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arXiv:cond-mat/9711204 · Physical review. B, Condensed matter

Properties of a Luttinger liquid with boundaries at finite temperature and size

Ann Elisabet Mattsson, Sebastian Eggert, Henrik Johannesson

Published Dec 15, 1997• 82 citations
arXivHTMLPDF

Abstract

We use bosonization methods to calculate the exact finite-temperature single-electron Green's function of a spinful Luttinger liquid confined by open boundaries. The corresponding local spectral density is constructed and analyzed in detail. The interplay between boundary, finite-size, and thermal effects are shown to dramatically influence the low-energy properties of the system. In particular, the well-known zero-temperature critical behavior in the bulk always crosses over to a boundary dominated regime in the vicinity of the Fermi level. Thermal fluctuations cause an enhanced depletion of spectral weight for small energies $\ensuremath{\omega}$, with the spectral density scaling as ${\ensuremath{\omega}}^{2}$ for $\ensuremath{\omega}$ much less than the temperature. Consequences for photoemission experiments are discussed.

DOI
10.1103/physrevb.56.15615

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We use bosonization methods to calculate the exact finite-temperature single-electron Green's function of a spinful Luttinger liquid confined by open boundaries. The corresponding local spectral density is constructed and analyzed in detail. The interplay between boundary, finite-size, and thermal effects are shown to dramatically influence the low-energy properties of the system. In particular, the well-known zero-temperature critical behavior in the bulk always crosses over to a boundary dominated regime in the vicinity of the Fermi level. Thermal fluctuations cause an enhanced depletion of spectral weight for small energies \ensuremathω\ensuremath{\omega}\ensuremathω, with the spectral density scaling as \ensuremathω2{\ensuremath{\omega}}^{2}\ensuremathω2 for \ensuremathω\ensuremath{\omega}\ensuremathω much less than the temperature. Consequences for photoemission experiments are discussed.
The single electron Green's function of the one-dimensional Tomonaga-Luttinger model in the presence of open boundaries is calculated with bosonization methods. We show that the critical exponents of the local spectral density and of the momentum distribution change in the presence of a boundary. The well understood universal bulk behavior always crosses over to a boundary dominated regime for small energies or small momenta. We show this crossover explicitly for the large-U Hubbard model in the low-temperature limit. Consequences for photoemission experiments are discussed.
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The spectral functions of tJ\mathrm{tJ}tJ and tJXY{\mathrm{tJ}}_{\mathrm{XY}}tJXY​ 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 LLL 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 ttt, which is much larger than the temperature.
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