arXiv:cond-mat/9704233 · Physical review. B, Condensed matter

Finite-temperature spectral functions of strongly correlated one-dimensional electron systems

Karlo Penc, Mohammed Serhan

Published Sep 15, 1997• 21 citations

Abstract

The spectral functions of $\mathrm{tJ}$ and ${\mathrm{tJ}}_{\mathrm{XY}}$ models in the limit of $J/t\ensuremath{\rightarrow}0$ and at finite temperatures $T\ensuremath{\ll}t$ are calculated using the spin-charge factorized wave function. We find that the Luttinger-liquid-like scaling behavior for a finite system with $L$ sites is restricted below temperatures of the order $T\ensuremath{\lesssim}J/L$. We also observe a weight redistribution in the photoemission spectral function in the energy range $t$, which is much larger than the temperature.

DOI: 10.1103/physrevb.56.6555

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arXiv:cond-mat/9704233 · Physical review. B, Condensed matter

Finite-temperature spectral functions of strongly correlated one-dimensional electron systems

Karlo Penc, Mohammed Serhan

Published Sep 15, 1997• 21 citations

arXiv HTML PDF

Abstract

The spectral functions of

\mathrm{tJ}

and

{\mathrm{tJ}}_{\mathrm{XY}}

models in the limit of

J/t\ensuremath{\rightarrow}0

and at finite temperatures

T\ensuremath{\ll}t

are calculated using the spin-charge factorized wave function. We find that the Luttinger-liquid-like scaling behavior for a finite system with

L

sites is restricted below temperatures of the order

T\ensuremath{\lesssim}J/L

. We also observe a weight redistribution in the photoemission spectral function in the energy range

t

, which is much larger than the temperature.

DOI: 10.1103/physrevb.56.6555

Related papers

Charge-spin separation and the spectral properties of Luttinger liquids

Johannes Voit

We compute the spectral function rho (q, omega ) of the one-dimensional Luttinger model. We discuss the distinct influences of charge-spin separation and of the anomalous dimensions of the fermion operators and their evolution with correlation strength. Charge-spin separation shows up in finite spectral weight at frequencies between v sigma q and v rho q, where v sigma and v rho are the velocities of spin and charge fluctuations, while spectral weight above v rho q and below -v rho q is generated by the hybridization of the Fermi surface at +or-k F by interactions. There are non-universal power-law singularities at these special frequencies. We discuss the consistency of recent photoemission experiments on low-dimensional conductors with a Luttinger-liquid picture, which then would suggest very strong long-range interactions. It is pointed out that many-particle correlation functions in principle exhibit similar singularities, but they probe different and complementary aspects of the Fermi-surface interactions.We compute the spectral function rho (q, omega ) of the one-dimensional Luttinger model. We discuss the distinct influences of charge-spin separation and of the anomalous dimensions of the fermion operators and their evolution with correlation strength. Charge-spin separation shows up in finite spectral weight at frequencies between v sigma q and v rho q, where v sigma and v rho are the velocities of spin and charge fluctuations, while spectral weight above v rho q and below -v rho q is generated by the hybridization of the Fermi surface at +or-k F by interactions. There are non-universal power-law singularities at these special frequencies. We discuss the consistency of recent photoemission experiments on low-dimensional conductors with a Luttinger-liquid picture, which then would suggest very strong long-range interactions. It is pointed out that many-particle correlation functions in principle exhibit similar singularities, but they probe different and complementary aspects of the Fermi-surface interactions.

