Thermal decoherence in a strongly correlated Bose liquid

TL;DR

This paper investigates how thermal fluctuations affect the spectral properties of a strongly correlated Bose liquid near the superfluid-Mott transition, revealing temperature-dependent damping and gapped spectra in different phases.

Contribution

It introduces a static path approximation combined with RPA to analyze thermal effects on the spectral function of a Bose liquid, capturing damping and excitation behavior across the transition.

Findings

Damping of excitations scales as T^0.5 with momentum dependence.

Superfluid phase exhibits amplitude and phase modes with temperature-independent dispersion.

Mott phase shows gapped dispersive spectra that widen with temperature.

Abstract

We compute the single particle spectral function of a Bose liquid on a lattice, at integer filling, close to the superfluid-Mott transition. We use a `static path approximation' that retains all the classical thermal fluctuations in the problem, and a real space implementation of the random phase approximation (RPA) for the Green's functions on the thermally fluctuating backgrounds. This leads to the standard RPA answers in the ground state but captures the progressive damping of the excitations with increasing temperature. We focus on the momentum resolved lineshape across the superfluid to Bose liquid thermal transition. In the superfluid regime we observe a gapped `amplitude' mode, and gapless `phase' modes of positive and negative energy. The dispersion and weight of these modes changes with interaction but are almost temperature independent, even into the normal state, except near critical coupling. The damping of the modes varies roughly as $T^{\alpha} f_{\bf k}$, where $T$ is the temperature and ${\bf k}$ the momentum, with $\alpha \sim 0.5$ and $f_{\bf k}$ having non trivial momentum dependence. The Mott phase has gapped dispersive spectra. Near critical coupling the thermal Bose `liquid' is gapped, with progressive widening of the gap with increasing temperature, a feature that it shares with the Mott insulator.