Based on random phase approximation, we numerically calculate dynamical structure factors of a balanced two-dimensional (2D) Fermi superfluid, and discuss their energy, momentum and interaction strength dependence in the 2D BEC–BCS crossover. At a small transferred momentum, a stable Higgs mode is observed in the unitary 2D Fermi superfluid gas where the particle–hole symmetry is not satisfied. Stronger interaction strength will make the visibility of the dispersion of Higgs mode harder to be observed. We also discuss the dimension effect and find that the signal of the Higgs mode in two dimension is more obvious than that in 3D case. At a large transferred momentum regime, stronger interaction strength will induce the weight of the molecules excitation increasing, while in verse the atomic one decreasing, which shows the pairing information of Fermi superfluid. The theoretical results qualitatively agree with the corresponding quantum Monte Carlo data.

The doping, temperature, and energy dependence of the dynamical spin structure factors of the underdoped lanthanum cuprates in the normal state are studied within the $t-J$ model using the fermion-spin transformation technique. Incommensurate peaks are found at $\left[\right(1\mathrm{}\pm \delta )\pi ,\pi ],$ $[\pi ,(1\mathrm{}\pm \delta \left)\pi \right]$ at relatively low temperatures, with $\delta$ linearly increasing with doping at the beginning and then saturating at higher dopings. These peaks broaden and weaken in amplitude with temperature and energy, in good agreement with experiments. The theory also predicts a rotation of these peaks by $\pi /4\mathrm{}$ at even higher temperatures, being shifted to $\left[\right(1\mathrm{}\pm \delta /\sqrt{2})\pi ,$ $(1\mathrm{}\pm \delta /\sqrt{2})\pi ].$

The $d$-wave superconductivity (dSC) and antiferromagnetism are analytically studied in a renormalized mean-field theory for a two-dimensional $t\text{‐}J$ model plus an on-site repulsive Hubbard interaction $U$. The purpose of introducing the $U$ term is to partially impose the no-double-occupancy constraint by employing the Gutzwiller approximation. The phase diagrams as functions of doping $\delta$ and $U$ are studied. Using the standard value of $t∕J=3.0$ and in the large-$U$ limit, we show that the antiferromagnetic (AF) order emerges and coexists with the dSC in the underdoped region below the doping $\delta \sim 0.1$. The dSC order parameter increases from zero as the doping increases and reaches a maximum near the optimal doping $\delta \sim 0.15$. In the small-$U$ limit, only the dSC order survives while the AF order disappears. As $U$ increases up to a critical value, the AF order shows up and coexists with the dSC in the underdoped regime. At half-filling, the system is in the dSC state for small $U$ and becomes an AF insulator for large $U$. Within the present mean-field approach, we show that the ground-state energy of the coexistent state is always lower than that of the pure dSC state.

Photoinduced excited-state energy transfer (EET) processes play a key role in the solar energy conversion of small molecule organic solar cells. We investigated intermolecular EET dynamics in the 2-[[7-(5-N,N-ditolylaminothiophen-2-yl)-2,1,3-benzothiadiazol-4-yl]methylene]malononitrile (DTDCTB) dimer embedded in a crystal environment using full quantum dynamics, i.e., the multilayer multiconfigurational time-dependent Hartree (ML-MCTDH) method. Two different stacking statuses of the DTDCTB dimers, which occur along the OA axis in the DTDCTB crystal, were considered. We built a vibronic diabatic Hamiltonian using the projection method based on quantum mechanics/molecular mechanics results. Different model Hamiltonians were considered in the full quantum dynamics studies. First, reduced-dimensional models were constructed by simply including more of the important vibrational modes. Second, we tried to construct a continuous spectral density based on the vibronic coupling strengths of different modes and then created a set of “pseudomodes” to represent electron–phonon couplings. The dynamics results based on these reduced models were compared with the results obtained with the full dimensional model. Our theoretical descriptions demonstrated that ultrafast intermolecular EET dynamics takes place in the well-stacked DTDCTB dimers. This work deepens our understanding of the photoinduced ultrafast EET dynamics of realistic organic photovoltaic systems at the full quantum mechanical level.

Based on the two-dimensional (2D) attractive Fermi-Hubbard model with Rashba spin–orbit coupling (SOC), the SOC strength and Zeeman field dependences of the phase diagram are investigated by calculating the pairing gap self-consistently. The results reveal that the phase transition from the BCS superfluid to the topological superfluid happens under proper Zeeman field strength and SOC strength. In particular, in contrast to the BCS superfluid decreasing monotonically as the SOC strength increasing, the topological superfluid region shows a dome with the SOC strength increasing. An optimal region in the phase diagram to find the topological superfluid can be found, which is important to realize the topological superfluid in optical lattice experimentally. Then we obtain the change of both band structure and density of states (DOSs) during the topological phase transition, and explain the four peaks of DOS in the topological superfluid by the topology change of the low-energy branch of quasiparticle energy spectra. Moreover, the topological superfluid can be suppressed by the doping concentration.