Existence of a first-order transition in the 1-D dipole-conserving chain beyond mean-field

Determine whether the transition between a gapped symmetry-unbroken phase and a gapless dipolar quasi–long-range ordered phase with Berry phase θ=π is genuinely first-order in the exact one-dimensional dipole-conserving fermion chain with two orbitals per unit cell and particle–hole symmetry at one fermion per unit cell, rather than an artifact of mean-field analysis.

Background

The paper analyzes a one-dimensional dipole-conserving fermionic model with two orbitals per unit cell, particle–hole symmetry, and one fermion per unit cell. A mean-field treatment yields a discontinuous jump in the dipole condensate, implying a first-order transition between a gapped symmetry-unbroken phase and a gapless ordered phase characterized by θ=π.

However, the authors caution that mean-field conclusions in (1+1) dimensions can be unreliable due to strong fluctuations. They explicitly note uncertainty about whether this first-order transition is present in the exact theory, motivating a precise determination of the true nature of the transition beyond mean-field methods.