The repulsive Fermi-Hubbard model on a square lattice has a rich phase diagram near half-filling ($n=1$): at $n=1$ the ground state is an antiferromagnetic insulator, at $0.6<n\lesssim 0.8$ the ground state is a $d_{x^2-y^2}$-wave superfluid (at least for moderately strong interactions, $U\lesssim 4$), and the region $1-n\ll 1$ is likely subject to phase separation. Much less is known about the nature of strong magnetic fluctuations at finite temperature and how they change with the doping level. Recent experiments on ultracold atoms have now reached this interesting fluctuation regime. In this work we employ the skeleton diagrammatic method to quantify the characteristic temperature scale $T_M\left(n\right)$ for the onset of magnetic fluctuations with a large correlation length.

We outline a general formalism of hydrodynamics for quantum systems with multiple particle species which undergo completely elastic scattering. In the thermodynamic limit, the complete kinematic data of the problem consist of the particle content, the dispersion relations, and a universal dressing transformation which accounts for interparticle interactions. We consider quantum integrable models and we focus on the one-dimensional fermionic Hubbard model. By linearizing hydrodynamic equations, we provide exact closed-form expressions for Drude weights, generalized static charge susceptibilities, and charge-current correlators valid on the hydrodynamic scale, represented as integral kernels operating diagonally in the space of mode numbers of thermodynamic excitations. We find that, on hydrodynamic scales, Drude weights manifestly display Onsager reciprocal relations even for generic (i.e., noncanonical) equilibrium states, and establish a generalized detailed balance condition for a general quantum integrable model. We present exact analytic expressions for the general Drude weights in the Hubbard model, and explain how to reconcile different approaches for computing Drude weights from the previous literature.

We theoretically study the spin and charge currents induced by a spin-motive force in a two-dimensional Dirac semimetal protected by nonsymmorphic symmetries. Glide mirror plane symmetry, a nonsymmorphic symmetry, leads to a constraint to the induced current; the spin-motive force acting on out-of-plane spin (in-plane spin) induces the pure spin (charge) current. We calculate the response function to the spin-motive force in linear-response theory and find that the conductivity for the pure spin current remains nonzero even if the Fermi energy is crossing the node of linear dispersion. We also find that the conserved spin current is induced at the charge neutral point.

We propose a tight-binding (TB) model, that includes spin-orbit coupling (SOC), to describe the electronic properties of methyl-substituted germanane (${\mathrm{GeCH}}_3$). This model gives an electronic spectrum in agreement with first principle results close to the Fermi level. Using the ${\mathbb{Z}}_2$ formalism, we show that a topological phase transition from a normal insulator (NI) to a quantum spin Hall (QSH) phase occurs at 11.6% biaxial tensile strain. The sensitivity of the electronic properties of this system on strain, in particular its transition to the topological insulating phase, makes it very attractive for applications in strain sensors and other microelectronic applications.

The phase transition evolution for ${\left[{\mathrm{KNbO}}_3\right]}_{1-x}{\left[{\mathrm{BaNi}}_{1/2}{\mathrm{Nb}}_{1/2}{\mathrm{O}}_{3-\delta }\right]}_x(x=0,0.1)$ is determined via complementary dielectric permittivity and Raman-scattering measurements. Raman scattering by optical phonons over the range of 100–$1000{\mathrm{cm}}^{-1}$ for 83 K $<T<873$ K reveals six discernible zone-center optical phonon modes. Mode behaviors are observed through structural and ferroelectric phases in the solid solution $x=0.1$ and compared with those for end member $x=0$ and with the results of temperature-dependent dielectric permittivity. Rigorous peak fitting analyses of spectra collected from the solid solution and end member indicate structural and ferroelectric phase transition temperatures that are close to those for the ${\mathrm{KNbO}}_3$ end member despite the inclusion of 5 atomic % of ferroelectrically inactive Ni cations. Density functional theory calculations were performed in the solid solution and end member using both cation displacement and Berry phase-based methods. Differences in the electronic and polar properties between the solid solution and the end member highlights local and nonlocal characteristics, which are discussed in relation to the experimental data.

We study the Hall conductance in a Floquet topological insulator in the long time limit after sudden switches of the driving amplitude. Based on a high frequency expansion of the effective Hamiltonian and the micromotion operator we demonstrate that the Hall conductance as a function of the driving amplitude follows universal nonanalytic laws close to phase transitions that are related to conic gap closing points, namely a logarithmic divergence for gapped initial states and jumps of a definite height for gapless initial states. This constitutes a generalization of the results known for the static systems to the driven case.

