Multidimensional bosonization

Bosonization of degenerate fermions yields insight both into Landau-Fermi liquids, and into non-Fermi liquids. We begin our review with a pedagogical introduction to bosonization, emphasizing its applicability in spatial dimensions greater than one. After a brief historical overview, we present the essentials of the method. Well known results of Landau theory are recovered, demonstrating that this new tool of many-body theory is robust. Limits of multidimensional bosonization are tested by considering several examples of non-Fermi liquids, in particular the composite fermion theory of the half-filled Landau level. Nested Fermi surfaces present a different challenge, and these may be relevant in the cuprate superconductors. We conclude by discussing the future of multidimensional bosonization.     

Quantum liquids of particles with generalized statistics

We propose a phenomenological approach to quantum liquids of particles obeying generalized statistics of a fermionic type, in the spirit of the Landau Fermi liquid theory. The approach is developed for fractional exclusion statistics. We discuss both equilibrium (specific heat, compressibility, and Pauli spin susceptibility) and nonequilibrium (current and thermal conductivities, thermopower) properties. Low-temperature quantities have the same temperature dependences as for the Fermi liquid, with the coefficients depending on the statistics parameter. The novel quantum liquids provide an explicit realization of systems with a non-Fermi liquid Lorentz ratio in two and more dimensions. Consistency of the theory is verified by deriving the compressibility and f-sum rules.     

Fermi systems with strong forward scattering

We review the theory of interacting Fermi systems whose low-energy physics is dominated by forward scattering, that is scattering processes generated by effective interactions with small momentum transfers. These systems include Fermi liquids as well as several important non-Fermi-liquid phases: one-dimensional Luttinger liquids, systems with long-range interactions, and fermions coupled to a gauge field. We report results for the critical dimensions separating different 'universality classes' and discuss the behaviour of physical quantities such as the momentum distribution function, the single-particle propagator and low-energy response functions in each class. The renormalization group for Fermi systems will be reviewed and applied as a link between microscopic models and effective lowenergy theories. Particular attention is paid to conservation laws, which constrain any effective low-energy theory of interacting Fermi systems. In scattering processes with small momentum transfers the velocity of each scattering particle is (almost) conserved. This asymptotic conservation law leads to non-trivial cancellations of Feynman diagrams and other simplifications, making thus possible a non-perturbative treatment of forward scattering via Ward identities or bosonization techniques.     

Quasiclassical boundary conditions for Fermi liquids at surfaces

The general boundary conditions at surfaces are derived within the quasiclassical theory of superfluidity in Fermi liquids (superconductors, superfluid³He). These conditions supplement the transport-like equations first introduced into the theory of superconductivity by G. Eilenberger, and allow a quantitative analysis of superfluids near a wall.     

Conservation of spin current as a consequence of a 2D Fermi surface

The possible existence of a previously unseen conservation in the theory of Fermi liquids is proposed for a two-dimensional geometry. If the ground state can be described by a smooth curve in momentum space then one expects spin current to be conserved, as it is not the case in three dimensions. Some immediate consequences that can be checked experimentally are pointed out.     

Fractionalized fermi liquids

In spatial dimensions d>or=2, Kondo lattice models of conduction and local moment electrons can exhibit a fractionalized, nonmagnetic state (FL(*)) with a Fermi surface of sharp electronlike quasiparticles, enclosing a volume quantized by (rho(a)-1)(mod 2), with rho(a) the mean number of all electrons per unit cell of the ground state. Such states have fractionalized excitations linked to the deconfined phase of a gauge theory. Confinement leads to a conventional Fermi liquid state, with a Fermi volume quantized by rho(a)(mod 2), and an intermediate superconducting state for the Z2 gauge case. The FL(*) state permits a second order metamagnetic transition in an applied magnetic field.     

Topological approach to Luttinger's theorem and the fermi surface of a kondo lattice

A nonperturbative proof of Luttinger's theorem, based on a topological argument, is given for Fermi liquids in arbitrary dimensions. Application to the Kondo lattice shows that even completely localized spins contribute to the Fermi sea volume as electrons, whenever the system can be described as a Fermi liquid.     