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We study the crossover from the one-dimensional to the two-dimensional Hubbard model in the photoemission spectra of weakly coupled chains. The chains with on-site repulsion are treated using the spin-charge factorized wave function, known to provide an accurate description of the dynamics of the model in the strong coupling limit, while the hoppings between the chains are considered as a perturbation. We calculate dynamical spectral functions at all energies in the random-phase approximation by resuming an infinite set of diagrams. Even though the hoppings drive the system from a fractionalized Luttinger-liquid-like system to a Fermi-liquid-like system at low energies, significant characteristics of the one-dimensional system remain in the two-dimensional system. Furthermore, we find that, of introducing (frustrated) hoppings beyond the nearest-neighbor one, the interference effects increase the energy and momentum range of the one-dimensional character.We study the crossover from the one-dimensional to the two-dimensional Hubbard model in the photoemission spectra of weakly coupled chains. The chains with on-site repulsion are treated using the spin-charge factorized wave function, known to provide an accurate description of the dynamics of the model in the strong coupling limit, while the hoppings between the chains are considered as a perturbation. We calculate dynamical spectral functions at all energies in the random-phase approximation by resuming an infinite set of diagrams. Even though the hoppings drive the system from a fractionalized Luttinger-liquid-like system to a Fermi-liquid-like system at low energies, significant characteristics of the one-dimensional system remain in the two-dimensional system. Furthermore, we find that, of introducing (frustrated) hoppings beyond the nearest-neighbor one, the interference effects increase the energy and momentum range of the one-dimensional character.

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Spectral function of the U→∞ one-dimensional Hubbard model at finite temperature and the crossover to the spin-incoherent regime

Mohammad Soltanieh-ha, Adrian E. Feiguin

The physics of the strongly interacting Hubbard chain (with $t/U\ensuremath{\ll}1$) at finite temperatures undergoes a crossover to a spin-incoherent regime when the temperature is very small relative to the Fermi energy, but larger than the characteristic spin energy scale. This crossover can be understood by means of Ogata and Shiba's factorized wave function, where charge and spin are totally decoupled, and assuming that the charge remains in the ground state, while the spin is thermally excited and at an effective ``spin temperature.'' We use the time-dependent density matrix renormalization group method to calculate the dynamical contributions of the spin, to reconstruct the single-particle spectral function of the electrons. The crossover is characterized by a redistribution of spectral weight both in frequency and momentum, with an apparent shift by ${k}_{F}$ of the minimum of the dispersion.The physics of the strongly interacting Hubbard chain (with $t/U\ensuremath{\ll}1$) at finite temperatures undergoes a crossover to a spin-incoherent regime when the temperature is very small relative to the Fermi energy, but larger than the characteristic spin energy scale. This crossover can be understood by means of Ogata and Shiba's factorized wave function, where charge and spin are totally decoupled, and assuming that the charge remains in the ground state, while the spin is thermally excited and at an effective ``spin temperature.'' We use the time-dependent density matrix renormalization group method to calculate the dynamical contributions of the spin, to reconstruct the single-particle spectral function of the electrons. The crossover is characterized by a redistribution of spectral weight both in frequency and momentum, with an apparent shift by ${k}_{F}$ of the minimum of the dispersion.

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Karlo Penc, Frédéric Mila, Hiroyuki Shiba

We show that the one-particle spectral functions of the one-dimensional Hubbard model diverge at the Fermi energy like $|\ensuremath{\omega}\ensuremath{-}{\ensuremath{\varepsilon}}_{F}{|}^{\ensuremath{-}3/8}$ in the $U\ensuremath{\rightarrow}+\ensuremath{\infty}$ limit. The Luttinger liquid behavior $|\ensuremath{\omega}\ensuremath{-}{\ensuremath{\varepsilon}}_{F}{|}^{\ensuremath{\alpha}}$, where $\ensuremath{\alpha}\ensuremath{\rightarrow}1/8$ as $U\ensuremath{\rightarrow}+\ensuremath{\infty}$, should be limited to $|\ensuremath{\omega}\ensuremath{-}{\ensuremath{\varepsilon}}_{F}|\ensuremath{\sim}{t}^{2}/U$ (for $U$ large but finite), which shrinks to a single point, $\ensuremath{\omega}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\varepsilon}}_{F}$, in that limit. The consequences for the observation of the Luttinger liquid behavior in photoemission and inverse photoemission experiments are discussed.We show that the one-particle spectral functions of the one-dimensional Hubbard model diverge at the Fermi energy like $|\ensuremath{\omega}\ensuremath{-}{\ensuremath{\varepsilon}}_{F}{|}^{\ensuremath{-}3/8}$ in the $U\ensuremath{\rightarrow}+\ensuremath{\infty}$ limit. The Luttinger liquid behavior $|\ensuremath{\omega}\ensuremath{-}{\ensuremath{\varepsilon}}_{F}{|}^{\ensuremath{\alpha}}$, where $\ensuremath{\alpha}\ensuremath{\rightarrow}1/8$ as $U\ensuremath{\rightarrow}+\ensuremath{\infty}$, should be limited to $|\ensuremath{\omega}\ensuremath{-}{\ensuremath{\varepsilon}}_{F}|\ensuremath{\sim}{t}^{2}/U$ (for $U$ large but finite), which shrinks to a single point, $\ensuremath{\omega}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\varepsilon}}_{F}$, in that limit. The consequences for the observation of the Luttinger liquid behavior in photoemission and inverse photoemission experiments are discussed.

