Functional renormalization group study of a dissipative Bose--Hubbard model

TL;DR

This study uses the nonperturbative functional renormalization group to analyze the phase diagram of a one-dimensional dissipative Bose-Hubbard model, revealing competing fixed points and a BKT transition.

Contribution

It introduces a FRG-based approach to systematically explore dissipative quantum phases in one dimension, capturing all fixed points from a microscopic action.

Findings

Identified two low-energy regimes: Luttinger-liquid line and dissipative fixed point.

Discovered a BKT transition separating these regimes.

Provided a unified framework for dissipative quantum phase analysis.

Abstract

We investigate the phase diagram of a one-dimensional dissipative Bose-Hubbard model using the nonperturbative functional renormalization group (FRG). Each lattice site is coupled to an independent bath, generating long-range temporal interactions that encode non-Markovian dissipation. For a broad class of bath spectra - ohmic, sub-ohmic, and super-ohmic - we identify two competing low-energy regimes: a Luttinger-liquid line of fixed points and a dissipative fixed point characterized by finite compressibility, vanishing superfluid stiffness, and universal scaling exponents, separated by a Berezinskii-Kosterlitz-Thouless transition. The FRG framework is essential here, as it provides access to the complete renormalization group flow and all fixed points from a single microscopic action, beyond the reach of perturbative or variational methods. This work establishes a unified and systematically improvable framework for describing dissipative quantum phases in one dimension.