Breakdown of Landau Fermi liquid theory: Restrictions on the degrees of freedom of quantum electrons

One challenge in contemporary condensed matter physics is to understand unconventional electronic physics beyond the paradigm of Landau Fermi-liquid theory. Here, we present a perspective that posits that most such examples of unconventional electronic physics stem from restrictions on the degrees of freedom of quantum electrons in Landau Fermi liquids. Since the degrees of freedom are deeply connected to the system’s symmetries and topology, these restrictions can thus be realized by external constraints or by interaction-driven processes via the following mechanisms: (i) symmetry breaking, (ii) new emergent symmetries, and (iii) nontrivial topology. Various examples of unconventional electronic physics beyond the reach of traditional Landau Fermi liquid theory are extensively investigated from this point of view. Our perspective yields basic pathways to study the breakdown of Landau Fermi liquids and also provides a guiding principle in the search for novel electronic systems and devices.     

Interacting particles as neither bosons nor fermions: A microscopic origin for fractional exclusion statistics

We study a quantum liquid of particles interacting via a long-ranged two-body potential in three dimensions where the original particles are supposed to be either bosons or fermions. We show that such liquids exhibit the nature of a quantum liquid with fractional exclusion statistics. In both quantum liquids enlarged pseudo-Fermi surfaces are formed from bosons and fermions, although with different excitations. Hence, we conclude that the microscopic origin of exclusion statistics comes from the nature of long-ranged two-body interactions between the particles.     

General properties of a magnetic-field-induced landau Fermi liquid in high-temperature superconductors and heavy fermion metals

It has been shown that the magnetic-field-induced transition from a non-Fermi-liquid state to a Fermi liquid state in the Tl₂Ba₂CuO_{6 + x} high-temperature superconductor is similar to a transition observed in heavy fermion metals. This behavior is explained in the theory of the Fermi condensate quantum-phase transition implying the existence of Landau quasiparticles. The Fermi condensate quantum-phase transition can be considered as a universal cause of the strongly correlated behavior observed in various metals and liquids such as high-temperature superconductors, heavy fermion metals, and two-dimensional Fermi systems.     

Antiferromagnetism in metals: from the cuprate superconductors to the heavy fermion materials

The critical theory of the onset of antiferromagnetism in metals, with concomitant Fermi surface reconstruction, has recently been shown to be strongly coupled in two spatial dimensions. The onset of unconventional superconductivity near this critical point is reviewed: it involves a subtle interplay between the breakdown of fermionic quasiparticle excitations on the Fermi surface and the strong pairing glue provided by the antiferromagnetic fluctuations. The net result is a logarithm-squared enhancement of the pairing vertex for generic Fermi surfaces, with a universal dimensionless coefficient independent of the strength of interactions, which is expected to lead to superconductivity at the scale of the Fermi energy. We also discuss the possibility that the antiferromagnetic critical point can be replaced by an intermediate 'fractionalized Fermi liquid' phase, in which there is Fermi surface reconstruction but no long-range antiferromagnetic order. We discuss the relevance of this phase to the underdoped cuprates and the heavy fermion materials.     

Quasiparticle renormalization of the memory function approach for response functions

The problem of renormalization of the double-time Green function method for response functions is treated in the framework of the Mori-theory for the special case of Fermi liquids and finite Fermi systems. It is shown that the quasiparticle-quasihole renormalization of the response function can be carried out under conditions which are physically equivalent to the conditions under which the quasiparticle-quasihole renormalization is performed in the many-time Green function theory of Fermi liquids.     

On the specific heat of Fermi liquids

The contributions of long-wavelength spin fluctuations to the specific heat of Fermi liquids is consistently calculated on the basis of the Landau theory of Fermi liquids. More satisfactory estimations of the Landau parameter F₁^a for liquid ³He are obtained.     

