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arXiv:1210.0921 · Physical Review B

Low-energy behavior of spin-liquid electron spectral functions

Evelyn Tang, Matthew P. A. Fisher, Patrick A. Lee

Published Jan 22, 2013• 17 citations
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Abstract

We calculate the electron spectral function for a spin liquid with a spinon Fermi surface and a Dirac spin liquid. Calculations are based upon the slave-rotor mean-field theory. We consider the effect of gauge fluctuations using a simple model and find the behavior is not strongly modified. The results, distinct from conventional Mott insulator or band theory predictions, suggest that measuring the spectral function, e.g., via ARPES could help in the experimental verification and characterization of spin liquids.

DOI
10.1103/physrevb.87.045119

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We calculate the electron spectral function for a spin liquid with a spinon Fermi surface and a Dirac spin liquid. Calculations are based upon the slave-rotor mean-field theory. We consider the effect of gauge fluctuations using a simple model and find the behavior is not strongly modified. The results, distinct from conventional Mott insulator or band theory predictions, suggest that measuring the spectral function, e.g., via ARPES could help in the experimental verification and characterization of spin liquids.
We present a theoretical approach to describing the Mott transition of electrons on a two-dimensional lattice that begins with the low-energy effective theory of the Fermi liquid. The approach to the Mott transition must be characterized by the suppression of density and current fluctuations that correspond to specific shape deformations of the Fermi surface. We explore the nature of the Mott insulator and the corresponding Mott transition when these shape fluctuations of the Fermi surface are suppressed without making any a priori assumptions about other Fermi surface shape fluctuations. Building on insights from the theory of the Mott transition of bosons, we implement this suppression by identifying and condensing vortex degrees of freedom in the phase of the low-energy electron operator. We show that the resulting Mott insulator is a quantum spin liquid with a spinon Fermi surface coupled to a U(1)U(1)U(1) gauge field, which is usually described within a slave particle formulation. Our approach thus provides a coarse-grained treatment of the Mott transition and the proximate spin liquid that is nevertheless equivalent to the standard slave particle construction. This alternate point of view provides further insight into the novel physics of the Mott transition and the spin liquid state that is potentially useful. We describe a generalization that suppresses spin antisymmetric fluctuations of the Fermi surface that leads to a spin-gapped charge metal previously also discussed in terms of slave particle constructions.
Electronic Density of States of a U(1)U\left(1\right)U(1) Quantum Spin Liquid with Spinon Fermi Surface. I. Orbital Magnetic Field Effects
Quantum spin liquid (QSL) with spinon Fermi surface is an exotic insulator that hosts neutral Fermi surfaces inside the gap. In an external magnetic field, it has been pointed out that the neutral Fermi surfaces are Landau quantized to form Landau levels (LLs) due to the induced emergent gauge magnetic field. In this work, we calculate the electronic density of states (DOS) of the QSL in an orbital magnetic field. We find that the LLs from the neutral Fermi surfaces give rise to a set of steps emerging at the upper and lower Hubbard band edges. Each of the Hubbard band edge steps further develop into a band edge resonance peak when a weak gauge binding from the gauge field fluctuations is taken into account. Importantly, each Hubbard band edge step and its resulting resonance peak in the weak gauge binding are found to have a correspondence LL from the neutral Fermi surfaces, so the Hubbard band edge steps and the band edge resonance peaks are the unique features that characterize the Landau quantization of the in-gap neutral Fermi surfaces. We further consider the strong gauge binding regime where the band edge resonance peaks move into the Mott gap and develop into true in-gap bound states. In the strong gauge binding regime, we solve the bound state LL spectrum. For the bound state with a Mexican hat like band dispersion, we find that the envelop energy to have a state excited from the bound state LL decreases quadratically with the magnetic field. The quadratic decrease behavior of the envelop energy is consistent with the intuition that applying magnetic field localizes the states and energetically promotes the in-gap bound states formation. Finally, we connect our results to the electronic DOS spectra measured in the layered 1T-TaS2_22​. We point out that a QSL with a quasi-bound state in the upper Hubbard band can give the DOS spectra similar to the one measured in the experiment.
We combine the pseudofermion functional renormalization group (PFFRG) method with a self-consistent Fock-like mean-field scheme to calculate low-energy effective theories for emergent spinon excitations in spin-1/2 quantum spin liquids. Using effective spin interactions from PFFRG as an input for the Fock equation and allowing for the most general types of free spinon Ans\"atze as classified by the projective symmetry group (PSG) method, we are able to systematically determine spinon band structures for spin-liquid candidate systems beyond mean-field theory. We apply this approach to the antiferromagnetic ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on the square lattice and to the antiferromagnetic nearest-neighbor Heisenberg model on the kagome lattice. For the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model, we find that in the regime of maximal frustration a SU(2) $\ensuremath{\pi}$-flux state with Dirac spinons yields the largest mean-field amplitudes. For the kagome model, we identify a gapless Z2{\mathbb{Z}}_{2}Z2​ spin liquid with a small circular spinon Fermi surface and approximate Dirac cones at low but finite energies.
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.
Motivated by recent experimental observations of Kondo resonances in cobalt atoms on single layer $1T\text{\ensuremath{-}}{\mathrm{TaSe}}_{2}$, we theoretically investigate the effect of coupling a U(1) quantum spin liquid with a spinon Fermi surface to a lattice of Anderson impurities. Within the slave-rotor formalism, we find that above a critical coupling strength between the spin liquid and impurity lattice, the spinons hybridize to form heavy quasiparticles near the Fermi level, realizing a spinon Kondo lattice phase analogous to heavy fermion materials. Using the Bethe-Salpeter equation and accounting for emergent gauge fluctuations, we compute the spectral density and density of states, revealing the formation of spinon-chargon bound states in the spinon Kondo lattice phase. We characterize the thermodynamic and spectroscopic signatures of this phase, demonstrating specific heat and neutron scattering responses distinct from a pure quantum spin liquid. Our findings establish the spinon Kondo lattice as a framework to study the rich physics of spin liquids.
Quantum spin liquids (QSLs) host exotic fractionalized magnetic and gauge-field excitations whose microscopic origins and experimental verification remain frustratingly elusive. In the absence of static magnetic order, the spin excitation spectrum constitutes the crucial probe of QSL behavior, but its theoretical computation is a serious challenge. Here we employ state-of-the-art tensor-network methods to obtain the full dynamical spectral function of the J1J_1J1​-J2J_2J2​ kagome Heisenberg model and benchmark our results by tracking their evolution across the magnetically ordered and QSL phases. Reducing ∣J2∣/J1|J_2|/J_1∣J2​∣/J1​ causes increasingly strong spin-wave renormalization, flattening these modes then merging them into a continuum characteristic of deconfined spinons at all finite energies in the QSL. The low-energy continuum and the occurrence of gap closure at multiple high-symmetry points identify this gapless QSL as the U(1) Dirac spin liquid. These results establish a unified understanding of spin excitations in highly frustrated quantum magnets and provide clear spectral fingerprints for experimental detection in candidate kagome QSL materials.