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Spectral properties of a spin-incoherent Luttinger liquid

Adrian E. Feiguin, Gregory A. Fiete

We present time-dependent density-matrix renormalization-group (DMRG) results for strongly interacting one-dimensional fermionic systems at finite temperature. When interactions are strong the characteristic spin energy can be greatly suppressed relative to the characteristic charge energy, allowing for the possibility of spin-incoherent Luttinger liquid physics when the temperature is high compared to the spin energy, but small compared to the charge energy. Using DMRG we compute the spectral properties of the $t\text{\ensuremath{-}}J$ model at arbitrary temperatures with respect to both spin and charge energies. We study the full crossover from the Luttinger liquid regime to the spin-incoherent regime, focusing on small $J/t$ , where the signatures of spin-incoherent behavior are more manifest. Our method allows us to access the analytically intractable regime where temperature is on the order of the spin energy, $T\ensuremath{\sim}J$. Our results should be helpful in the interpretation of experiments that may be in the crossover regime, $T\ensuremath{\sim}J$, and apply to one-dimensional cold atomic gases where finite-temperature effects are appreciable. The technique may also be used to guide the development of analytical approximations for the crossover regime.We present time-dependent density-matrix renormalization-group (DMRG) results for strongly interacting one-dimensional fermionic systems at finite temperature. When interactions are strong the characteristic spin energy can be greatly suppressed relative to the characteristic charge energy, allowing for the possibility of spin-incoherent Luttinger liquid physics when the temperature is high compared to the spin energy, but small compared to the charge energy. Using DMRG we compute the spectral properties of the $t\text{\ensuremath{-}}J$ model at arbitrary temperatures with respect to both spin and charge energies. We study the full crossover from the Luttinger liquid regime to the spin-incoherent regime, focusing on small $J/t$, where the signatures of spin-incoherent behavior are more manifest. Our method allows us to access the analytically intractable regime where temperature is on the order of the spin energy, $T\ensuremath{\sim}J$. Our results should be helpful in the interpretation of experiments that may be in the crossover regime, $T\ensuremath{\sim}J$, and apply to one-dimensional cold atomic gases where finite-temperature effects are appreciable. The technique may also be used to guide the development of analytical approximations for the crossover regime.

arXiv:0910.3957Physical Review BFeb 10, 201052 citations

The spectral functions of

\mathrm{tJ}

and

{\mathrm{tJ}}_{\mathrm{XY}}

models in the limit of

J/t\ensuremath{\rightarrow}0

and at finite temperatures

T\ensuremath{\ll}t

are calculated using the spin-charge factorized wave function. We find that the Luttinger-liquid-like scaling behavior for a finite system with

L

sites is restricted below temperatures of the order

T\ensuremath{\lesssim}J/L

. We also observe a weight redistribution in the photoemission spectral function in the energy range

t

, which is much larger than the temperature.

{k}_{F}

of the minimum of the dispersion.

U

large but finite), which shrinks to a single point, $\ensuremath{\omega}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\varepsilon}}_{F}$, in that limit. The consequences for the observation of the Luttinger liquid behavior in photoemission and inverse photoemission experiments are discussed.

J/t

, where the signatures of spin-incoherent behavior are more manifest. Our method allows us to access the analytically intractable regime where temperature is on the order of the spin energy, $T\ensuremath{\sim}J$. Our results should be helpful in the interpretation of experiments that may be in the crossover regime, $T\ensuremath{\sim}J$, and apply to one-dimensional cold atomic gases where finite-temperature effects are appreciable. The technique may also be used to guide the development of analytical approximations for the crossover regime.