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

Physical review. B, Condensed matter

Space-time tunneling bosonization: An application to theN-coupled Luttinger chains

D. Schmeltzer

Published Feb 1, 1995• 8 citations
Publisher

Abstract

The space-time tunneling bosonization has been introduced to study N-coupled Luttinger liquids. The interaction is separated into a forward exchange and a cooperon part. At T=0 the cooperon part is described by tunneling events which form a Coulomb gas in the plasma phase. At T\ensuremath{\ne}0 we ignore the cooperon part and show that the correlation functions show a Luttinger-liquid behavior. In the limit N\ensuremath{\rightarrow}\ensuremath{\infty}, we extract the two-dimensional behavior and show that for a certain range of parameters the Luttinger liquid survives.

DOI
10.1103/physrevb.51.3709

Related papers

Bosonization in two dimensions: A space-time tunneling approach

D. Schmeltzer, A. R. Bishop

Using the space-time curve representation, a bosonization scheme is constructed which includes density excitations around each point on the Fermi surface (FS) and space-time tunneling of charges which belong to different FS points. The space-time tunneling reproduces the two-dimensional Jordan-Wigner transformation. In two dimensions, since the tunneling involves two electrons, the total Jordan-Wigner phase maps boson into boson. Therefore, the tunneling corresponds to instantons in 2e bosonic systems. Using this formalism, a spinless fermion model with short-range repulsive interactions is investigated. We find two components: sound-wave excitations in the normal direction of the FS reproduce the Fermi liquid (FL); the second component corresponds to the cooperon channel, violates charge conservation, and gives rise to two-particle coherent tunneling. As a result, the FL phase is destroyed at temperature T=0, and a tunneling gap for charge 2e is formed with angular momentum l\ensuremath{\ne}0. We apply our formalism to the U(1) gauge field coupled to a spinless fermion and find that at T\ensuremath{\ne}0 the FL is again destroyed. We also make some remarks concerning the t-J model.

Physical review. B, Condensed matter•Nov 1, 1994•7 citations

Tunneling conductance of long-range Coulomb interacting Luttinger liquid

DinhDuy Vu, Iucci, Carlos Aníbal, S. Das Sarma

The theoretical model of the short-range interacting Luttinger liquid predicts a power-law scaling of the density of states and the momentum distribution function around the Fermi surface, which can be readily tested through tunneling experiments. However, some physical systems have long-range interaction, most notably the Coulomb interaction, leading to significantly different behaviors from the short-range interacting system. In this paper, we revisit the tunneling theory for the one-dimensional electrons interacting via the long-range Coulomb force. We show that even though in a small dynamic range of temperature and bias voltage, the tunneling conductance may appear to have a power-law decay similar to short-range interacting systems, the effective exponent is scale-dependent and slowly increases with decreasing energy. This factor may lead to the sample-to-sample variation in the measured tunneling exponents. We also discuss the crossover to a free Fermi gas at high energy and the effect of the finite size. Our work demonstrates that experimental tunneling measurements in one-dimensional electron systems should be interpreted with great caution when the system is a Coulomb Luttinger liquid.

•Jan 1, 2020•8 citations

Crossover between Luttinger and Fermi-liquid behavior in weakly coupled metallic chains

Peter Kopietz, V. Meden, Kurt Schönhammer

We use higher-dimensional bosonization to study the normal state of electrons in weakly coupled metallic chains interacting with long-range Coulomb forces. Particular attention is paid to the crossover between Luttinger and Fermi-liquid behavior as the interchain hopping ${t}_{\ensuremath{\perp}}$ is varied. Although in the physically interesting case of finite but small ${t}_{\ensuremath{\perp}}$ the quasiparticle residue does not vanish, the single-particle Green's function exhibits the signature of Luttinger-liquid behavior (i.e., anomalous scaling and spin-charge separation) in a large intermediate parameter regime. Using realistic parameters, we find that the scaling behavior in this regime is characterized by an anomalous dimension of the order of unity, as suggested by recent experiments on quasi-one-dimensional conductors. Our calculation also gives insights into the approximations inherent in higher-dimensional bosonization; in particular, we show that the replacement of a curved Fermi surface by a finite number $M$ of flat patches can give rise to unphysical nesting singularities in the single-particle Green's function, which disappear only in the limit $M\ensuremath{\rightarrow}\ensuremath{\infty}$ or if curvature effects are included. We also compare our approach with other methods. This work extends our recent letter [Phys. Rev. Lett. 74, 2997 (1995)].

arXiv:cond-mat/9701023•Physical review. B, Condensed matter•Sep 15, 1997•23 citations

Nonequilibrium dynamics of coupled Luttinger liquids

Laura Foini, Thierry Giamarchi

The dynamics of two initially tunnel-coupled chains of bosonic atoms after a quench in the tunneling strength is studied, and the correlation functions of relative phase (directly measured in interference experiments), relative density, and current are computed.

arXiv:1412.6377•Physical Review A•Feb 25, 2015•42 citations

Luttinger-liquid physics in wire and dot geometries

Hans Peter Wächter

In a first part, I study the electronic transport through a one-dimensional, finite-length quantum wire of correlated electrons (Luttinger liquid) coupled at arbitrary position via tunnel barriers to two semi-infinite, one-dimensional as well as stripe-like (two-dimensional) leads, thereby bringing theory closer towards systems resembling setups realized in experiments. In particular, I compute the temperature dependence of the linear conductance of a system without bulk impurities. The appearance of new temperature scales introduced by the lengths of the overhanging parts of the leads and the wire implies a conductance function which is much more complex than the simple power-law behavior obtained in earlier approaches. My results can be used to optimize the experimental setups designed for a verification of Luttinger-liquid scaling. In a second part, I suggest a setup to study Luttinger-liquid behavior in quantum wires which allows to determine the Luttinger-liquid parameter from two independent measurements: transport through a quantum dot embedded in the wire and the charge on the dot. To this end, I identified novel Luttinger-liquid power-laws in the charging of the dot. In a more technical part, I extended an adaption of the functional renormalization group such that it can be used on correlated electrons in complex geometries like the wire-lead structures described above and arbitrary dot structures coupled to Luttinger-liquid leads.

