# Deconfined quantum critical point in one dimension

## TL;DR

This paper numerically investigates a one-dimensional spin-1/2 model exhibiting a continuous phase transition akin to two-dimensional deconfined quantum critical points, revealing novel critical behavior and an intermediate coexistence phase.

## Contribution

It demonstrates a one-dimensional DQCP with continuous transition and coexistence phase, extending the understanding of deconfined criticality beyond two dimensions.

## Key findings

- Evidence for a direct continuous phase transition outside LGW paradigm
- Close power law exponents for magnetic and VBS correlations
- Continuous variation of critical exponents along the phase boundary

## Abstract

We perform a numerical study of a spin-1/2 model with $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry in one dimension which demonstrates an interesting similarity to the physics of two-dimensional deconfined quantum critical points (DQCP). Specifically, we investigate the quantum phase transition between Ising ferromagnetic and valence bond solid (VBS) symmetry-breaking phases. Working directly in the thermodynamic limit using uniform matrix product states, we find evidence for a direct continuous phase transition that lies outside of the Landau-Ginzburg-Wilson paradigm. In our model, the continuous transition is found everywhere on the phase boundary. We find that the magnetic and VBS correlations show very close power law exponents, which is expected from the self-duality of the parton description of this DQCP. Critical exponents vary continuously along the phase boundary in a manner consistent with the predictions of the field theory for this transition. We also find a regime where the phase boundary splits, as suggested by the theory, introducing an intermediate phase of coexisting ferromagnetic and VBS order parameters. Interestingly, we discover a transition involving this coexistence phase which is similar to the DQCP, being also disallowed by Landau-Ginzburg-Wilson symmetry-breaking theory.