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Register a new userRobust d-wave superconductivity in the square-lattice $t$-$J$ model
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Unravelling competing orders emergent in doped Mott insulators and their interplay with unconventional superconductivity is one of the major challenges in condensed matter physics. To explore possible superconductivity state in the doped Mott insulator, we study a square-lattice $t$-$J$ model with both the nearest and next-nearest-neighbor electron hoppings and spin Heisenberg interactions. By using the state-of-the-art density matrix renormalization group simulations with imposing charge $U(1)$ and spin $SU(2)$ symmetries on the large-scale six-leg cylinders, we establish a quantum phase diagram including three phases: a stripe charge density wave phase, a superconducting phase without static charge order, and a superconducting phase coexistent with a weak charge stripe order. Crucially, we demonstrate that the superconducting phase has a power-law pairing correlation decaying much slower than the charge density and spin correlations, which is a quasi-1D descendant of the uniform d-wave superconductor in two dimensions. These findings reveal that enhanced charge and spin fluctuations with optimal doping is able to produce robust d-wave superconductivity in doped Mott insulators, providing a foundation for connecting theories of superconductivity to models of strongly correlated systems.
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It is expected that at weak to intermediate coupling, d-wave superconductivity can be induced by antiferromagnetic fluctuations. However, one needs to clarify the role of Fermi surface topology, density of states, pseudogap, and wave vector of the magnetic fluctuations on the nature and strength of the induced d-wave state. To this end, we study the generalized phase diagram of the two-dimensional half-filled Hubbard model as a function of interaction strength $U/t$, frustration induced by second-order hopping $t^{prime}/t$, and temperature $T/t$. In experiment, $U/t$ and $t^{prime}/t$ can be controlled by pressure. We use the two-particle self-consistent approach (TPSC), valid from weak to intermediate coupling. We first calculate as a function of $t^{prime}/t$ and $U/t$ the temperature and wave vector at which the spin response function begins to grow exponentially.D-wave superconductivity in a half-filled band can be induced by such magnetic fluctuations at weak to intermediate coupling, but only if they are near commensurate wave vectors and not too close to perfect nesting conditions where the pseudogap becomes detrimental to superconductivity. For given $U/t$ there is thus an optimal value of frustration $t^{prime}/t$ where the superconducting $T_c$ is maximum. The non-interacting density of states plays little role. The symmetry d$_{x^{2}-y^{2}}$ vs d$_{xy}$ of the superconducting order parameter depends on the wave vector of the underlying magnetic fluctuations in a way that can be understood qualitatively from simple arguments.
We present a systematic study of the phase diagram of the $t{-}t^prime{-}J$ model by using the Greens function Monte Carlo (GFMC) technique, implemented within the fixed-node (FN) approximation and a wave function that contains both antiferromagnetic and d-wave pairing. This enables us to study the interplay between these two kinds of order and compare the GFMC results with the ones obtained by the simple variational approach. By using a generalization of the forward-walking technique, we are able to calculate true FN ground-state expectation values of the pair-pair correlation functions. In the case of $t^prime=0$, there is a large region with a coexistence of superconductivity and antiferromagnetism, that survives up to $delta_c sim 0.10$ for $J/t=0.2$ and $delta_c sim 0.13$ for $J/t=0.4$. The presence of a finite $t^prime/t<0$ induces a strong suppression of both magnetic (with $delta_c lesssim 0.03$, for $J/t=0.2$ and $t^prime/t=-0.2$) and pairing correlations. In particular, the latter ones are depressed both in the low-doping regime and around $delta sim 0.25$, where strong size effects are present.
Variational studies of the t-J model on the square lattice based on infinite projected-entangled pair states (iPEPS) confirm an extremely close competition between a uniform d-wave superconducting state and different stripe states. The site-centered stripe with an in-phase d-wave order has an equal or only slightly lower energy than the stripe with anti-phase d-wave order. The optimal stripe filling is not constant but increases with J/t. A nematic anisotropy reduces the pairing amplitude and the energies of stripe phases are lowered relative to the uniform state with increasing nematicity.
In our previous work [arXiv:1803.00999, Phys. Rev. Lett. 121, 046401 (2018)], we found a quantum spin liquid phase with a spinon Fermi surface in the two dimensional spin-1/2 Heisenberg model with four-spin ring exchange on a triangular lattice. In this work we dope the spinon Fermi surface phase by studying the $t$-$J$ model with four-spin ring exchange. We perform density matrix renormalization group calculations on four-leg cylinders of a triangular lattice and find that the dominant pair correlation function is that of a pair density wave; i.e., it is oscillatory while decaying with distance with a power law. The doping dependence of the period is studied. This is the first example where pair density wave is the dominant pairing in a generic strongly interacting system where the pair density wave cannot be explained as a composite order and no special symmetry is required.
We present numeric results for ground state and angle resolved photoemission spectra (ARPES) for single hole in t-J model coupled to optical phonons. The systematic-error free diagrammatic Monte Carlo is employed where the Feynman graphs for the Matsubara Green function in imaginary time are summed up completely with respect to phonons variables, while magnetic variables are subjected to non-crossing approximation. We obtain that at electron-phonon coupling constants relevant for high Tc cuprates the polaron undergoes self-trapping crossover to strong coupling limit and theoretical ARPES demonstrate features observed in experiment: a broad peak in the bottom of the spectra has momentum dependence which coincides with that of hole in pure t-J model.
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