•Jan 1, 2010•0 citations

Bosonization of the two coupled spinon-holon chains

D. Schmeltzer

The two coupled spinon-holon chains are investigated. One finds that for the set of parameters which allows us to map the model into two coupled Hubbard chains tunnelling occurs and the Luttinger liquid is destroyed. In addition we find that t perpendicular to 2 /J perpendicular to >>t/sub /// 2 /J/sub /// preserves the Luttinger liquid.

Journal of Physics Condensed Matter•Feb 6, 1995•0 citations
The space-time tunneling bosonization has been introduced to study N-coupled Luttinger liquids. The interaction is separated into a forward exchange and a cooperon part. At T=0 the cooperon part is described by tunneling events which form a Coulomb gas in the plasma phase. At T\ensuremath{\ne}0 we ignore the cooperon part and show that the correlation functions show a Luttinger-liquid behavior. In the limit N\ensuremath{\rightarrow}\ensuremath{\infty}, we extract the two-dimensional behavior and show that for a certain range of parameters the Luttinger liquid survives.
Using the space-time curve representation, a bosonization scheme is constructed which includes density excitations around each point on the Fermi surface (FS) and space-time tunneling of charges which belong to different FS points. The space-time tunneling reproduces the two-dimensional Jordan-Wigner transformation. In two dimensions, since the tunneling involves two electrons, the total Jordan-Wigner phase maps boson into boson. Therefore, the tunneling corresponds to instantons in 2e bosonic systems. Using this formalism, a spinless fermion model with short-range repulsive interactions is investigated. We find two components: sound-wave excitations in the normal direction of the FS reproduce the Fermi liquid (FL); the second component corresponds to the cooperon channel, violates charge conservation, and gives rise to two-particle coherent tunneling. As a result, the FL phase is destroyed at temperature T=0, and a tunneling gap for charge 2e is formed with angular momentum l\ensuremath{\ne}0. We apply our formalism to the U(1) gauge field coupled to a spinless fermion and find that at T\ensuremath{\ne}0 the FL is again destroyed. We also make some remarks concerning the t-J model.
The theoretical model of the short-range interacting Luttinger liquid predicts a power-law scaling of the density of states and the momentum distribution function around the Fermi surface, which can be readily tested through tunneling experiments. However, some physical systems have long-range interaction, most notably the Coulomb interaction, leading to significantly different behaviors from the short-range interacting system. In this paper, we revisit the tunneling theory for the one-dimensional electrons interacting via the long-range Coulomb force. We show that even though in a small dynamic range of temperature and bias voltage, the tunneling conductance may appear to have a power-law decay similar to short-range interacting systems, the effective exponent is scale-dependent and slowly increases with decreasing energy. This factor may lead to the sample-to-sample variation in the measured tunneling exponents. We also discuss the crossover to a free Fermi gas at high energy and the effect of the finite size. Our work demonstrates that experimental tunneling measurements in one-dimensional electron systems should be interpreted with great caution when the system is a Coulomb Luttinger liquid.
We use higher-dimensional bosonization to study the normal state of electrons in weakly coupled metallic chains interacting with long-range Coulomb forces. Particular attention is paid to the crossover between Luttinger and Fermi-liquid behavior as the interchain hopping ${t}_{\ensuremath{\perp}}$ is varied. Although in the physically interesting case of finite but small ${t}_{\ensuremath{\perp}}$ the quasiparticle residue does not vanish, the single-particle Green's function exhibits the signature of Luttinger-liquid behavior (i.e., anomalous scaling and spin-charge separation) in a large intermediate parameter regime. Using realistic parameters, we find that the scaling behavior in this regime is characterized by an anomalous dimension of the order of unity, as suggested by recent experiments on quasi-one-dimensional conductors. Our calculation also gives insights into the approximations inherent in higher-dimensional bosonization; in particular, we show that the replacement of a curved Fermi surface by a finite number MMM of flat patches can give rise to unphysical nesting singularities in the single-particle Green's function, which disappear only in the limit $M\ensuremath{\rightarrow}\ensuremath{\infty}$ or if curvature effects are included. We also compare our approach with other methods. This work extends our recent letter [Phys. Rev. Lett. 74, 2997 (1995)].
In a first part, I study the electronic transport through a one-dimensional, finite-length quantum wire of correlated electrons (Luttinger liquid) coupled at arbitrary position via tunnel barriers to two semi-infinite, one-dimensional as well as stripe-like (two-dimensional) leads, thereby bringing theory closer towards systems resembling setups realized in experiments. In particular, I compute the temperature dependence of the linear conductance of a system without bulk impurities. The appearance of new temperature scales introduced by the lengths of the overhanging parts of the leads and the wire implies a conductance function which is much more complex than the simple power-law behavior obtained in earlier approaches. My results can be used to optimize the experimental setups designed for a verification of Luttinger-liquid scaling. In a second part, I suggest a setup to study Luttinger-liquid behavior in quantum wires which allows to determine the Luttinger-liquid parameter from two independent measurements: transport through a quantum dot embedded in the wire and the charge on the dot. To this end, I identified novel Luttinger-liquid power-laws in the charging of the dot. In a more technical part, I extended an adaption of the functional renormalization group such that it can be used on correlated electrons in complex geometries like the wire-lead structures described above and arbitrary dot structures coupled to Luttinger-liquid leads.