Deconfined criticality, runaway flow in the two-component scalar electrodynamics and weak first-order superfluid-solid transitions

TL;DR

This study uses Monte Carlo simulations and a novel numerical flowgram method to analyze phase transitions in two-component scalar electrodynamics, revealing weakly first-order transitions and the nature of runaway flow in the deconfined critical point framework.

Contribution

It introduces a numerical flowgram method to precisely study runaway flows and clarifies the nature of phase transitions in the easy-plane deconfined critical point model.

Findings

The long-range DCP action exhibits runaway flow to a first-order transition.

Short-range model features a tricritical point and continuous transition.

The easy-plane DCP action describes a weakly first-order transition between valence bond solid and antiferromagnet.

Abstract

We perform a comparative Monte Carlo study of the easy-plane deconfined critical point (DCP) action and its short-range counterpart to reveal close similarities between the two models for intermediate and strong coupling regimes. For weak coupling, the structure of the phase diagram depends on the interaction range: while the short-range model features a tricritical point and a continuous U(1)xU(1) transition,the long-range DCP action is characterized by the runaway renormalization flow of coupling into a first (I) order phase transition. We develop a "numerical flowgram" method for high precision studies of the runaway effect, weakly I-order transitions, and polycritical points. We prove that the easy-plane DCP action is the field theory of a weakly I-order phase transition between the valence bond solid and the easy-plane antiferromagnet (or superfluid, in particle language) for any value of the weak coupling strength. Our analysis also solves the long standing problem of what is the ultimate fate of the runaway flow to strong coupling in the theory of scalar electrodynamics in three dimensions with U(1)xU(1) symmetry of quartic interactions