We study scattering of a composite quasiparticle, which possesses a degree of freedom corresponding to relative separation between two bound excitations, by a $\delta$-like impurity potential on a one-dimensional discrete lattice. First, we show that, due to specific properties of their dispersion, lattice excitations bind to impurities with both negative and positive potentials. We demonstrate that the finite size of the composite excitation leads to formation of multiple excitation-impurity bound states. The number and the degree of localization of these bound states depend on the signs and relative magnitudes of the impurity potential and the binding strength of two quasiparticles. We also report the existence of excitation-impurity bound states whose energies are located in the continuum band. Secondly, we study a change in the entanglement between the center of mass and relative coordinate degrees of freedom of a biexciton wave packet during single impurity scattering and decoherence caused by it. For a composite quasiparticle on a lattice, the entanglement between its relative and center of mass coordinate degrees of freedom arises naturally due to inseparability of the two-particle Hamiltonian. One of the main focuses of our study is to investigate how this inseparability affects the creation of the biexciton-impurity bound states and the entanglement dynamics.

We apply imaginary-time evolution with the operator $e^{-\tau H}$ to study relaxation dynamics of gapless quantum antiferromagnets described by the spin-rotation-invariant Heisenberg Hamiltonian $H$. Using quantum Monte Carlo simulations to obtain unbiased results, we propagate an initial state with maximal order parameter $m_s^z$ (the staggered magnetization) in the $z$ spin direction and monitor the expectation value $\langle m_s\rangle$ as a function of imaginary time $\tau$. Results for different system sizes (lengths) $L$ exhibit an initial essentially size independent relaxation of $\langle m_s\rangle$ toward its value in the infinite-size spontaneously symmetry broken state, followed by a strongly size dependent final decay to zero when the $\mathrm{O}\left(3\right)$ rotational symmetry of the order parameter is restored. We develop a generic finite-size scaling theory that shows the relaxation time diverges asymptotically as $L^z$, where $z$ is the dynamic exponent of the low-energy excitations. We use the scaling theory to develop a practical way of extracting the dynamic exponent from the numerical finite-size data, systematically eliminating scaling corrections. We apply the method to spin-$1/2$ Heisenberg antiferromagnets on two different lattice geometries: the standard two-dimensional (2D) square lattice and a site-diluted 2D square lattice at the percolation threshold. In the 2D case we obtain $z=2.001\left(5\right)$, which is consistent with the known value $z=2$, while for the site-diluted lattice we find $z=3.90\left(1\right)$ or $z=2.056\left(8\right)D_f$, where $D_f=91/48$ is the fractal dimensionality of the percolating system. This is an improvement on previous estimates of $z\approx 3.7$. The scaling results also show a fundamental difference between the two cases; for the 2D square lattice, the data can be collapsed onto a common scaling function even when $\langle m_s\rangle$ is relatively large, reflecting the Anderson tower of quantum rotor states with a common dynamic exponent $z=2$. For the diluted 2D square lattice, the scaling works well only for small $\langle m_s\rangle$, indicating a mixture of different relaxation-time scalings between the low-energy states. Nevertheless, the low-energy dynamic here also corresponds to a tower of excitations.

We have performed first-principles investigations on the native defects in the half-metallic, ferromagnetic full Heusler alloys ${\mathrm{Co}}_2\mathrm{Ti}Z$ $(Z$ one of the group IV elements Si, Ge, Sn), determining their formation energies and how they influence the transport properties. We find that the Co vacancies $\left({\mathrm{Vc}}_{\mathrm{Co}}\right)$ and the ${\mathrm{Ti}}_{\text{Sn}}$ as well as the ${\mathrm{Co}}_Z$ or ${\mathrm{Co}}_{\text{Ti}}$ antisites exhibit the smallest formation energies. The most abundant native defects were modeled as dilute alloys, treated with the coherent potential approximation in combination with the multiple-scattering theory Green function approach. The self-consistent potentials determined this way were used to calculate the residual resistivity via the Kubo-Greenwood formula and, based on its energy dependence, the Seebeck coefficient of the systems. The latter is shown to depend significantly on the type of defect, leading to variations that are related to subtle, spin-orbit coupling induced changes in the electronic structure above the half-metallic gap. Two of the systems, ${\mathrm{Vc}}_{\text{Co}}$ and ${\mathrm{Co}}_Z$, are found to exhibit a negative Seebeck coefficient. This observation, together with their low formation energy, offers an explanation for the experimentally observed negative Seebeck coefficient of the ${\mathrm{Co}}_2\mathrm{Ti}Z$ compounds as being due to unintentionally created native defects.

