Abstract We aim to clarify the confusion and inconsistency in our recent works (Luo et al 2023 Commun. Theor. Phys. 75 095702; Liang et al 2024 Phys. Rev. B 110 075125), and to address the incompleteness therein. In order to avoid the ill-defined nature of the free propagator of the gauge field in the ordered states of the t – J model, we adopted a gauge fixing that was not of the Becchi–Rouet–Stora–Tyutin (BRST) exact form in our previous work (Liang et al 2024 Phys. Rev. B 110 075125). This led to the situation where Dirac’s second-class constraints, namely, the slave particle number constraint and the Ioffe–Larkin current constraint, were not rigorously obeyed. Here we show that a consistent gauge fixing condition that enforces the exact constraints is BRST-exact in our theory. An example is the Lorenz gauge. On the other hand, we prove that although the free propagator of the gauge field in the Lorenz gauge is ill-defined, the full propagator is still well-defined. This implies that the strongly correlated t – J model can be exactly mapped to a perturbatively controllable theory within the slave particle representation.
We develop a slave-boson theory for the $t\ensuremath{-}J$ model at finite doping that respects an SU(2) symmetry: a symmetry previously known to be important at half filling. The mean-field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contain
d-wave superconductor, spin-gap, strange metal, and Fermi-liquid phases. The spin-gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The physical electron spectral function shows small Fermi segments at low doping that continuously evolve into the large Fermi surface at high-doping concentrations. The close relation between the SU(2) and the U(1) slave-boson theory is discussed. The low-energy effective theory for the low-lying fluctuations is derived and additional lying modes [which were overlooked in the U(1) theory] are identified.
We develop a slave-boson theory for the $t\ensuremath{-}J$ model at finite doping which respects an
SU(2) symmetry---a symmetry previously known to be important at half filling. The mean field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contain
d-wave superconductor, spin gap, strange metal, and Fermi liquid phases. The spin gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The electron spectral function shows small Fermi pockets at low doping which continuously evolve into the large Fermi surface at high doping concentrations.
The strange metal is an enigma within the field of many-body quantum physics, as it defies the standard Fermi liquid theory of metals due to the absence of well-defined, electron-like quasiparticles. It has been presumed that strange metal behavior arises due to strong correlations between electrons that are not present in ordinary Fermi liquids, but the exact nature of these correlations is unknown. To this end, this thesis aims to address the fundamental question: What, precisely, is so strongly correlated about charge in the strange metal? This question is tackled by experimentally measuring the dynamic charge response function, which directly encodes charge correlations in momentum and energy, using the technique of Momentum-resolved Electron Energy-loss Spectroscopy (M-EELS). In particular, two prototypical members of the cuprate and ruthenate strange metal families are studied: Bi-2212 and Sr
2RuO
4. By studying Bi-2212 at optimal doping, it is found that the charge response of the strange metal is characterized by a broad continuum of fluctuations that are momentum and energy independent over a large range of parameter space, unlike Fermi liquid charge correlations which exhibit propagating density waves of charge with well defined energy and momentum (i.e. plasmons). We argue that, in essence, the charge correlations of the strange metal are highly localized in both space and time, unlike the Fermi Liquid where they are localized in momentum and energy instead. To understand how charge correlations change as one leaves the strange metal regime, the M-EELS response of Bi-2212 is mapped out as a function of doping and temperature. At high temperature, it is found that the continuum is largely doping independent. However, upon cooling, very large changes in spectral weight are observed over a range of energy scales nearly two orders of magnitude larger than the thermal scale
kBT. Moreover, this change in spectral weight undergoes a sign reversal as a function of doping, with spectral weight enhancement on the underdoped side, suppression in the overdoped regime, and no change at optimal doping. These changes in spectral weight are completely unlike the case of the Fermi liquid, where doping only acts to rigidly shift the plasmon energy and no significant changes occur as a function of temperature. Finally, we venture further and ask whether strange metal and Fermi liquid charge correlations can simultaneously coexist in a material. To explore this possibility, we measured the M-EELS response of Sr
2RuO
4, a material which exhibits strange and bad metal behavior at high temperature, but transitions to a well-defined Fermi liquid at low temperature. Surprisingly, in the strange metal regime, Sr
2RuO
4 exhibits both a broad continuum similar to Bi-2212 and a propagating Fermi liquid collective mode at low-energies and momentum. Upon cooling, low-energy spectral weight is suppressed in the strange metal continuum and the Fermi liquid collective mode velocity is strongly renormalized. These findings confirm the strange metal and Fermi liquid can coexist and demonstrate that Sr
2RuO
4 exhibits charge correlations with strange metal character at high energies and short length scales and Fermi liquid character at low energies and long wavelengths.
