Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1910.06371

Dissipative Luttinger liquids

Aaron J. Friedman

Published Oct 14, 2019• 2 citations
arXivHTMLPDF

Abstract

We investigate a one dimensional quantum fluid coupled to a dissipative bath. The quantum fluid is captured by the canonical Luttinger liquid; the bath is given by the model of Caldeira and Leggett, i.e. a tower of oscillators coupled linearly to the fluid density, $ρ$. The bath can be integrated out exactly, producing an effective interaction for the fluid that is nonlocal in time; we argue that the form corresponding to Ohmic dissipation is generic. Compared to previous works, we compute correlation functions for this minimal model without approximation, including at finite temperature $T>0$. From these and a Kubo calculation, we conclude that arbitrary dissipation destroys the perfect conductivity of the Luttinger liquid via Zeno localization, even in the absence of a spatial potential; from RG analysis of harmonic terms, we also find that the open Luttinger liquid is significantly more prone to localization by such potentials, in contrast to the usual intuition that baths make systems less localized.

DOI
10.48550/arxiv.1910.06371

Related papers

Unification of electromagnetic noise and Luttinger liquid via a quantum dot

Karyn Le Hur, Mei-Rong Li

We investigate the effect of dissipation on a small quantum dot (resonant level) tunnel coupled to a chiral Luttinger liquid (LL) with the LL parameter $K$. The dissipation stems from the coupling of the dot to an electric environment, being characterized by the resistance $R$, via Coulomb interactions. We show that this problem can be mapped onto a Caldeira-Leggett model where the (ohmic) bath of harmonic oscillators is governed by the effective dissipation strength $\ensuremath{\alpha}={(2\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{K})}^{\ensuremath{-}1}$ with ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{K}}^{\ensuremath{-}1}={K}^{\ensuremath{-}1}+2R∕{R}_{K}$ and ${R}_{K}=h∕{e}^{2}$ the quantum of resistance. Experimental consequences are discussed and the limit $K=1∕{2}^{+}$ is thoroughly studied at small $R∕{R}_{K}$ through the spin-boson-fermion model.

arXiv:cond-mat/0410446•Physical Review B•Aug 9, 2005•61 citations

Dissipation-induced Luttinger liquids in the Caldeira-Leggett formalism

S. Eigenhuis

It is well known that dissipation usually induces decoherence in quantum systems. However, recently it has been employed to engineer zero-energy Majorana modes on the boundary of a one-dimensional fermionic chain. In this thesis, by employing the Caldeira-Leggett theory of quantum dissipation, we study the equivalence between a particle on a one-dimensional lattice coupled to a thermal bath, and the massless Luttinger liquid with an impurity on the boundary in a closed system. In particular, the Luttinger liquid with a single impurity at the boundary of a semi-infinite chain is bosonized into the boundary sine-Gordon theory. Here, a zero-energy Majorana mode appears at the boundary when the Luttinger parameter K=1/2. The equivalence is shown to apply also in the case of helical Luttinger liquids, which play an important role in topological insulators. This equivalence is then generalized to the full sine-Gordon theory, such that massive Luttinger liquids can be mapped to a single-particle one-dimensional tunneling Hamiltonian with a dissipative Ohmic Caldeira-Leggett bath.

•Jan 1, 2016•0 citations

Bath-induced phase transition in a Luttinger liquid

Saptarshi Majumdar, Laura Foini, Thierry Giamarchi +1 more

We study an XXZ spin chain, where each spin is coupled to an independent ohmic bath of harmonic oscillators at zero temperature. Using bosonization and numerical techniques, we show the existence of two phases separated by a Kosterlitz-Thouless transition. At low coupling with the bath, the chain remains in a Luttinger liquid (LL) phase with a reduced but finite spin stiffness, while above a critical coupling, the system is in a dissipative phase characterized by a vanishing spin stiffness. We argue that the transport properties are also inhibited: The LL is a perfect conductor, while the dissipative phase displays finite resistivity. Our results show that the effect of the bath can be interpreted as annealed disorder-inducing signatures of localization.

arXiv:2210.01590•Physical review. B./Physical review. B•Apr 7, 2023•9 citations

Dissipation-induced long-range order in the one-dimensional Bose-Hubbard model

Ana Beatriz Landim Ribeiro, Paul McClarty, Pedro Ribeiro +1 more

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.

arXiv:2311.07683•Physical review. B./Physical review. B•Sep 24, 2024•6 citations

Transport in a Dissipative Luttinger Liquid

Zoran Ristivojević, Thomas Nattermann

We study theoretically the transport through a single impurity in a one-channel Luttinger liquid coupled to a dissipative (Ohmic) bath. For nonzero dissipation, the single impurity is always a relevant perturbation which suppresses transport strongly. At zero temperature, the current voltage relation of the link is $I\ensuremath{\sim}\mathrm{exp}(\ensuremath{-}{E}_{0}/eV)$, where ${E}_{0}\ensuremath{\sim}\ensuremath{\eta}/\ensuremath{\kappa}$ and $\ensuremath{\kappa}$ denotes the compressibility. At nonzero temperature $T$, the linear conductance is proportional to $\mathrm{exp}(\ensuremath{-}\sqrt{\mathcal{C}{E}_{0}/{k}_{B}T})$. The decay of Friedel oscillation saturates for a distance larger than ${L}_{\ensuremath{\eta}}\ensuremath{\sim}1/\ensuremath{\eta}$ from the impurity.

arXiv:0803.2971•Physical Review Letters•Jul 3, 2008•13 citations

Low-temperature properties of a quantum particle coupled to dissipative environments

