Cluster Luttinger liquids and emergent supersymmetric conformal critical points in the one-dimensional soft-shoulder Hubbard model

TL;DR

This paper explores novel quantum phases in a one-dimensional extended Hubbard model with soft-shoulder interactions, revealing a conformal cluster Luttinger liquid phase with emergent supersymmetry and its experimental observability.

Contribution

It introduces the conformal cluster Luttinger liquid phase with central charge c=1 and identifies an exotic critical point with supersymmetry, expanding understanding of quantum phase transitions in 1D systems.

Findings

Identification of the cluster Luttinger liquid phase with c=1

Discovery of a critical point with c=3/2 indicating supersymmetry

Demonstration of phase stability at finite temperatures

Abstract

We investigate the quantum phases of hard-core bosonic atoms in an extended Hubbard model where particles interact via soft-shoulder potentials in one dimension. Using a combination of field-theoretical methods and strong-coupling perturbation theory, we demonstrate that the low-energy phase can be a conformal cluster Luttinger liquid (CLL) phase with central charge $c=1$, where the microscopic degrees of freedom correspond to mesoscopic ensembles of particles. Using numerical density-matrix-renormalization-group methods, we demonstrate that the CLL phase, first predicted in [Phys. Rev. Lett. 111, 165302 (2013)], is separated from a conventional Tomonaga-Luttinger liquid by an exotic critical point with central charge $c=3/2$. The latter is expression of an emergent conformal supersymmetry, which is not present in the original Hamiltonian. We discuss the observability of the CLL phase in realistic experimental settings with weakly-dressed Rydberg atoms confined to optical lattices. Using quantum Monte-Carlo simulations, we show that the typical features of CLLs are stable up to comparatively high temperatures. Using exact diagonalizations and quantum trajectory methods, we provide a protocol for adiabatic state preparation as well as quantitative estimates on the effects of particle losses.