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arXiv:2312.05893 · Physical review. B./Physical review. B

Phase diagram of the square-lattice t − J − V model for electron-doped cuprates

Qianqian Chen, Lei Qiao, Fu‐Chun Zhang, Zheng Zhu

Published Jul 17, 2024• 7 citations
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Abstract

Motivated by significant discrepancies between experimental observations of electron-doped cuprates and numerical results of the Hubbard and $t\text{\ensuremath{-}}J$ models, we investigate the role of intersite interactions $V$ by studying the $t\text{\ensuremath{-}}J\text{\ensuremath{-}}V$ model on square lattices. Based on large-scale density matrix renormalization group simulations, we identify the ground-state phase diagram across varying intersite interactions $V$ and doping concentration $\ensuremath{\delta}$. We find that the phase diagram with finite intersite interactions $2\ensuremath{\lesssim}V/J\ensuremath{\lesssim}3$ offers a more accurate description of electron-doped cuprates than the conventional Hubbard and $t\text{\ensuremath{-}}J$ models. Moreover, we reveal the role of intersite interactions $V$ at varying doping levels: at light doping, intersite interactions favor N\'eel antiferromagnetic order, and suppress both superconductivity and charge density wave; around optimal doping, these interactions support a pseudogap-like phase while suppressing superconductivity, and we further perform the slave-boson mean-field analysis to understand the numerical results microscopically; at higher doping, the effects of intersite interactions become insignificant, with our numerical predictions suggesting the emergence of an incommensurate spin density wave phase. Our specific focus around optimal doping with various intersite interactions identifies successive phases including phase separation, uniform $d$-wave SC, and a pseudogap-like phase, and reveals a relative insensitivity of the charge density wave to superconductivity. Our study suggests the $t\text{\ensuremath{-}}J\text{\ensuremath{-}}V$ model as the minimal model to capture the essential physics of electron-doped cuprates.

