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arXiv:1711.04479 · Physical review. B./Physical review. B

Variational Monte Carlo study of spin dynamics in underdoped cuprates

Zuodong Yu, Yuan Zhou, Chang-De Gong

Published Nov 22, 2017• 0 citations
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Abstract

The hour-glass-like dispersion of spin excitations is a common feature of underdoped cuprates. It was qualitatively explained by the random-phase approximation based on various ordered states with some phenomenological parameters; however, its origin remains elusive. Here, we present a numerical study of spin dynamics in the $t\text{\ensuremath{-}}J$ model using the variational Monte Carlo method. This parameter-free method satisfies the no double-occupancy constraint of the model and thus provides a better evaluation on the spin dynamics with respect to various mean-field trial states. We conclude that the lower branch of the hour-glass dispersion is a collective mode and the upper branch more than the other candidates is likely the consequence of the stripe state.

DOI
10.1103/physrevb.96.195144

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The hour-glass-like dispersion of spin excitations is a common feature of underdoped cuprates. It was qualitatively explained by the random-phase approximation based on various ordered states with some phenomenological parameters; however, its origin remains elusive. Here, we present a numerical study of spin dynamics in the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model using the variational Monte Carlo method. This parameter-free method satisfies the no double-occupancy constraint of the model and thus provides a better evaluation on the spin dynamics with respect to various mean-field trial states. We conclude that the lower branch of the hour-glass dispersion is a collective mode and the upper branch more than the other candidates is likely the consequence of the stripe state.
We carry out the variational Monte Carlo calculation to examine spatially inhomogeneous states in hole- and electron-doped cuprates. By using Gutzwiller approximation, we consider the excitations, arising from charge density, spin density, and pair field, of the mean-field ground state of the ttt-JJJ model. It leads to the stripe patterns we have found numerically in a generalized ttt-JJJ-type model including mass renormalization from the electron-phonon coupling. In the hole-doped side, a robust ddd-wave superconducting order results in the formation of the half-doped antiferromagnetic resonating-valence-bond (AF-RVB) stripes shown by the well-known Yamada plot. On the other hand, due to a long-range AF order in electron-doped materials, a stripe structure with the ``in-phase'' magnetic domain (IPMD) is obtained in the underdoped regime instead of the AF-RVB stripe. The IPMD stripe with the largest period permitted by lattice size is stabilized near the underdoped region and it excludes the Yamada plot from electron-doped cases. Based on finite lattice size to which we can reach, the existence of IPMD stripes may imply an electronic phase separation into an electron-rich and an insulating half-filled AF long-range ordered domains in electron-doped compounds.
We investigate the properties of the frustrated underdoped Hubbard model on the square lattice using two complementary approaches, i.e., the dynamical cluster extension of the dynamical mean-field theory and the variational Monte Carlo simulations of Gutzwiller-Jastrow wave functions with backflow corrections. We compare and discuss data for the energy and the double occupancies, as obtained from both approaches. At small dopings, we observe a rapid crossover from a weakly correlated metal at low interaction strength UUU to a non-Fermi-liquid correlated state with strong local spin correlations. Furthermore, we investigate the stability of the correlated state against phase separation. We observe phase separation only for large values of UUU or very large frustration. No phase separation is present for the parameter range relevant for the cuprates.
We carry out the variational Monte Carlo calculation to examine spatially inhomogeneous states in hole- and electron-doped cuprates. By using Gutzwiller approximation, we consider the excitations, arising from charge density, spin density and pair field, of the mean-field ground state of the t-J model. It leads to the stripe patterns we have found numerically in a generalized t-J-type model including mass renormalization from the electron-phonon coupling. In the hole-doped side, a robust d-wave superconducting order results in the formation of the half-doped antiferromagnetic resonating-valence-bond (AF-RVB) stripes shown by the well-known Yamada plot. On the other hand, due to a long-range AF order in electron-doped materials, a stripe structure with the "in-phase" magnetic domain (IPMD) is obtained in the underdoped regime instead of the AF-RVB stripe. The IPMD stripe with the largest period permitted by lattice size is stabilized near the underdoped region and it excludes the Yamada plot from electron-doped cases. Based on finite lattice size to which we can reach, the existence of IPMD stripes may imply an electronic phase separation into an electron-rich and an insulating half-filled AF long-range ordered domains in electron-doped compounds.
We present variational Monte Carlo (VMC) results for the Gutzwiller-projected coexisting state including both antiferromagnetic (AFM) order and superconducting (SC) order in the two-dimensional t-t'-t"-J model. By further considering off-site spin correlation between electrons, in contrast to earlier VMC results [Phys. Rev. Lett. 102, 027002 (2009)], we find the apparent competition between AFM order and SC order near the underdoped regime instead of coexistence. The local ferromagnetic correlation introduced by spin-spin Jastrow correlators seem to be responsible for the disappearance of the coexisting state. We also demonstrate that the quasiparticle spectral weight from upper (lower) AFM band are strongly diminished (enhanced) by the spin-spin correlation. This result obviously leads to the loss of antinodal electron pockets and the appearance of nodal hole pockets as passing from the AFM phase to the SC phase in hole-doped cuprates, which is in consistent with the observation by angle-resolved photoemission spectroscopy.
Two-particle (2-p) excitations such as spin and charge excitations play a key role in high- T c cuprate superconductors (HTSC). On the basis of a parameter-free theory, which extends the variational cluster approach (a recently developed embedded cluster method) to 2-p excitations, the magnetic excitations of HTSC are shown to be reproduced for a Hubbard model within the relevant strong-coupling regime. In particular, the resonance mode in the underdoped regime, its intensity and "hour-glass" dispersion are in good overall agreement with experiments.
© Kazan Federal University (KFU). We derive the dynamical spin susceptibility in the t-J-G model combining the random phase approximation (RPA) and projection operator method, which allows describing the mutual interplay between the local and the itinerant components of susceptibility. Near the antifer- romagnetic wave vector the calculated dispersion of the spin excitations reproduces well the so-called hour-glass dispersion, characteristic for several layered cuprates. It is formed as a result of competition between the original spin-gap in magnon-like excitations spectrum and the superconducting gap, which affects the itinerant component of the susceptibility. Further- more, the calculated collective spin excitations along (0, 0)-(0, π) are in agreement with the positions of the absorption peaks in the inelastic X-ray scattering spectra. They refer to the paramagnon-like modes, characteristic to the itinerant spin system, rather than magnon-like excitations that originate from short range order effect in the system of local spins at Cu sites.