There have been continuous efforts in searching for unconventional superconductivity in the past five decades. Compared to the well-established $d$-wave superconductivity in cuprates, the existence of superconductivity with pairing symmetries of other high angular momentum is less conclusive. Bi/Ni epitaxial bilayer is a potential unconventional superconductor with broken time reversal symmetry (TRS), for that it demonstrates superconductivity and ferromagnetism simultaneously at low temperatures. We employ a specially designed superconducting quantum interference device (SQUID) to detect, on the Bi/Ni bilayer, the orbital magnetic moments which are expected if the TRS is broken. An anomalous hysteretic magnetic response is indeed observed in the superconducting state, providing the evidence for the existence of chiral superconducting domains in the material.

We study many-body localization (MBL) in an interacting one-dimensional system with a deterministic aperiodic potential. Below the threshold potential $h<h_c$, the noninteracting system has single particle mobility edges (MEs) at $\pm E_c$ while for $h>h_c$ all the single particle states are localized. We demonstrate that even in the presence of single particle MEs, interactions do not always delocalize the system and the interacting system can have MBL. Our numerical calculation of energy level spacing statistics, participation ratio in the Fock space, and Shannon entropy shows that for some regime of particle densities, even for $h<h_c$, many-body states at the top (with $E>E_2$) and the bottom of the spectrum (with $E<E_1$) remain localized, though states in the middle of the spectrum are delocalized. Variance of entanglement entropy (EE) also diverges at $E_{1,2}$, indicating a transition from MBL to a delocalized regime, though transitions from volume to area law scaling for EE and from thermal to nonthermal behavior occur inside the MBL regime much below $E_1$ and above $E_2$.

Sound velocity and attenuation measurements on the frustrated garnet material ${\mathrm{Gd}}_3{\mathrm{Ga}}_5{\mathrm{O}}_{12}$ (GGG) are presented as a function of field and temperature, with two different magnetic field orientations: $\left[100\right]$ and $\left[110\right]$. We demonstrate that the phase diagram is highly anisotropic, with two distinct field-induced ordered phases for $H\left|\right|\left[110\right]$ and only one for $H\left|\right|\left[100\right]$. Extensive lattice softening is found to occur at low fields, which can be associated with spin fluctuations. However, deep within the spin liquid phase a low-temperature stiffening of the lattice and reduced attenuation provide evidence for a spin gap which may be related to short-range antiferromagnetic correlations over minimal ten-spin loops.

The Berezinskii-Kosterlitz-Thouless (BKT) transition in two-dimensional superconductors is usually expected to be protected against disorder. However, its fingerprints in a real system, such as, e.g., the universal superfluid-density jump, are often at odds with this expectation. Here, we show that the disorder-induced granularity of the superconducting state modifies the nucleation mechanism for vortex-antivortex pairs. This leads to a considerable smearing of the universal superfluid-density jump as compared to the paradigmatic clean case, in agreement with experimental observations.

The long-sought quantum spin liquid is a quantum-entangled magnetic state leading to the fractionalization of spin degrees of freedom. Quasiparticles emergent from the fractionalization affect not only the ground-state properties but also thermodynamic behavior in a peculiar manner. Here we investigate how the spin dynamics evolves from the high-temperature paramagnet to the quantum spin-liquid ground state, for the Kitaev spin model describing the fractionalization into itinerant matter fermions and localized $Z_2$ fluxes. Beyond the previous studies [J. Yoshitake, J. Nasu, and Y. Motome, Phys. Rev. Lett. 117, 157203 (2016); J. Yoshitake, J. Nasu, Y. Kato, and Y. Motome, Phys. Rev. B 96, 024438 (2017)], in which the mean-field nature of the cluster dynamical mean-field theory prevented us from studying low-temperature properties, we develop a numerical technique by applying the continuous-time quantum Monte Carlo (CTQMC) method to statistical samples generated by the quantum Monte Carlo (QMC) method in a Majorana fermion representation. This QMC+CTQMC method is fully unbiased and enables us to investigate the low-temperature spin dynamics dominated by thermally excited $Z_2$ fluxes, including the unconventional phase transition caused by $Z_2$ flux loops in three dimensions, which was unreachable by the previous methods. We apply this technique to the Kitaev model in both two and three dimensions. Our results clearly distinguish two cases: while the dynamics changes smoothly through the crossover in the two-dimensional honeycomb case, it exhibits singular behaviors at the phase transition in the three-dimensional hyperhoneycomb case. We show that the low-temperature spin dynamics is a sensitive probe for thermally fluctuating $Z_2$ fluxes that behave very differently between two and three dimensions.