DOI
10.1103/physrevb.110.045134

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Motivated by significant discrepancies between experimental observations of electron-doped cuprates and numerical results of the Hubbard and t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J models, we investigate the role of intersite interactions VVV by studying the t\ensuremath-J\ensuremath-Vt\text{\ensuremath{-}}J\text{\ensuremath{-}}Vt\ensuremath-J\ensuremath-V model on square lattices. Based on large-scale density matrix renormalization group simulations, we identify the ground-state phase diagram across varying intersite interactions VVV and doping concentration \ensuremathδ\ensuremath{\delta}\ensuremathδ. We find that the phase diagram with finite intersite interactions 2\ensuremath≲V/J\ensuremath≲32\ensuremath{\lesssim}V/J\ensuremath{\lesssim}32\ensuremath≲V/J\ensuremath≲3 offers a more accurate description of electron-doped cuprates than the conventional Hubbard and t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J models. Moreover, we reveal the role of intersite interactions VVV at varying doping levels: at light doping, intersite interactions favor N'eel antiferromagnetic order, and suppress both superconductivity and charge density wave; around optimal doping, these interactions support a pseudogap-like phase while suppressing superconductivity, and we further perform the slave-boson mean-field analysis to understand the numerical results microscopically; at higher doping, the effects of intersite interactions become insignificant, with our numerical predictions suggesting the emergence of an incommensurate spin density wave phase. Our specific focus around optimal doping with various intersite interactions identifies successive phases including phase separation, uniform ddd-wave SC, and a pseudogap-like phase, and reveals a relative insensitivity of the charge density wave to superconductivity. Our study suggests the t\ensuremath-J\ensuremath-Vt\text{\ensuremath{-}}J\text{\ensuremath{-}}Vt\ensuremath-J\ensuremath-V model as the minimal model to capture the essential physics of electron-doped cuprates.
Motivated by significant discrepancies between experimental observations of electron-doped cuprates and numerical results of the Hubbard model, we investigate the role of nearest-neighbor (NN) electron interactions VVV by studying the t−U−Vt-U-Vt−U−V model on square lattices. Upon doping δδδ= 0.153, by using constrained path quantum Monte Carlo (CPQMC) method, we find that NN electron attraction VVV can notably drive an exotic ppp-wave spin-triplet pairing, while the NN electron repulsion VVV will suppress the dx2−y2d_{x^2-y^2}dx2−y2​-wave (ddd-wave) pairing and triggers the dxyd_{xy}dxy​-wave pairing. Especially in the intermediate coupling regime, as NN repulsion increases, the intensity of dxyd_{xy}dxy​-wave pairing also increases, further suppressing the presence of ddd-wave pairing, which may help explain the notable suppression of ddd-wave pairing in electron-doped cuprate superconductors. Besides the pairing phase, we also find that the NN electron attraction VVV has no significant effect on spin density wave (SDW) and charge density wave (CDW), but repulsion VVV significantly enhanced CDW and suppressed SDW. Our study suggests the t−U−Vt-U-Vt−U−V Hubbard model can serve as the minimal model to capture the essential physics of the electron-doped cuprates.
The Hubbard and closely related t-J models are exciting platforms for unconventional superconductivity (SC). Through state-of-the-art density matrix renormalization group calculations using the grand canonical ensemble, we address open issues regarding the ground-state phase diagram of the extended t-J model on a square lattice in the parameter regime relevant to cuprate superconductors. On large 8-leg cylinders, we demonstrate that the pure t-J model with only nearest-neighbor hoppings and superexchange interactions, for a wide range of doping ( δ = 0.1 to 0.2 ), hosts robust d-wave superconductivity possibly coexisting with weak unidirectional pair density wave. Furthermore, a small next nearest neighbor hopping t 2 suppresses pair and charge density waves, resulting in a uniform d-wave SC phase in both electron- and hole-doped cuprate model systems. Our work validates the t-J model as a proper minimum model for the emergence of superconductivity in cuprate superconductors.
The square-lattice Hubbard and closely related t-J models are considered as basic paradigms for understanding strong correlation effects and unconventional superconductivity (SC). Recent large-scale density matrix renormalization group simulations on the extended t-J model have identified d-wave SC on the electron-doped side (with the next-nearest-neighbor hopping t_{2}>0) but a dominant charge density wave (CDW) order on the hole-doped side (t_{2}<0), which is inconsistent with the SC of hole-doped cuprate compounds. We re-examine the ground-state phase diagram of the extended t-J model by employing the state-of-the-art density matrix renormalization group calculations with much enhanced bond dimensions, allowing more accurate determination of the ground state. On six-leg cylinders, while different CDW phases are identified on the hole-doped side for the doping range δ=1/16-1/8, a SC phase emerges at a lower doping regime, with algebraically decaying pairing correlations and d-wave symmetry. On the wider eight-leg systems, the d-wave SC also emerges on the hole-doped side at the optimal 1/8 doping, demonstrating the winning of SC over CDW by increasing the system width. Our results not only suggest a new path to SC in general t-J model through weakening the competing charge orders, but also provide a unified understanding on the SC of both hole- and electron-doped cuprate superconductors.
Having cuprate superconductors in mind, we study the effect of intersite repulsion on antiferromagnetism (AF) and superconductivity (SC) in an extended Hubbard model on a square lattice with a diagonal transfer t′, using a variational Monte Carlo method. In the trial wave function, essential factors for Mott physics and band renormalization are included. It is found by introducing small intersite repulsion that the SC dome shrinks but AF is almost unchanged for U/t=10 (likely for cuprates). Meanwhile, instable range of doping rate (δ) toward phase separation becomes narrower. This instable range of δ almost coincides with the range of a finite AF gap, especially in good coincidence for t′/t=0.
In the first part of the paper, we study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the t-J-U-V model of strongly correlated electrons by using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term V in stabilizing the CDW phase. In particular, we show that the charge ordering appears only above a critical value of V in a limited hole-doping range δ. The effect of the V term on SC and AF phases is that a strong interaction suppresses SC, whereas the AF order is not significantly influenced by its presence. In the second part, separate calculations for the case of a pure SC phase have been carried out within an extended approach (the diagrammatic expansion for the Gutzwiller wave function, DE-GWF) in order to analyze the influence of the intersite Coulomb repulsion on the SC phase with the higher-order corrections included beyond the SGA method. The upper concentration for the SC disappearance decreases with increasing V, bringing the results closer to experiment. In appendices A and B we discuss the ambiguity connected with the choice of the Gutzwiller renormalization factors within the renormalized mean filed theory when either AF or CDW orders are considered. At the end, we overview briefly the possible extensions of the current models to put descriptions of the SC, AF, and CDW states on equal footing.
Recently, a flurry of works have found strong competition between charge density wave (CDW) and superconductivity (SC) in the doped Hubbard and $t\text{\ensuremath{-}}J$ models on the square lattice. Interestingly, some recent results suggest that the electron-phonon coupling may suppress CDW order and enhance SC. In this work, we consider the square-lattice Hubbard model with the Holstein or Su-Schrieffer-Heeger electron-phonon coupling at the large-UUU and antiadiabatic (infinite phonon frequency) limits, which gives an effective $t\text{\ensuremath{-}}J$ model with either a density attractive interaction VVV or a JP{J}_{P}JP​ term that contributes a larger spin exchange and a density repulsive interaction. To explore how these effective couplings may tune the competition between CDW and SC, we implement the density matrix renormalization group simulations on the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ model with VVV or JP{J}_{P}JP​ coupling. We focus on the six-leg cylinder system with the next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$, which hosts partially filled stripe and ddd-wave SC in phase diagram. By tuning ${t}^{\ensuremath{'}}/t>0$ and VVV or JP{J}_{P}JP​, we establish two quantum phase diagrams at 112\frac{1}{12}121​ doping ratio. In the SC phases, the increased VVV or JP{J}_{P}JP​ coupling can enhance the quasi-long-range SC order, consistent with some previous findings. Nonetheless, no SC emerges when the partially filled stripe phase disappears with increased VVV or JP{J}_{P}JP​. Instead, the system has a transition to either a phase-separation-like regime or a filled stripe phase. On the other hand, with increased ${t}^{\ensuremath{'}}/t$, not only the partially filled stripe but the phase separation and filled stripe can also be tuned to SC phase. Our results suggest that although VVV and JP{J}_{P}JP​ couplings may strengthen hole binding, the hole dynamics controlled by ${t}^{\ensuremath{'}}/t$ appears to play a more crucial role for obtaining a SC in the $t\text{\ensuremath{-}}J$ model.