Nonuniform quadrupolar orders in the spin-3/2 generalized Heisenberg chain

TL;DR

This paper explores nonuniform quadrupolar orders in a spin-3/2 Heisenberg chain, revealing new phases with broken translation symmetry and analyzing critical points using advanced numerical methods.

Contribution

It introduces the identification of tetramerization and stripe-Q phases in a generalized spin-3/2 chain using DMRG, and characterizes the phase transition with a WZW model.

Findings

Identification of tetramerization phase with four-cycle quadrupole order

Discovery of stripe-Q phase with striped quadrupole pattern

Evidence of a WZW model at the phase transition point

Abstract

The generation of nonuniform quadrupole states plays a crucial role in understanding various fascinating phenomena observed in the advancement of several research areas, e.g., multiferroic compounds, nonmagnetic superconductors, etc. In this work, we investigate the ground-state phase diagram of a generalized spin-3/2 bilinear-biquadratic-bicubic Heisenberg chain in the representation of multipolar operators. By numerical simulations with the large-scale density-matrix renormalization group (DMRG) method, we successfully identify a tetramerization phase and a stripe-Q phase. These phases are characterized by the emergence of nonuniform quadrupole orders resulting from the spontaneous breaking of translation symmetry. In particular, tetramerization phase refers to the quadrupole operators take a four-cycle, while the stripe-Q phase represents a striped pattern in quadrupole operators. Additionally, we demonstrate the presence of a Wess-Zumino-Witten (WZW) model with level k = 1 at the transition point between the dimerized (DM) phase and the Luttinger liquid (LL) phase, based on strong numerical findings.