# One-dimensional extended Hubbard model with soft-core potential

### Submission summary

 As Contributors: Thomas Botzung Arxiv Link: https://arxiv.org/abs/1909.12168v1 Date submitted: 2019-09-27 Submitted by: Botzung, Thomas Submitted to: SciPost Physics Domain(s): Theoretical Subject area: Quantum Physics

### Abstract

We investigate the $T=0$ phase diagram of a variant of the one-dimensional extended Hubbard model where particles interact via a finite-range soft-shoulder potential. Using Density Matrix Renormalization Group (DMRG) simulations, we evidence the appearance of Cluster Luttinger Liquid (CLL) phases, similarly to what first predicted in a hard-core bosonic chain [M. Dalmonte, W. Lechner, Z. Cai, M. Mattioli, A. M. L\"auchli and G. Pupillo, Phys. Rev. B 92, 045106 (2015)]. As the interaction strength parameters change, we find different types of clusters, that encode the order of the ground state in a semi-classical approximation and give rise to different types of CLLs. Interestingly, we find that the conventional Tomonaga Luttinger Liquid (TLL) is separated by a critical line with a central charge $c=5/2$, along which the two (spin and charge) bosonic degrees of freedom (corresponding to $c=1$ each) combine in a supersymmetric way with an emergent fermionic excitation ($c=1/2$). We also demonstrate that there are no significant spin correlations.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission 1909.12168v1 on 27 September 2019