Remarks on Bloch's Method of Sound Waves applied to Many-Fermion Problems

Tomonaga, Sin-itirô

doi:10.1143/ptp/5.4.544

Cited by 1,215 publications

(367 citation statements)

References 2 publications

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“…We will concentrate particularly on the Tomonaga's model [1] but the extension of the arguments to the Luttinger's model [4] is absolutely straightforward.…”

Section: Appendix B: Bosonization In One Spatial Dimensionmentioning

confidence: 99%

“…In the early 50's Tomonaga [1], generalizing earlier work by Bloch [2] on sound waves in dense Fermi systems, gave an explicit construction of the Bloch waves for systems in one dimension. Three years after the seminal work of Tomonaga, Bohm and Pines [3] showed that there was a natural connection between bosonization and the Random Phase Approximation (RPA).…”

Section: Introductionmentioning

confidence: 98%

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Bosonization of Fermi liquids

1994

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We bosonize a Fermi liquid in any number of dimensions in the limit of long wavelengths. From the bosons we construct a set of coherent states which are related with the displacement of the Fermi surface due to particle-hole excitations. We show that an interacting hamiltonian in terms of the original fermions is quadratic in the bosons. We obtain a path integral representation for the generating functional which in real time, in the semiclassical limit, gives the Landau equation for sound waves and in the imaginary time gives us the correct form of the specific heat for a Fermi liquid even with the corrections due to the interactions between the fermions. We also discuss the similarities between our results and the physics of quantum crystals.

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“…We will concentrate particularly on the Tomonaga's model [1] but the extension of the arguments to the Luttinger's model [4] is absolutely straightforward.…”

Section: Appendix B: Bosonization In One Spatial Dimensionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Bosonization of Fermi liquids

1994

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“…Shortly after the seminal works of Tomonaga and Luttinger [1,2], it was understood that one-dimensional electron gases (1DEG) display many interesting non-Fermi liquid properties [3][4][5][6][7][8][9][10]. Their universal validity was first fully appreciated in the 1980's, in particular by Haldane who coined the term Luttinger liquid [11,12].…”

Section: Introductionmentioning

confidence: 99%

Gold-induced nanowires on the Ge(100) surface yield a 2D and not a 1D electronic structure

et al. 2016

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Atomic nanowires on semiconductor surfaces induced by the adsorption of metallic atoms have attracted a lot of attention as possible hosts of the elusive, one-dimensional Tomonaga-Luttinger liquid. The Au/Ge(100) system in particular is the subject of controversy as to whether the Au-induced nanowires do indeed host exotic, 1D metallic states. In light of this debate, we report here a thorough study of the electronic properties of high quality nanowires formed at the Au/Ge(100) surface. The high resolution ARPES data show the low-lying Auinduced electronic states to possess a dispersion relation that depends on two orthogonal directions in k-space. Comparison of the E(kx,ky) surface measured using high-resolution ARPES to tight-binding calculations yields hopping parameters in the two different directions that differ by a factor of two. Additionally, by pinpointing the Au-induced surface states in the first, second and third surface Brillouin zones, and analysing their periodicity in k || , the nanowire propagation direction seen clearly in STM can be imported into the ARPES data. We find that the larger of the two hopping parameters corresponds, in fact, to the direction perpendicular to the nanowires (tperp). This, the topology of the E=EF contour in k || , and the fact that t || /tperp∼0.5 proves that the Au-induced electron pockets possess a two-dimensional, closed Fermi surface, and this firmly places the Au/Ge(100) nanowire system outside potential hosts of a Tomonaga-Luttinger liquid. We combine these ARPES data with scanning tunneling spectroscopic measurements of the spatially-resolved electronic structure and find that the spatially straight -wire-like -conduction channels observed up to energies of order one electron volt below the Fermi level do not originate from the Au-induced states seen in the ARPES data. The former are rather more likely to be associated with bulk Ge states that are localized to the subsurface region. Despite our proof of the 2D nature of the Au-induced nanowire and sub-surface Ge-related states, an anomalous suppression of the density of states at the Fermi level is observed in both the STS and ARPES data, and this phenomenon is discussed in the light of the effects of disorder.

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“…This lead to Tomonaga's [60] and Luttinger's models [61]. While Tomonaga solved the many-body problem at finite densities correctly, Luttinger found a solution to his model which is only correct if the Fermi sea is not filled.…”

Section: B Linear Dispersionsmentioning

confidence: 99%

Quantum collision theory in flat bands

Valiente

Zinner

2017

J. Phys. B: At. Mol. Opt. Phys.

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We consider quantum scattering of particles in media exhibiting strong dispersion degeneracy. In particular, we study flat-banded lattices and linearly dispersed energy bands. The former constitute a prime example of single-particle frustration while the latter show degeneracy at the few-and manyparticle level. We investigate both impurity and two-body scattering and show that, quite generally, scattering does not occur, which we relate to the fact that transition matrices vanish on the energy shell. We prove that scattering is instead replaced by projections onto band-projected eigenstates of the interaction potential. We then use the general results to obtain localised flat band states that are eigenstates of impurity potentials with vanishing eigenvalues in one-dimensional flat bands and study the particular case of a sawtooth lattice. We also uncover the relation between certain solutions of one-dimensional systems that have been categorised as "strange", and the scattering states in linearly dispersed continuum systems.

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Remarks on Bloch's Method of Sound Waves applied to Many-Fermion Problems

Cited by 1,215 publications

References 2 publications

Bosonization of Fermi liquids

Bosonization of Fermi liquids

Gold-induced nanowires on the Ge(100) surface yield a 2D and not a 1D electronic structure

Quantum collision theory in flat bands

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