows an isolated quasiparticle peak of weak intensity at small \ensuremath{\omega} and a broad but structured incoherent part at higher \ensuremath{\omega}.

Physical review. B, Condensed matterJul 1, 199058 citations

Role of dynamical non-double-occupancy excitations on the quasiparticle damping of the t−J model in the large- N limit

A. Foussats, A. Greco, Matías Bejas

One-electron self-energy in the $t\ensuremath{-}J$ model was computed using a recently developed large- $N$ method based on the path-integral representation for Hubbard operators. One of the main features of the self-energy is its strong asymmetry with respect to the Fermi level, showing the spectra mostly concentrated at high negative energy. This asymmetry is responsible for the existence of incoherent structures at high negative energy in the spectral functions. It is shown that dynamical non-double-occupancy excitations are relevant for the behavior of the self-energy. It is difficult to understand the asymmetry shown by the self-energy from weak-coupling treatments. We compare our results with others in recent literature. Finally, the possible relevance of our results for the recent high energy features observed in photoemission experiments is discussed.One-electron self-energy in the $t\ensuremath{-}J$ model was computed using a recently developed large-$N$ method based on the path-integral representation for Hubbard operators. One of the main features of the self-energy is its strong asymmetry with respect to the Fermi level, showing the spectra mostly concentrated at high negative energy. This asymmetry is responsible for the existence of incoherent structures at high negative energy in the spectral functions. It is shown that dynamical non-double-occupancy excitations are relevant for the behavior of the self-energy. It is difficult to understand the asymmetry shown by the self-energy from weak-coupling treatments. We compare our results with others in recent literature. Finally, the possible relevance of our results for the recent high energy features observed in photoemission experiments is discussed.

arXiv:0810.1410Physical Review BOct 27, 20085 citations

d

density wave phase occurs. Fermi liquid behavior with scattering rate $\ensuremath{\sim}{\ensuremath{\omega}}^{2}$ and a finite quasiparticle weight

Z

was obtained.

Z

decreases with decreasing doping taking low values for low doping. Results are compared with others obtained by analytical and numerical methods like the slave-boson and Lanczos diagonalization approaches, finding agreement. We discuss our results in the light of recent angle-resolved photoemission spectroscopy experiments in cuprates.

t-J

model one-electron renormalizations: high energy features in photoemission experiments of high-

T_c

cuprates

t-J

model, one-electron spectral properties were calculated. A strongly renormalized quasiparticle band near the Fermi surface and incoherent spectra at high energy were obtained. Among different current experimental interpretations, the obtained results are closer to the interpretation given by Pan {\it et al.}\cite{pan}. The self-energy shows large high energy contributions which are responsible for the incoherent structures showed by the spectral functions and the reduction of the quasiparticle weight and bandwidth. According to the calculation, collective charge fluctuations are the main source for the self-energy renormalizations. For testing if the obtained self-energy is compatible with transport measurement the resistivity versus temperature was estimated.

Several thermodynamic quantities within the planar $t\ensuremath{-}J$ model are calculated using the

T>0

Lanczos method on clusters of up to 26 sites. The hole density ${c}_{h}(\ensuremath{\mu},T)$ shows a non-Fermi-liquid behavior as a function of

T

and suggests a transition from small to large Fermi surfaces at ${c}_{h}\ensuremath{\sim}0.15$. The specific heat reveals a maximum at the exchange energy scale up to

{c}_{h}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.2

, where it becomes almost

T

independent for $T\ensuremath{\gtrsim}0.15t$. At constant

T

the entropy has maximum for ${c}_{h}\ensuremath{\sim}0.15$ with large values at low

T

, consistent with experiments on cuprates. In the underdoped regime the spin susceptibility ${\ensuremath{\chi}}_{0}(T)$ exhibits a maximum at finite

{T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}T}^{*}

, with

{T}^{*}

decreasing with doping and disappearing for

{c}_{h}>0.15

{\mathit{m}}^{\mathrm{*}}

of the quasiparticle and the frequency-dependent conductivity \ensuremath{\sigma}(\ensuremath{\omega}) are calculated for clusters with 4\ifmmode\times\else\texttimes\fi{}4 and 8\ifmmode\times\else\texttimes\fi{}4 sites. In particular, \ensuremath{\sigma}(\ensuremath{\omega}) shows an isolated quasiparticle peak of weak intensity at small \ensuremath{\omega} and a broad but structured incoherent part at higher \ensuremath{\omega}.

One-electron self-energy in the $t\ensuremath{-}J$ model was computed using a recently developed large-

N

method based on the path-integral representation for Hubbard operators. One of the main features of the self-energy is its strong asymmetry with respect to the Fermi level, showing the spectra mostly concentrated at high negative energy. This asymmetry is responsible for the existence of incoherent structures at high negative energy in the spectral functions. It is shown that dynamical non-double-occupancy excitations are relevant for the behavior of the self-energy. It is difficult to understand the asymmetry shown by the self-energy from weak-coupling treatments. We compare our results with others in recent literature. Finally, the possible relevance of our results for the recent high energy features observed in photoemission experiments is discussed.