Super Riemann surfaces: Uniformization and Teichmüller theory

Teichmüller theory for super Riemann surfaces is rigorously developed using the supermanifold theory of Rogers. In the case of trivial topology in the soul directions, relevant for superstring applications, the following results are proven. The super Teichmüller space is a complex super-orbifold whose body is the ordinary Teichmüller space of the associated Riemann surfaces with spin structure. For genusg>1 it has 3g-3 complex even and 2g-2 complex odd dimensions. The super modular group which reduces super Teichmüller space to super moduli space is the ordinary modular group; there are no new discrete modular transformations in the odd directions. The boundary of super Teichmüller space contains not only super Riemann surfaces with pinched bodies, but Rogers supermanifolds having nontrivial topology in the odd dimensions as well. We also prove the uniformization theorem for super Riemann surfaces and discuss their representation by discrete supergroups of Fuchsian and Schottky type and by Beltrami differentials. Finally we present partial results for the more difficult problem of classifying super Riemann surfaces of arbitrary topology.Enrico Fermi Fellow. Research supported by the NSF (PHY 83-01221) and DOE (DE-AC02-82-ER-40073).     

二维费密液体理论(Ⅰ)

通过关于二维低密度费密系统准粒子寿命和二维巡游电子系的自旋涨落的计算,本文证明朗道费密液体理论适用于二维相互作用费密粒子系。 关键词：     

Dominance of the final state in photoemission mapping of the fermi surface of Co/Cu(001)

The Fermi surface of tetragonally distorted fcc Co films grown on Cu(001) has been investigated with first-principles calculations and compared with an experimental determination using angle-resolved photoemission. The angular distributions for hnu=21-45 eV are dominated by the structure of the final states rather than by the shape of the Fermi surface. Theoretical estimates of the photoemission matrix elements support this observation. This suggests that photoemission can have limitations in mapping Fermi surfaces, especially for materials that exhibit flat, closely spaced valence bands.     

A density functional theory study of H2S decomposition on the (1 1 1) surfaces of model Pd-alloys

In this work, we report density functional theory calculations exploring H₂S dissociation on the (1 1 1) surfaces of Pd, Cu, Ag, Au, and various bimetallic surfaces consisting of those metals. To understand the contributions of lattice strain and electronic ligand effects, the thermodynamics of each elementary dissociation step were explored on model bimetallic surfaces, including PdMPd sandwiches and Pd pseudomorphic overlayers, as well as strained Pd(1 1 1) surfaces and homogeneous Pd₃M alloys. Sulfuric (H₂S, SH, and S) adsorption energies were found to correlate very well with lattice constant, which can be explained by the strong correlation of the lattice constant with d-band center, Fermi energy, and density of states at the Fermi level for strained Pd(1 1 1) surfaces. Compressing the Pd lattice shifts the d-band center away from the Fermi level, lowers the Fermi energy, and reduces the density of d-states at the Fermi level. All three effects likely contribute to the destabilization of sulfuric adsorption on Pd alloys. Introducing ligand effects was found to alter the distribution of the d-states and shift the Fermi level, which eliminates the correlation of the d-band center with the density of states at the Fermi level and the Fermi energy. As a result, the d-band center by itself is a poor metric of the H₂S reaction energetics for bimetallic surfaces. Furthermore, combining strain with ligand effects was found to lead to unpredictable alterations of the d-band. Therefore, adsorption of H₂S, SH, and S on PdMPd surfaces do not accurately predict adsorption on Pd₃M surfaces.     

Localization on short-range potentials in dissipative quantum mechanics

In this Letter, the problem of the existence of a state localized on a weak short-range attractive potential in the presence of dissipation is considered. It is shown that, contrary to the pure quantum case, a localized state is produced in any number of dimensions, while in low dimensions dissipation leads to much stronger localization. The results have physical implications for the dissipative dynamics of objects such as heavy particles in Fermi liquids and for superconductivity in high- T(c) materials.     

Fermi-liquid behavior of the normal phase of a strongly interacting gas of cold atoms

We measure the magnetic susceptibility of a Fermi gas with tunable interactions in the low-temperature limit and compare it to quantum Monte Carlo calculations. Experiment and theory are in excellent agreement and fully compatible with the Landau theory of Fermi liquids. We show that these measurements shed new light on the nature of the excitations of the normal phase of a strongly interacting Fermi gas.