The Fermi liquid theory is a central concept in modern condensed matter physics used to describe conventional metals. A state of this universality class consists of well-defined quasiparticles, which occupy a finite number of states within a Fermi volume defined in momentum space. According to the Luttinger’s theorem, such a state encloses a Fermi volume proportional to the electron density modulo the filled bands if no symmetry is broken. In the past decades strong deviations from Fermi liquid theory have been observed in the scaling behavior of thermodynamic observables in different materials, among which are for instance cuprates and iron pnictides. This thesis is about two prototypical systems that can not be described by Fermi liquid theory. The first part of this work investigates two-dimensional effective models, which are in a Mott insulating state at half-filling and have a finite conductivity when doped with holes. In such a Mott insulating state, the charge carriers are strongly localized due to the Coulomb repulsion. Hence, strong correlations are assumed to have a strong impact on the formation of the ground state, also in the regime of small hole concentration. In a first project we have used a so-called spinon dopon mean-field theory to represent the two-dimensional Fermi-Hubbard model with strong on-site repulsive interaction in effective degrees of freedom, in which the holes can be embedded into a quantum spin liquid. The corresponding SU(2) invariant ground state belongs to the class of fractionalized Fermi liquids. In a second project we investigate a quantum dimer model, an effective model based on a Hilbert space spanned by short range singlets and bound states of holes and spins. The focus here is on the calculation of the hole-part of the electron spectral function by using exact diagonalization and its comparison with two analytic methods, a diagrammatic computation based on the Bethe-Salpeter equation and a so-called two-mode approximation. The electron spectral function shows a similar analytic form in momentum space between nodal and antinodal point when compared to results from photoemission spectroscopy experiments on cuprates. Furthermore, in a subsequent work we calculate the exact ground state of the quantum dimer model along a certain parameter line. In order to analyze the behavior of the elctron spectral function when increasing the density of holes, we investigate the Fermi-Hubbard model in a current project using a dynamical mean-field approach. To solve the 4-site cluster impurity problem, we use a numerical renormalization group approach. However, numerical limitations force us to restrict the analysis to spin-polarized baths. According to the spectral data, the system is similar to the SU(2) invariant case at half-filling in a Mott insulating state and posseses a momentum-selective energy gap at finite doping. The topology of the Fermi surface shows a Lifshitz transition when increasing the hole concentration. Here, the curvature of the Fermi surface changes from electron- to hole-like. For comparison we apply the dynamical mean-field theory also to the quantum dimer model and observe that the electron spectral functions at finite doping are qualitatively similar to that of the two-dimensional Fermi-Hubbard model. The second half of the work is about Tomonaga-Luttinger liquid theory, which is used to describe the low-energy effective degrees of freedom of one-dimensional systems. Here, we first discuss a conceptional extension of the operator-based bosonization theory for one-dimensional systems. This extension is especially suited for inhomogeneous one-dimensional systems. First, we investigate a one-dimensional system with a local interation potential and compute an exact solution of the single particle propagator at T = 0. The critical exponent of the single particle propagator has an unconventional form as a function of the microscopic Tomonaga-Luttinger parameters, which is not covered by the original Luttinger paradigm postulated by F. Duncan M. Haldane. In a second project on one-dimensional systems, we study the impact of scattering processes among bosonic low-energy excitations on the thermalization process. Such scattering processes are irrelevant on large length scales, however strongly affect the dynamics. In our analytic analysis we focus on a experimental setup, where a one-dimensional Bose gas is instantaneously splitted in two identical, however strongly correlated, halves of one-dimensional electronic systems. In the following, the corresponding non-equilibrium state runs through multiple regimes in time, such as a metastable prethermalization regime. However, above a certain threshold in time such scattering processes cause an effective thermalization of the system. In order to demonstrate this, we compute the kinetic equation in the Keldysh field integral formalism from a diagrammatic expansion based on a self-consistent Born approximation.
The anomalous strange metal phase found in high-T c cuprates does not follow the conventional condensed-matter principles enshrined in the Fermi liquid and presents a great challenge for theory.Highly precise experimental determination of the electronic self-energy can provide a test bed for theoretical models of strange metals, and angle-resolved photoemission can provide this as a function of frequency, momentum, temperature and doping.Here we show that constant energy cuts through the nodal spectral function in (Pb,Bi) 2 Sr 2-x La x CuO 6+δ have a non-Lorentzian lineshape, consistent with a selfenergy that is k dependent.This provides a new test for aspiring theories.Here we show that the experimental data are captured remarkably well by a power law with a k-dependent scaling exponent smoothly evolving with doping, a description that emerges naturally from anti-de Sitter/conformal-field-theory based semi-holography.This puts a spotlight on holographic methods for the quantitative modelling of strongly interacting quantum materials like the cuprate strange metals.The rich temperature versus doping diagram of the cuprate high-T c superconductors presents a cornucopia of non-conformity 1 .The superconductivity does not follow BCS theory anywhere in the phase diagram 2,3 , and in their normal state these unusual metals display qualitatively different experimental behaviour compared to the Fermi liquid, with the linear-in-T resistivity and quadratic-in-T Hall angle being among the most strange.One intriguing possible explanation of strange metal phenomenology is that it is controlled by a strongly interacting quantum critical phase.If so, the question follows whether their properties can be