Fate of the one-dimensional Ising quantum critical point coupled to a gapless boson

TL;DR

This paper studies how coupling a one-dimensional Ising quantum critical point to a gapless bosonic mode affects its nature, revealing conditions under which the transition remains continuous or becomes first order, with a novel tri-critical point.

Contribution

It combines RG analysis and DMRG calculations to uncover the phase transition behavior of the coupled system, identifying a tri-critical point separating different regimes.

Findings

Transition can be continuous or first order depending on velocity ratio.

A novel tri-critical point separates the two regimes.

Coupling effects significantly alter the critical behavior.

Abstract

The problem of a quantum Ising degree of freedom coupled to a gapless bosonic mode appears naturally in many one dimensional systems, yet surprisingly little is known how such a coupling affects the Ising quantum critical point. We investigate the fate of the critical point in a regime, where the weak coupling renormalization group (RG) indicates a flow toward strong coupling. Using a renormalization group analysis and numerical density matrix renormalization group (DMRG) calculations we show that, depending on the ratio of velocities of the gapless bosonic mode and the Ising critical fluctuations, the transition may remain continuous or become fluctuation-driven first order. The two regimes are separated by a tri-critical point of a novel type.