Quantum Critical Behavior of One-Dimensional Soft Bosons in the Continuum

TL;DR

This paper investigates the quantum critical behavior of one-dimensional soft bosons in the continuum, revealing clustering, secondary gapless modes, and a transition characterized by a central charge of 3/2, using quantum Monte Carlo simulations.

Contribution

It provides the first detailed analysis of the dynamical structure factor and critical phenomena in 1D soft bosons with Rydberg-like interactions, highlighting cluster phases and criticality.

Findings

Observation of rotonic spectrum indicating clustering tendency

Emergence of cluster liquid phases with composite harmonic chain spectrum

Identification of a secondary gapless mode and critical behavior with central charge 3/2

Abstract

We consider a zero-temperature one-dimensional system of bosons interacting via the soft-shoulder potential in the continuum, typical of dressed Rydberg gases. We employ quantum Monte Carlo simulations, which allow for the exact calculation of imaginary-time correlations, and a stochastic analytic continuation method, to extract the dynamical structure factor. At finite densities, in the weakly-interacting homogeneous regime, a rotonic spectrum marks the tendency to clustering. With strong interactions, we indeed observe cluster liquid phases emerging, characterized by the spectrum of a composite harmonic chain. Luttinger theory has to be adapted by changing the reference lattice density field. In both the liquid and cluster liquid phases, we find convincing evidence of a secondary mode, which becomes gapless only at the transition. In that region, we also measure the central charge and observe its increase towards c = 3/2, as recently evaluated in a related extended Bose-Hubbard model, and we note a fast reduction of the Luttinger parameter. For 2-particle clusters, we then interpret such observations in terms of the compresence of a Luttinger liquid and a critical transverse Ising model, related to the instability of the reference lattice density field towards coalescence of sites, typical of potentials which are flat at short distances. Even in the absence of a true lattice, we are able to evaluate the spatial correlation function of a suitable pseudo-spin operator, which manifests ferromagnetic order in the cluster liquid phase, exponential decay in the liquid phase, and algebraic order at criticality.