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arXiv:2607.00086

Single-worldline theory for a dissipative Mott transition

Oscar Bouverot-Dupuis, Alberto Rosso, Laura Foini

Published Jun 30, 2026• 0 citations
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Abstract

In one dimension at zero temperature, local baths with spectral exponent $s$ can stabilize a compressible, non-superfluid dissipative phase between the Mott insulator and Luttinger liquid. The dissipative-to-Mott transition is accessible neither to perturbative renormalization-group methods nor to the free-fermion description of the conventional Mott transition. Here, we show it is governed by the worldline of a single doped excitation, whose geometrical roughness determines the critical exponents. Without dissipation, this worldline undergoes Brownian motion, recovering $β=ν=1/z=1/2$. Dissipation turns it into a long-range interacting interface, yielding continuously varying exponents $β=ν=1/z=s-1$ for $1

DOI
10.48550/arxiv.2607.00086

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Physical review. B, Condensed matter•Jul 1, 1989•3,511 citations
In one dimension at zero temperature, local baths with spectral exponent sss can stabilize a compressible, non-superfluid dissipative phase between the Mott insulator and Luttinger liquid. The dissipative-to-Mott transition is accessible neither to perturbative renormalization-group methods nor to the free-fermion description of the conventional Mott transition. Here, we show it is governed by the worldline of a single doped excitation, whose geometrical roughness determines the critical exponents. Without dissipation, this worldline undergoes Brownian motion, recovering β=ν=1/z=1/2β=ν=1/z=1/2β=ν=1/z=1/2. Dissipation turns it into a long-range interacting interface, yielding continuously varying exponents β=ν=1/z=s−1β=ν=1/z=s-1β=ν=1/z=s−1 for $1
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.
Understanding the stability of strongly correlated phases of matter when coupled to environmental degrees of freedom is crucial for identifying the conditions under which these states may be observed. Here, we focus on the paradigmatic one-dimensional Bose-Hubbard model, and study the stability of the Luttinger-liquid and Mott insulating phases in the presence of local particle exchange with site-independent baths of noninteracting bosons. We perform a numerically exact analysis of this model by adapting the recently developed wormhole quantum Monte Carlo method for retarded interactions to a continuous-time formulation with worm updates; we show how the wormhole updates can be easily implemented in this scheme. For an Ohmic bath, our numerical findings confirm the scaling prediction that the Luttinger-liquid phase becomes unstable at infinitesimal bath coupling. We show that the ensuing phase is a long-range-ordered superfluid with spontaneously broken U(1) symmetry. While the Mott insulator remains a distinct phase for small bath coupling, it exhibits diverging compressibility and noninteger local boson occupation in the thermodynamic limit. Upon increasing the bath coupling, this phase undergoes a transition to a long-range-ordered superfluid. Finally, we discuss the effects of super-Ohmic dissipation on the Luttinger-liquid phase. Our results are compatible with a stable dissipative Luttinger-liquid phase that transitions to a long-range-ordered superfluid at a finite system-bath coupling.
We consider the two-terminal conductance of a one-dimensional Mott insulator undergoing the commensurate-incommensurate quantum phase transition to a conducting state. We treat the leads as Luttinger liquids. At a specific value of compressibility of the leads, corresponding to the Luther-Emery point, the conductance can be described in terms of the free propagation of noninteracting fermions with charge e∕2e∕\sqrt{2}e∕2​. At that point, the temperature dependence of the conductance across the quantum phase transition is described by a Fermi function. The deviation from the Luther-Emery point in the leads changes the temperature dependence qualitatively. In the metallic state, the low-temperature conductance is determined by the properties of the leads, and is described by the conventional Luttinger-liquid theory. In the insulating state, conductance occurs via activation of e∕2e∕\sqrt{2}e∕2​ charges, and is independent of the Luttinger-liquid compressibility.
