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Journal of Physics Conference Series

Band-renormalization effects on antiferromagnetism and d-wave superconductivity in two-dimensional t-J model

Ryo Sato, Hisatoshi Yokoyama

Published Jul 1, 2017• 1 citation
Publisher

Abstract

Recent studies reported that antiferromagnetic (AF) states become stable and d -wave superconducting ( d -SC) states are almost excluded in underdoped strongly correlated Hubbard models in two dimensions. In a viewpoint of many-body variational theory, this result stems from a band-renormalization effect (BRE) in AF states. Here, using a variational Monte Carlo method, BRE on AF and d -SC states are studied in the t-t'-J model, in which d -SC (AF) states have been considered to be more stable (fragile) than in the Hubbard model. Many features are qualitatively similar to the Hubbard model including effectiveness of BRE and the existence of a Lifshitz transition in AF states. However, a d -SC state becomes more stable than an AF state widely in the underdoped regime for J/t =0.3, in contrast to the Hubbard model.

DOI
10.1088/1742-6596/871/1/012014

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Recent studies reported that antiferromagnetic (AF) states become stable and d -wave superconducting ( d -SC) states are almost excluded in underdoped strongly correlated Hubbard models in two dimensions. In a viewpoint of many-body variational theory, this result stems from a band-renormalization effect (BRE) in AF states. Here, using a variational Monte Carlo method, BRE on AF and d -SC states are studied in the t-t'-J model, in which d -SC (AF) states have been considered to be more stable (fragile) than in the Hubbard model. Many features are qualitatively similar to the Hubbard model including effectiveness of BRE and the existence of a Lifshitz transition in AF states. However, a d -SC state becomes more stable than an AF state widely in the underdoped regime for J/t =0.3, in contrast to the Hubbard model.
The coexistence or exclusivity of dx2−y2d_{x^{2} - y^{2}}dx2−y2​-wave superconducting (d-SC) and antiferromagnetic (AF) orders and instability toward phase separation (PS) are reconsidered for the square-lattice t–J model with the diagonal transfer (t′) term near half filling. To reliably treat the strong correlation including the local constraint of no double occupancy, we use a variational Monte Carlo method, in which the band-renormalization effect (BRE) is also incorporated. The results are compared with those recently obtained for the corresponding Hubbard model [J. Phys. Soc. Jpn. 85, 074701 (2016)]. It is found that BRE has a very strong effect on the AF order and greatly modifies the ground-state phase diagram in the t′–δ space (δ: doping rate) proposed in previous studies, especially for large |t′/t|. In a wide range of t′/t (|t′/t| ≤ 0.5) and for any underdoped δ (≲ \lesssim ≲ 0.15), the AF order arises for J/t = 0.3, similarly to in the Hubbard model. In contrast with the Hubbard model, however, the d-SC order also arises down to small δ in a wide range of t′/t (≳ \gtrsim ≳ −0.2) and coexists with the AF order even for t′/t < 0 (type-II AF regime). Furthermore, there is no instability toward PS for any t′/t and δ for J/t = 0.3.
Most studies of square-lattice Hubbard models in view of cuprate superconductors hitherto have neglected a band-renormalization effect (BRE) owing to strong electron correlation, especially, for an antiferromagnetic (AF) order. In this study, we introduce BRE into a d -wave superconducting and an AF states independently in the framework of many-body variation theory. It is found that, in sharp contrast to usual understandings, energy of an AF state is sizably reduced by BRE, and the AF area in the ground-state phase diagram is greatly expanded to cover the whole underdoped regime. The AF state with BRE exhibits distinct features according as the value of diagonal hopping ratio t ′/ t is greater or less than t ′/ t ∼ – 0.05.
Band renormalization effects (BRE) are comprehensively studied for a mixed state of dx2-y2-wave superconducting (d-SC) and antiferromagnetic (AF) orders, in addition to simple d-SC, AF, and normal (paramagnetic) states, by applying a variational Monte Carlo method to a two-dimensional Hubbard (t-t'-U) model. In a weakly correlated regime (U=tt'L [t't'L, because the existence of Fermi surfaces near (pi,0) is a requisite for the electron scattering of q=(pi,pi). Actually, the coexistent state appears mainly for t'L/t
Having cuprate superconductors in mind, we study a band-renormalization effect on a coexisting state of antiferromagnetism (AF) and superconductivity (SC) in a t-J model on a square lattice with a diagonal transfer t ′ and three-site hopping terms, using a variational Monte Carlo method. It is found that this t-J model with t ′/ t = –0.3 exhibits coexistence of AF and SC orders in lightly doped regime and robust SC for a wide range of doping rate δ . This result contrasts with the previous results of a large- U/t Hubbard model, in which the two orders are mutually exclusive and a coexisting state does not appear; the SC state appears only in heavily doped regime (δ≳ 0.2), after the pure AF state vanishes at δ ∼ 0.2.
To study the relationship between antiferromagnetism (AF) and superconductivity (SC) in cuprate superconductors, we have performed a variational Monte Carlo calculation on the two-dimensional Hubbard model with a diagonal transfer t' [1,2]. The following improvements are introduced into the variational function: (1) Coexistence of AF and d-wave singlet gaps that allows a continuous description of their interplay, (2) band renormalization effect owing to the electron correlation up to the fourth-neighbor hoppings, and (3) refined doublon-holon correlation factors. It is found that the AF and SC orders become coexistent or competitive according to the values of model parameters, U/t, t'/t, and δ (doping rate), and the effective band is strongly renormalized for large U/t and low doping rates, so as to recover the nesting condition favorable to AF.
We have performed a variational Monte Carlo simulation on a two-dimensional Hubbard model with first- and second-neighbor hopping terms in order to study the coexistence state of a static stripe state and a modulated d-wave superconductivity in the underdoped cuprates. In addition to a Gutzwiller, a Jastrow and a doublon-holon correlation effects, the band-renormalization effect was considered in the trial wave function. The condensation energies of an 8-period stripe state was computed as a function of a Coulomb energy under the hole-density x=1/8. Our results reveal that the renormalization of higher hopping parameters due to the strong correlation effect enhances the one-dimensional hole motion on a quarter-filled band in the stripe state, and brings quasi-Fermi surface close to the magnetic zone boundary in the coexistence state.