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Acta Physica Polonica A

Electron Spectral Functions in the Presence of the Antiferromagnetic Order in the Two-Dimensional Hubbard Model

T. A. Zaleski, T. K. Kopeć

Published Aug 1, 2010• 0 citations
Publisher

Abstract

We use a recently proposed quantum SU(2) × U(1) rotor approach for the Hubbard model to calculate electronic spectral functions in a presence of an antiferromagnetic state for any value of the Coulomb interaction.We isolate the collective variables for charge and spin in the form of the space-time fluctuating U(1) phase field and SU(2) rotating spin quantization axis, respectively.As a result, the fermion Green function in the space-time domain becomes a product of a CP 1 propagator resulting from the SU(2) gauge fields, U(1) phase propagator and the pseudo-fermion correlation function.In turn, the spectral lines are obtained by performing the convolution of spin, charge and pseudo-fermion Green's functions.We observe an emergence of a sharp peak in the electron spectral functions within the antiferromagnetic phase, whose spectral weight is equal to the antiferromagnetic order parameter.

DOI
10.12693/aphyspola.118.267

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We use a recently proposed quantum SU(2) × U(1) rotor approach for the Hubbard model to calculate electronic spectral functions in a presence of an antiferromagnetic state for any value of the Coulomb interaction.We isolate the collective variables for charge and spin in the form of the space-time fluctuating U(1) phase field and SU(2) rotating spin quantization axis, respectively.As a result, the fermion Green function in the space-time domain becomes a product of a CP 1 propagator resulting from the SU(2) gauge fields, U(1) phase propagator and the pseudo-fermion correlation function.In turn, the spectral lines are obtained by performing the convolution of spin, charge and pseudo-fermion Green's functions.We observe an emergence of a sharp peak in the electron spectral functions within the antiferromagnetic phase, whose spectral weight is equal to the antiferromagnetic order parameter.
Abstract We study the electron spectral function of the antiferromagnetically ordered phase of the three dimensional Hubbard model, using recently formulated low‐energy theory based on the 2D half‐filled Hubbard model which describes both collective spin and charge fluctuations for arbitrary value of the Coulomb repulsion U. The model then is solved by a saddle‐point approximation within the CP1 representation for the Neel field. The single‐particle properties are obtained by writing the fermion field in terms of a U(1) phase, Schwinger boson SU(2) fields and a pseudofermion variables. We demonstrate that the appearance of a sharp peak in the electron spectral function in the antiferromagnetic state points to the emergence of the bosonic mode, which is associated with spin ordering.
We compute the electronic Green's function of the topologically ordered Higgs phase of a SU(2) gauge theory of fluctuating antiferromagnetism on the square lattice. The results are compared with cluster extensions of dynamical mean field theory, and quantum Monte Carlo calculations, on the pseudogap phase of the strongly interacting hole-doped Hubbard model. Good agreement is found in the momentum, frequency, hopping, and doping dependencies of the spectral function and electronic self-energy. We show that lines of (approximate) zeros of the zero-frequency electronic Green's function are signs of the underlying topological order of the gauge theory and describe how these lines of zeros appear in our theory of the Hubbard model. We also derive a modified, nonperturbative version of the Luttinger theorem that holds in the Higgs phase.
The antiferromagnetic phase of two-dimensional (2D) and three-dimensional (3D) Hubbard model with nearest neighbor hopping is studied on a bipartite cubic lattice by means of the quantum $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ rotor approach that yields a fully self-consistent treatment of the antiferromagnetic state that respects the symmetry properties of the model and satisfy the Mermin-Wagner theorem. The collective variables for charge and spin are isolated in the form of the space-time fluctuating U(1) phase field and rotating spin-quantization axis governed by the SU(2) symmetry, respectively. As a result interacting electrons appear as composite objects consisting of bare fermions with attached U(1) and SU(2) gauge fields. An effective action consisting of a spin-charge rotor and a fermionic field is derived as a function of the Coulomb repulsion UUU and hopping parameter ttt. At zero temperature, our theory describes the evolution from a Slater (U⪡t)(U⪡t)(U⪡t) to a Mott-Heisenberg (U⪢t)(U⪢t)(U⪢t) antiferromagnet. The results for zero-temperature sublatice magnetization (2D) and finite temperature (3D) phase diagram of the antiferromagnetic Hubbard model as a function of the crossover parameter U∕tU∕tU∕t are presented and the role of the spin Berry phase in the interaction driven crossover is analyzed.