We compute the single particle spectral function of a Bose liquid on a lattice, at integer filling, close to the superfluid-Mott transition. We use a `static path approximation' that retains all the classical thermal fluctuations in the problem, and a real space implementation of the random phase approximation (RPA) for the Green's functions on the thermally fluctuating backgrounds. This leads to the standard RPA answers in the ground state but captures the progressive damping of the excitations with increasing temperature. We focus on the momentum resolved lineshape across the superfluid to Bose liquid thermal transition. In the superfluid regime we observe a gapped `amplitude' mode, and gapless `phase' modes of positive and negative energy. The dispersion and weight of these modes changes with interaction but are almost temperature independent, even into the normal state, except near critical coupling. The damping of the modes varies roughly as TαfkT^α f_{\bf k}Tαfk​, where TTT is the temperature and k{\bf k}k the momentum, with α∼0.5α\sim 0.5α∼0.5 and fkf_{\bf k}fk​ having non trivial momentum dependence. The Mott phase has gapped dispersive spectra. Near critical coupling the thermal Bose `liquid' is gapped, with progressive widening of the gap with increasing temperature, a feature that it shares with the Mott insulator.
We present a non-perturbative renormalization-group approach to the Bose-Hubbard model. By taking as initial condition of the RG flow the (local) limit of decoupled sites, we take into account both local and long-distance fluctuations in a nontrivial way. This approach yields a phase diagram in very good quantitative agreement with the quantum Monte Carlo results and reproduces the two universality classes of the superfluid--Mott-insulator transition with a good estimate of the critical exponents. Furthermore, it reveals the crucial role of the Ginzburg as a crossover length between a weakly- and a strongly-correlated superfluid phase.
The phase diagrams and phase transitions of bosons with short-ranged repulsive interactions moving in periodic and/or random external potentials at zero temperature are investigated with emphasis on the superfluid-insulator transition induced by varying a parameter such as the density. Bosons in periodic potentials (e.g., on a lattice) at T=0 exhibit two types of phases: a superfluid phase and Mott insulating phases characterized by integer (or commensurate) boson densities, by the existence of a gap for particle-hole excitations, and by zero compressibility. Generically, the superfluid onset transition in d dimensions from a Mott insulator to superfluidity is ``ideal,'' or mean field in character, but at special multicritical points with particle-hole symmetry it is in the universality class of the (d+1)-dimensional XY model. In the presence of disorder, a third, ``Bose glass'' phase exists. This phase is insulating because of the localization effects of the randomness and analogous to the Fermi glass phase of interacting fermions in a strongly disordered potential.The Bose glass phase is characterized by a finite compressibility, no gap, but an infinite superfluid susceptibility. In the presence of disorder the transition to superfluidity is argued to occur only from the Bose glass phase, and never directly from the Mott insulator. This zero-temperature superfluid-insulator transition is studied via generalizations of the Josephson scaling relation for the superfluid density at the ordinary \ensuremath{\lambda} transition, highlighting the crucial role of quantum fluctuations. The transition is found to have a dynamic critical exponent z exactly equal to d and correlation length and order-parameter correlation exponents \ensuremath{\nu} and \ensuremath{\eta} which satisfy the bounds \ensuremath{\nu}\ensuremath{\ge}2/d and \ensuremath{\eta}\ensuremath{\le}2-d, respectively. It is argued that the superfluid-insulator transition in the presence of disorder may have an upper critical dimension dc{d}_{c}dc​ which is infinite, but a perturbative renormalization-group calculation wherein the critical exponents have mean-field values for weak disorder above d=4 is also discussed. Many of these conclusions are verified by explicit calculations on a model of one-dimensional bosons in the presence of both random and periodic potentials. The general results are applied to experiments on 4He^{4}\mathrm{He}4He absorbed in porous media such as Vycor. Some measurable properties of the superfluid onset are predicted exactly [e.g., the exponent x relating the \ensuremath{\lambda} transition temperature to the zero-temperature superfluid density is found to be d/2(d-1)], while stringent bounds are placed on others. Analysis of preliminary data is consistent with these predictions.