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Register a new userCoexistence of Nematic Order and Superconductivity in the Hubbard Model
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We study the interplay of nematic and superconducting order in the two-dimensional Hubbard model and show that they can coexist, especially when superconductivity is not the energetically dominant phase. Due to a breaking of the $C_4$ symmetry, the coexisting phase inherently contains admixture of the $s$-wave pairing components. As a result, the superconducting gap exhibits very non-standard features including changed nodal directions. Our results also show that in the optimally doped regime the superconducting phase is typically unstable towards developing nematicity (breaking of the $C_4$ symmetry). This has implications for the cuprate high-$T_c$ superconductors, for which in this regime the so-called intertwined orders have recently been observed. Namely, the coexisting phase may be viewed as a precursor to such more involved patterns of symmetry breaking.
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Antiferromagnetism and $d$-wave superconductivity are the most important competing ground-state phases of cuprate superconductors. Using cellular dynamical mean-field theory (CDMFT) for the Hubbard model, we revisit the question of the coexistence and competition of these phases in the one-band Hubbard model with realistic band parameters and interaction strengths. With an exact diagonalization solver, we improve on previous works with a more complete bath parametrization which is carefully chosen to grant the maximal possible freedom to the hybridization function for a given number of bath orbitals. Compared with previous incomplete parametrizations, this general bath parametrization shows that the range of microscopic coexistence of superconductivity and antiferromagnetism is reduced for band parameters for NCCO, and confined to electron-doping with parameters relevant for YBCO.
Unidirectional (stripe) charge-density-wave order has now been established as a ubiquitous feature in the phase diagram of the cuprate high temperature (HT) superconductors, where it generally competes with superconductivity (SC). None-the-less, on theoretical grounds it has been conjectured that stripe order (or other forms of optimal inhomogeneities) may play an essential positive role in the mechanism of HTSC. Here we report density matrix renormalization group studies of the Hubbard model on long 4 and 6 leg cylinders where the hopping matrix elements transverse to the long direction are periodically modulated - mimicing the effect of putative period-2 stripe order. We find even modest amplitude modulations can enhance the long-distance SC correlations by many orders of magnitude, and drive the system into a phase with a substantial spin gap and SC quasi-long-range-order with a Luttinger exponent, $K_{sc} sim 1$.
Short-range antiferromagnetic correlations are known to open a spin gap in the repulsive Hubbard model on ladders with $M$ legs, when $M$ is even. We show that the spin gap originates from the formation of correlated pairs of electrons with opposite spin, captured by the hidden ordering of a spin-parity operator. Since both spin gap and parity vanish in the two-dimensional limit, we introduce the fractional generalization of spin parity and prove that it remains finite in the thermodynamic limit. Our results are based upon variational wave functions and Monte Carlo calculations: performing a finite size-scaling analysis with growing $M$, we show that the doping region where the parity is finite coincides with the range in which superconductivity is observed in two spatial dimensions. Our observations support the idea that superconductivity emerges out of spin gapped phases on ladders, driven by a spin-pairing mechanism, in which the ordering is conveniently captured by the finiteness of the fractional spin-parity operator.
In strongly correlated multi-orbital systems, various ordered phases appear. In particular, the orbital order in iron-based superconductors attracts much attention since it is considered to be the origin of the nematic state. In order to clarify the essential condition for realizing orbital orders, we study simple two-orbital ($d_{xz}$, $d_{yz}$) Hubbard model. We find that the orbital order, which corresponds to the nematic order, appears due to the vertex corrections even in the two-orbital model. Thus, $d_{xy}$ orbital is not essential to realize the nematic orbital order. The obtained orbital order depends on the orbital dependence and the topology of fermi surfaces. We also find that another type of orbital order, which is rotated $45^circ$, appears in the heavily hole-doped case.
We study the unitary time evolution of antiferromagnetic order in the Hubbard model after a quench starting from the perfect Neel state. In this setup, which is well suited for experiments with cold atoms, one can distinguish fundamentally different pathways for melting of long-range order at weak and strong interaction. In the Mott insulating regime, melting of long-range order occurs due to the ultra-fast transfer of energy from charge excitations to the spin background, while local magnetic moments and their exchange coupling persist during the process. The latter can be demonstrated by a local spin-precession experiment. At weak interaction, local moments decay along with the long-range order. The dynamics is governed by residual quasiparticles, which are reflected in oscillations of the off-diagonal components of the momentum distribution. Such oscillations provide an alternative route to study the prethermalization phenomenon and its influence on the dynamics away from the integrable (noninteracting) limit. The Hubbard model is solved within nonequilibrium dynamical mean-field theory, using the density matrix-renormalization group as an impurity solver.
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