The basic question is addressed, how the space dimension d is encoded in the Hilbert space of N identical fermions. There appears a finite number N ! d−1 of many-body wave functions, called shapes, which cannot be generated by trivial combinatorial extension of the one-dimensional ones. A general algorithm is given to list them all in terms of standard Slater determinants. Conversely, excitations which can be induced from the one-dimensional case are bosonised into a system of distinguishable bosons, called Euler bosons, much like the electromagnetic field is quantized in terms of photons distinguishable by their wave numbers. Their wave functions are given explicitly in terms of elementary symmetric functions, reflecting the fact that the fermion sign problem is trivial in one dimension. The shapes act as vacua for the Euler bosons. They are the natural generalization of the single-Slater-determinant form for the ground state to more than one dimension. In terms of algebraic invariant theory, the shapes are antisymmetric invariants which finitely generate the N -fermion Hilbert space as a graded algebra over the ring of symmetric polynomials. Analogous results hold for identical bosons.

We study the effect of antiferromagnetic (AF) correlations in the three-band Emery model, with respect to the experimental situation in weakly underdoped and optimally doped BSCCO. In the vicinity of the vH singularity of the conduction band there appears a central peak in the middle of a pseudogap, which is in an antiadiabatic regime, insensitive to the time scale of the mechanism responsible for the pseudogap. We find a quantum low-temperature regime corresponding to experiment, in which the pseudogap is created by zero-point motion of the magnons, as opposed to the usual semiclassical derivation, where it is due to a divergence of the magnon occupation number. Detailed analysis of the spectral functions along the (π, 0)-(π, π) line show significant agreement with experiment, both qualitative and, in the principal scales, quantitative. The observed slight approaching-then-receding of both the wide and narrow peaks with respect to the Fermi energy is also reproduced. We conclude that optimally doped BSCCO has a well-developed pseudogap of the order of 1000 K. This is only masked by the narrow antiadiabatic peak, which provides a small energy scale, unrelated to the AF scale, and primarily controlled by the position of the chemical potential. I. INTRODUCTIONThe Fermi surface phenomena in the high-T c cuprates, and especially BSCCO, have been extensively investigated, and a broad consensus has developed concerning their main features. The Fermi surface is large and hole-like, with a simple topology of a rounded square, or barrel, centered around the M-point [1]. Single-particle phenomenology is routinely invoked on the ARPES spectra, thus the 'self-energy' and 'damping' are often extracted from the main peak as if it were a coherent, weakly perturbed quasiparticle [2]. However, in the underdoped regime and below a temperature scale T * , the metallic state is surfeit with low-energy correlations, about whose relevance for either the pseudogap, or the superconducting mechanism itself, there is no general agreement at present. Various experimental observations at low energy have been interpreted in terms of stripes [3], paramagnons [4], phonons [5], and superconducting fluctuations above T c [6]. All these correlations are at present the object of intense scrutiny, mainly with a view to ascertaining whether they enhance or suppress superconductivity.Theoretical understanding of the measured electronic spectral functions of high-T c superconductors has received significant attention in the context of these efforts [7,8,9,10,11,12,13,14,15]. Physically, conduction occurs in the copper oxide planes, so the most important electronic states are directly accessible to surface probes such as ARPES. This naturally allows for a concentration of theoretical effort, especially because the observed spectra offer some outstanding puzzles of their own. Such a long-standing issue is the appearance of the pseudogap [16], observed near the vH points for underdoped systems, and its connection with the AF gap at lower doping on the o...

A review of the phenomenology and microscopy of cuprate superconductors is presented, with particular attention to universal conductance features, which reveal the existence of two electronic subsystems. The overall electronic system consists of $$1+p$$ 1 + p charges, where p is the doping. At low dopings, exactly one hole is localized per planar copper–oxygen unit, while upon increasing doping and temperature, the hole is gradually delocalized and becomes itinerant. Remarkably, the itinerant holes exhibit identical Fermi liquid character across the cuprate phase diagram. This universality enables a simple count of carrier density and yields comprehensive understanding of the key features in the normal and superconducting state. A possible superconducting mechanism is presented, compatible with the key experimental facts. The base of this mechanism is the interaction of fast Fermi liquid carriers with localized holes. A change in the microscopic nature of chemical bonding in the copper oxide planes, from ionic to covalent, is invoked to explain the phase diagram of these fascinating compounds.

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The doping mechanism and realistic Fermi surface (FS) evolution of La2−xSrxCuO4 (LSCO) are modelled within an extensive ab initio framework including advanced band-unfolding techniques. We show that ordinary Kohn-Sham DFT+U can reproduce the observed metalinsulator transition, when not restricted to the paramagnetic solution space. Arcs are self-doped by orbital charge transfer within the Cu-O planes, while the introduced Sr charge is strongly localized. Arc protection and the inadequacy of the rigid-band picture are consequences of a rapid change in orbital symmetry at the Fermi energy: the material undergoes a dimensional crossover along the Fermi surface, between the nodal (2D) and antinodal (3D) regions. In LSCO, this crossover accounts for FS arcs, the antinodal pseudogap, and insulating behavior in c-axis conductivity, all ubiquitous phenomena in high-Tc cuprates. Ligand Coulomb integrals involving out-of-plane sites are principally responsible for the most striking effects observed by ARPES in LSCO.

We report on the interplay of localized and extended degrees of freedom in the metallic state of high-temperature superconductors in a multiband setting. Various ways in which the bare magnetic response may become incommensurate are measured against both phenomenological and theoretical requirements. In particular, the pseudogap temperature is typically much higher than the incommensurability temperature. When microscopic strong-coupling effects with real-time dynamics between copper and oxygen sites are included, they tend to restore commensurability. Quantum transport equations for low-dimensional multiband electronic systems are used to explain the linear doping dependence of the dc conductivity and the doping and temperature dependence of the Hall number in the underdoped LSCO compounds. Coulomb effects of dopands are inferred from the doping evolution of the Hartree-Fock model parameters.

Understanding the physical properties of unconventional superconductors as well as of other correlated materials presents a formidable challenge. Their unusual evolution with doping, frequency, and temperature, has frequently led to non-Fermi-liquid (non-FL) interpretations. Optical conductivity is a major challenge in this context. Here, the optical spectra of two archetypal cuprates, underdoped HgBa 2 CuO 4+δ and optimally-doped Bi 2 Sr 2 CaCu 2 O 8+δ , are interpreted based on the standard Fermi liquid (FL) paradigm. At both dopings, perfect frequency-temperature FL scaling is found to be modified by the presence of a second, gapped electronic subsystem. This non-FL component emerges as a well-defined mid-infrared spectral feature after the FL contribution-determined independently by transport-is subtracted. Temperature, frequency and doping evolution of the MIR feature identifies a gapped rather than dissipative response.In contrast, the dissipative response is found to be relevant for pnictides and ruthenates. Such an unbiased FL/non-FL separation is extended across the cuprate phase diagram, providing a natural explanation why the superfluid density is attenuated on the overdoped side. Thus, we obtain a unified interpretation of optical responses and transport measurements in all analyzed physical regimes and all analyzed compounds.

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