Properties of a Luttinger Liquid with Boundaries at Finite Temperature and Size

TL;DR

This paper uses bosonization to exactly analyze how boundaries, finite size, and temperature affect the spectral properties of a spinful Luttinger liquid, revealing boundary-dominated regimes and thermal effects relevant for experiments.

Contribution

It provides the first exact finite-temperature Green's function for a boundary-confined spinful Luttinger liquid, highlighting the interplay of boundary, size, and thermal effects.

Findings

Boundary effects dominate low-energy spectral behavior.

Thermal fluctuations cause spectral weight depletion at low energies.

Spectral density scales as E^2 near zero energy at finite temperature.

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 E, with the spectral density scaling as E^2 for E much less than the temperature. Consequences for photoemission experiments are discussed.