Confined coherence in quasi-one-dimensional metals

Abstract

We present a functional renormalization group calculation of the effect of strong interactions on the shape of the Fermi surface of weakly coupled metallic chains. In the regime where the bare interchain hopping is small, we show that scattering processes involving large momentum transfers perpendicular to the chains can completely destroy the warping of the true Fermi surface, leading to a confined state where the renormalized interchain hopping vanishes and a coherent motion perpendicular to the chains is impossible.PACS numbers: 71.10.Pm, 71.27.+a,71.10.Hf Introduction.Electron-electron interactions can strongly modify the Fermi surface (FS) of a metal. A well known example is the Pomeranchuk transition, where the symmetry of the FS is spontaneously broken due to strong interactions in the zero-sound channel [1]. However, there are other quantum phase transitions associated with the geometry or the topology of the FS without symmetry breaking, such as the Lifshitz transition [2,3] or the truncation transition [4,5], where certain sectors of the FS are washed out by interactions, while others remain intact. Another example is the interactioninduced confinement transition, which has been proposed by Clarke, Strong, and Anderson more than ten years ago [6]: they considered metallic chains with small interchain hopping t ⊥,0 . For weak interactions, the FS consists then of two disconnected weakly curved sheets as shown Fig. 1. The amplitude of the warping of the FS is proportional to the renormalized interchain hopping t ⊥ . Clarke et al. [6] suggested that, at least for sufficiently strong interactions and small t ⊥,0 , the renormalized t ⊥ vanishes. The true FS is then completely flat, so that a coherent motion of the electrons in the direction perpendicular to the chains is not possible (confined coherence).In the past decade the confinement problem in weakly coupled metallic chains has been studied by many authors [6,7,8,9,10], but the results have not converged

Metanematic, smectic, and crystalline phases of dipolar fermions in an optical lattice

“…This quasi-1D to 2D transition induced by inter -chain interactions is in some sense the opposite of confinement [32] (a quasi-1D to 1D transition induced by intra-chain interactions [33]). A similar phenomenon is believed to occur in stacks of integer quantum Hall systems [34], where the chiral Luttinger liquids on the edges couple together, creating a 2D Fermi surface (the chiral Fermi liquid).…”

Lifshitz transitions and crystallization of fully polarized dipolar fermions in an anisotropic two-dimensional lattice

“…25 These electronic liquid crystal phases also have a strong relation to dimensional crossover phenomena, where one can ask the question whether an array of one-dimensional chains ͑Luttinger liquids͒ coupled by a weak interchain hopping t Ќ remains strictly one-dimensional ͑confinement͒, 26 or becomes a quasi-one-dimensional ͑quasi-1D͒ Fermi liquid ͑de-confinement͒. Indeed, calculation methods such as selfconsistent perturbation theory 27,28 and functional renormalization 29 support the idea that the warped Fermi surface is unstable for sufficiently small t Ќ , in principle, therefore leading to a Fermi-surface modifying transition at some finite value of interchain hopping. While the issue of the Luttinger liquid to Fermi-liquid crossover/transition is not yet fully resolved, it is possible to ask a much simpler question: what happens if an array of one-dimensional Fermi liquids are coupled together?…”

Breakdown of the Fermi-liquid regime in the two-dimensional Hubbard model from a two-loop field-theoretical renormalization group approach

“…In recent years, there has been some progress in analyzing this problem in quasi-onedimensional systems. 33,34 However, a two-loop RG calculation of this effect in two-dimensional systems still remains a very difficult task and, to our knowledge, has not been calculated so far. Another important aspect which deserves future investigation concerns the actual importance of quantum fluctuations beyond the two-loop RG level for this model.…”

“…How the renormalization of the FS induced by interactions affects the RG flow is still not considered in our RG scheme. In recent years, there has been some progress in analyzing this problem in quasi-one dimensional systems 33,34 . However, a two-loop RG calculation of this effect in twodimensional systems still remains a very difficult task and, to our knowledge, has not been calculated so far.…”