By introducing multiple-site correlation functions, we propose a hierarchical Green’s function approach, and apply it to study the characteristic properties of a two-dimensional (2D) square lattice Hubbard model by solving the equation of motions of a one-particle Green’s function and related multiple-site correlation functions. Under a cut-off approximation and taking the Fourier representation of multiple-site correlation functions, we obtain an analytical expression of one-particle Green’s function with static correlation functions. Then we calculate the spectral density function of electrons, and obtain that besides two main peaks corresponding to the lower and upper Hubbard bands in the spectral density function, there emerge some novel states between these two main peaks, and the total spectral weight of these emerged states is proportional to the hole doping concentration [Formula: see text]. Meanwhile, there also emerge some collective modes related to possible charge/spin density wave and/or electronic pairing density wave ordering states. This calculation is completely consistent with the spectroscopy observations of the cuprate superconductors in normal states. On the other hand, the appearance of the static correlation functions in the one-particle Green’s function can be used to describe the intertwined orders observed in the normal state of the cuprate superconductors.
We present an SU(2) gauge theory of fluctuating stripe order in the two-dimensional Hubbard model. The theory is based on a fractionalization of the electron operators in fermionic chargons with a pseudospin degree of freedom, and charge-neutral spinons capturing fluctuations of the spin orientation. The chargons are treated in a renormalized mean-field theory. We focus on regions of the phase diagram where they undergo stripe order. The spinons are described by a nonlinear sigma model with pseudospin stiffnesses determined by the chargons. They prevent breaking of the physical SU(2) spin symmetry at any finite temperature, resulting in a charge-ordered pseudogap phase with a reconstructed Fermi surface and a spin gap. The spectral function for single-particle excitations exhibits a collection of Fermi arcs and other structures. The arcs appear in various regions of the Brillouin zone, but never exclusively near the Brillouin zone diagonals. For a suitable choice of the bare dispersion relation, the form of the low energy spectral function resembles experimental observations from angular resolved photoemission on cuprates in which stripe fluctuations play an important role.
An analytic approach is presented of electronic one-particle spectra of the one-band Hubbard model at half filling in the antiferromagnetic phase. Starting from the strong-coupling regime U\ensuremath{\gg}:t, a projection technique is used to set up self-consistent coupled equations for the electron Green function, which are valid down to values U\ensuremath{\approx}t. The self-consistent equation for the hole propagator is a direct generalization of the one found from the t-J model. This gives further support to the ``string'' picture, where propagation of holes creates strings of overturned spins with which the holes interact. In the present work hopping of holes (or electrons) with up spin on the down sublattice is also taken into acount, as well as transitions between the lower and upper Hubbard bands. These are shown to change significantly the incoherent part of the t-J model spectra, by smearing out the shake-off peaks, reminiscent of higher bound string states due to multispin scattering. Coherent (quasiparticle) peaks exist at the band edges, on both sides of the insulating gap. We show that with decreasing U the quasiparticle concept loses its meaning for wave vectors at the center of the magnetic Brillouin zone (MBZ). For large values of U the dispersion of the quasiparticle is found to scale with its band width, which is of order J. Extrema are always found at k=(\ensuremath{\pi}/2,\ensuremath{\pi}/2). The weight of the quasiparticle at this k value decreases logarithmically with increasing U. In the strong-coupling limit the spectrum tends to be symmetric, i.e., to become an even function of the frequency around the chemical potential, for any wave vector. For small values of U the dispersion at the edge of the MBZ flattens away, as expected when approaching the noninteracting limit. The spectral function in this regime, for wave vectors away from the edge of the MBZ, is concentrated mainly on one side of the chemical potential.