F. Guinea

We study the dynamics of a quantum particle coupled to dissipative (Ohmic) environments, such as an electron liquid. For certain choices of couplings, the properties of the particle can be described in terms of an effective mass. A particular case is the three-dimensional dirty electron liquid. In other environments, like the one described by the Caldeira-Leggett model, the effective mass diverges at low temperatures, and quantum effects are strongly suppressed. For interactions within this class, arbitrarily weak potentials lead to localized solutions. Particles bound to external potentials, or moving in closed orbits, can show a first-order transition, between strongly and weakly localized regimes.

arXiv:cond-mat/0207381•Physical review. B, Condensed matter•Jan 16, 2003•15 citations
We investigate a one dimensional quantum fluid coupled to a dissipative bath. The quantum fluid is captured by the canonical Luttinger liquid; the bath is given by the model of Caldeira and Leggett, i.e. a tower of oscillators coupled linearly to the fluid density, ρρρ. The bath can be integrated out exactly, producing an effective interaction for the fluid that is nonlocal in time; we argue that the form corresponding to Ohmic dissipation is generic. Compared to previous works, we compute correlation functions for this minimal model without approximation, including at finite temperature T>0T>0T>0. From these and a Kubo calculation, we conclude that arbitrary dissipation destroys the perfect conductivity of the Luttinger liquid via Zeno localization, even in the absence of a spatial potential; from RG analysis of harmonic terms, we also find that the open Luttinger liquid is significantly more prone to localization by such potentials, in contrast to the usual intuition that baths make systems less localized.
We investigate the effect of dissipation on a small quantum dot (resonant level) tunnel coupled to a chiral Luttinger liquid (LL) with the LL parameter KKK. The dissipation stems from the coupling of the dot to an electric environment, being characterized by the resistance RRR, via Coulomb interactions. We show that this problem can be mapped onto a Caldeira-Leggett model where the (ohmic) bath of harmonic oscillators is governed by the effective dissipation strength $\ensuremath{\alpha}={(2\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{K})}^{\ensuremath{-}1}$ with ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{K}}^{\ensuremath{-}1}={K}^{\ensuremath{-}1}+2R∕{R}_{K}$ and RK=h∕e2{R}_{K}=h∕{e}^{2}RK​=h∕e2 the quantum of resistance. Experimental consequences are discussed and the limit K=1∕2+K=1∕{2}^{+}K=1∕2+ is thoroughly studied at small R∕RKR∕{R}_{K}R∕RK​ through the spin-boson-fermion model.
It is well known that dissipation usually induces decoherence in quantum systems. However, recently it has been employed to engineer zero-energy Majorana modes on the boundary of a one-dimensional fermionic chain. In this thesis, by employing the Caldeira-Leggett theory of quantum dissipation, we study the equivalence between a particle on a one-dimensional lattice coupled to a thermal bath, and the massless Luttinger liquid with an impurity on the boundary in a closed system. In particular, the Luttinger liquid with a single impurity at the boundary of a semi-infinite chain is bosonized into the boundary sine-Gordon theory. Here, a zero-energy Majorana mode appears at the boundary when the Luttinger parameter K=1/2. The equivalence is shown to apply also in the case of helical Luttinger liquids, which play an important role in topological insulators. This equivalence is then generalized to the full sine-Gordon theory, such that massive Luttinger liquids can be mapped to a single-particle one-dimensional tunneling Hamiltonian with a dissipative Ohmic Caldeira-Leggett bath.
We study an XXZ spin chain, where each spin is coupled to an independent ohmic bath of harmonic oscillators at zero temperature. Using bosonization and numerical techniques, we show the existence of two phases separated by a Kosterlitz-Thouless transition. At low coupling with the bath, the chain remains in a Luttinger liquid (LL) phase with a reduced but finite spin stiffness, while above a critical coupling, the system is in a dissipative phase characterized by a vanishing spin stiffness. We argue that the transport properties are also inhibited: The LL is a perfect conductor, while the dissipative phase displays finite resistivity. Our results show that the effect of the bath can be interpreted as annealed disorder-inducing signatures of localization.
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 study theoretically the transport through a single impurity in a one-channel Luttinger liquid coupled to a dissipative (Ohmic) bath. For nonzero dissipation, the single impurity is always a relevant perturbation which suppresses transport strongly. At zero temperature, the current voltage relation of the link is $I\ensuremath{\sim}\mathrm{exp}(\ensuremath{-}{E}_{0}/eV)$, where ${E}_{0}\ensuremath{\sim}\ensuremath{\eta}/\ensuremath{\kappa}$ and $\ensuremath{\kappa}$ denotes the compressibility. At nonzero temperature TTT, the linear conductance is proportional to $\mathrm{exp}(\ensuremath{-}\sqrt{\mathcal{C}{E}_{0}/{k}_{B}T})$. The decay of Friedel oscillation saturates for a distance larger than ${L}_{\ensuremath{\eta}}\ensuremath{\sim}1/\ensuremath{\eta}$ from the impurity.
We study the dynamics of a quantum particle coupled to dissipative (Ohmic) environments, such as an electron liquid. For certain choices of couplings, the properties of the particle can be described in terms of an effective mass. A particular case is the three-dimensional dirty electron liquid. In other environments, like the one described by the Caldeira-Leggett model, the effective mass diverges at low temperatures, and quantum effects are strongly suppressed. For interactions within this class, arbitrarily weak potentials lead to localized solutions. Particles bound to external potentials, or moving in closed orbits, can show a first-order transition, between strongly and weakly localized regimes.