Commensurate and incommensurate magnetic order in the doped two-dimensional Hubbard model: dynamical mean-field theory analysis

Abstract

We develop a dynamical mean-field theory approach for the spiral magnetic order, changing to a local coordinate frame with preferable spin alignment along the $z$-axis, which can be considered with the impurity solvers treating the spin diagonal local Green's function. We furthermore solve the Bethe-Salpeter equations for nonuniform dynamic magnetic susceptibilities in the local coordinate frame. We apply this approach to describe the evolution of magnetic order with doping in the $t-t^{\prime }$ Hubbard model with $t^{\prime }=0.15$, which is appropriate for the description of the doped La${}_2$CuO${}_4$ high-temperature superconductor. We find that with doping the antiferromagnetic order changes to the $(Q,\pi )$ incommensurate one, and then to the paramagnetic phase. The spectral weight at the Fermi level is suppressed near half filling and continuously increases with doping. The dispersion of holes in the antiferromagnetic phase shows qualitative agreement with the results of the $t$-$J$ model consideration. In the incommensurate phase we find two branches of hole dispersions, one of which crosses the Fermi level. The resulting Fermi surface forms hole pockets. We also consider the dispersion of the magnetic excitations, obtained from the non-local dynamic magnetic susceptibilities. The transverse spin excitations are gapless, fulfilling the Goldstone theorem; in contrast to the mean-field approach the obtained magnetic state is found to be stable. The longitudinal excitations are characterized by a small gap, showing the rigidity of the spin excitations. For realistic hopping and interaction parameters we reproduce the experimentally measured spin-wave dispersion of La${}_2$CuO${}_4$.

arXiv comment11 pages, 9 figures

References in corpus (41)

• Spin Liquid State in an Organic Mott Insulator with Triangular Lattice
• Spin waves and electronic interactions in La2CuO4
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Mott Transition from a Spin Liquid to a Fermi Liquid in the Spin-Frustrated Organic Conductor kappa-(ET)2Cu2(CN)3
• Observation of New Incommensurate Magnetic Correlations at the Lower Critical Concentration for Superconductivity (x=0.05) in La(2-x)Sr(x)CuO4
• Weak Pseudogap Behavior in the Underdoped Cuprate Superconductors
• Microscopic theory of weak pseudogap behavior in the underdoped cuprate superconductors I: General theory and quasiparticle properties
• Fluctuation diagnostics of the electron self-energy: Origin of the pseudogap physics
• Incommensurate magnetic order and phase separation in the two-dimensional Hubbard model with nearest and next-nearest neighbor hopping
• On the self-consistent spin-wave theory of layered Heisenberg magnets
• Topological order in the pseudogap metal
• Pseudogap and Fermi surface topology in the two-dimensional Hubbard model
• Static vs. dynamical mean field theory of Mott antiferromagnets
• Magnetism and Phase Separation in the Ground State of the Hubbard Model
• Quantum Spin Liquids Unveil the Genuine Mott State
• Magnetic Phases of the 2D Hubbard Model at Low Doping
• Spin Excitations in La2CuO4: Consistent Description by Inclusion of Ring-Exchange
• $i$QIST: An open source continuous-time quantum Monte Carlo impurity solver toolkit
• Distinct doping dependences of the pseudogap and superconducting gap La${}_{2-x}$Sr${}_x$CuO${}_4$ cuprate superconductors
• Spiral magnetism in the single-band Hubbard model: the Hartree-Fock and slave-boson approaches
• Self-consistent Dual Boson approach to single-particle and collective excitations in correlated systems
• New scenario for high-T_c cuprates: electronic topological transition as a motor for anomalies in the underdoped regime
• Models of the Pseudogap State of Two-Dimensional Systems
• Dynamical Mean-Field Theory for Doped Antiferromagnets
• Explaining the pseudogap through damping and antidamping on the Fermi surface by imaginary spin scattering
• $i$QIST v0.7: An open source continuous-time quantum Monte Carlo impurity solver toolkit
• Dynamical functional renormalization group computation of order parameters and critical temperatures in the two-dimensional Hubbard model
• SU(2) gauge theory of the pseudogap phase in the two-dimensional Hubbard model
• The dynamical vertex approximation for many-electron systems with spontaneously broken SU(2)-symmetry
• Normal state pseudogap and (π,0) feature in the underdoped high-T_c cuprates. A microscopical theory
• Quantum spin fluctuations and evolution of electronic structure in cuprates
• High-frequency asymptotic behavior of self-energies in quantum impurity models
• Incommensurate spiral magnetic order on anisotropic triangular lattice: Dynamical mean field study in a spin-rotating frame
• Improved treatment of fermion-boson vertices and Bethe-Salpeter equations in non-local extensions of dynamical mean field theory
• Coherent quasi-particles-to-incoherent hole-carriers crossover in underdoped cuprates
• Spiral Magnets as Gapless Mott Insulators
• Charge disproportionation in the spin-liquid candidate $\kappa$-(ET)${}_2$Cu${}_2$(CN)${}_3$ at 6 K revealed by ${}^{63}$Cu NQR measurements
• Two Dimensional Incommensurate and Three Dimensional Commensurate Magnetic Order and Fluctuations in $L{a}_{2-x}B{a}_{x}Cu{O}_4$
• Correlation Effects and Non-Collinear Magnetism in the Doped Hubbard Model
• Generalized dynamical mean-field theory of two-subalttice systems with non-local interactions and its application to study charge and spin correlations in graphene
• Charge and spin correlations in insulating and incoherent metal states of twisted bilayer graphene

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