We theoretically show that terahertz pulses with controlled amplitude and frequency can be used to switch between stable transport modes in layered superconductors, modeled as stacks of Josephson junctions. We find pulse shapes that deterministically switch the transport mode between superconducting, resistive, and solitonic states. We develop a simple model that explains the switching mechanism as a destabilization of the center-of-mass excitation of the Josephson phase, made possible by the highly nonlinear nature of the light-matter coupling.

We analyze, from a quantum information theory perspective, the possibility of realizing an SU(4) entangled Kondo regime in semiconductor double quantum dot devices. We focus our analysis on the ground-state properties and consider the general experimental situation where the coupling parameters of the two quantum dots differ. We model each quantum dot with an Anderson-type Hamiltonian including an interdot Coulomb repulsion and tunnel couplings for each quantum dot to independent fermionic baths. We find that the spin and pseudospin entanglements can be made equal, and the SU(4) symmetry recovered, if the gate voltages are chosen in such a way that the average charge occupancies of the two quantum dots are equal, and the double occupancy on the double quantum dot is suppressed. We present density matrix renormalization group numerical results for the spin and pseudospin entanglement entropies, and analytical results for a simplified model that captures the main physics of the problem.

In topological quantum computing, unitary operations on qubits are performed by adiabatic braiding of non-Abelian quasiparticles, such as Majorana zero modes, and are protected from local environmental perturbations. In the adiabatic regime, with timescales set by the inverse gap of the system, the errors can be made arbitrarily small by performing the process more slowly. To enhance the performance of quantum information processing with Majorana zero modes, we apply the theory of optimal control to the diabatic dynamics of Majorana-based qubits. While we sacrifice complete topological protection, we impose constraints on the optimal protocol to take advantage of the nonlocal nature of topological information and increase the robustness of our gates. By using the Pontryagin's maximum principle, we show that robust equivalent gates to perfect adiabatic braiding can be implemented in finite times through optimal pulses. In our implementation, modifications to the device Hamiltonian are avoided. Focusing on thermally isolated systems, we study the effects of calibration errors and external white and $1/f$ (pink) noise on Majorana-based gates. While a noise-induced antiadiabatic behavior, where a slower process creates more diabatic excitations, prohibits indefinite enhancement of the robustness of the adiabatic scheme, our fast optimal protocols exhibit remarkable stability to noise and have the potential to significantly enhance the practical performance of Majorana-based information processing.

We study a single-photon super-radiance under the conditions of cyclotron resonance in a perfect single-crystal $p$-type semiconductor film with cubic structure. We show that the rate of super-radiant emission scales with the film area, which allows one to specify the size of the film at which the probability of a single-photon super-radiance becomes much greater than the probabilities of other scattering channels. The power of super-radiant emission depends only on three fundamental constants: the electron charge $q_e$, the speed of light $c$, the electron mass $m_e$, and on the electric- to magnetic-field ratio.

We theoretically study the lattice relaxation in the twisted bilayer graphene (TBG) and its effect on the electronic band structure. We develop an effective continuum theory to describe the lattice relaxation in general TBGs and obtain the optimized structure to minimize the total energy. At small rotation angles $<2^{\circ }$, in particular, we find that the relaxed lattice drastically reduces the area of the AA stacking region and forms a triangular domain structure with alternating AB and BA stacking regions. We then investigate the effect of the domain formation on the electronic band structure. The most notable change from the nonrelaxed model is that an energy gap of up to 20 meV opens at the superlattice subband edges on the electron and hole sides. We also find that the lattice relaxation significantly enhances the Fermi velocity, which was strongly suppressed in the nonrelaxed model.