We identify and describe unique early time behavior of a quantum system initially in a superposition, interacting with its environment. This behavior—the copycat process—occurs after the system begins to decohere, but before complete einselection. To illustrate this behavior analytic solutions for the system density matrix, its eigenvalues, and eigenstates a short time after system-environment interactions begin are provided. Features of the solutions and their connection to observables are discussed, including predictions for the continued evolution of the eigenstates towards einselection, time dependence of spin expectation values, and an estimate of the system's decoherence time. In particular we explore which aspects of the early stages of decoherence exhibit quadratic evolution to leading order, and which aspects exhibit more rapid linear behavior. Many features of our early time perturbative solutions are agnostic of the spectrum of the environment. We also extend our work beyond short time perturbation theory to compare with numerical work from a companion paper.

We present a variant of the Caldeira-Leggett (CL) model of a harmonic oscillator coupled to an environment. The CL model is a standard tool for studying the physics of decoherence. Our “adapted Caldeira-Leggett” (ACL) model is built in a finite Hilbert space which makes it suitable for numerical studies. Taking a numerical approach allows us to avoid the limitations of standard approximation schemes used with the CL model. We are able to evolve the ACL model in a fully reversible unitary manner, without the built-in time asymmetry and other assumptions that come with the master equation methods typically used. We have used the ACL model to study topics in the field of decoherence and einselection where the full unitary evolution is essential to our work. Those results (reported in companion papers) include an examination of the relationship between einselection and the arrow of time, and studies of the very earliest stages of einselection. This paper provides details about the ACL model and our numerical methods. Our numerical approach makes it straightforward to explore and plot any property of the physical system. Thus we believe the examples and illustrations we present here may provide a helpful resource for those wishing to improve their familiarity with standard decoherence results, as well as those looking to probe the underpinnings of our companion papers. We expect the ACL model will be a useful tool for exploring additional phenomena that cannot be studied using traditional approximation schemes.

In this paper, we determine the volume-fraction reduction of sheared fragile glass-forming liquids. We consider a group of hypothetical systems that consist of particles with anisotropic size modulations yet have almost the same average particle configuration as actual systems under shear flow. Our molecular dynamics (MD) simulations demonstrate that one specific hypothetical system can reproduce the relaxation dynamics of an actual sheared system, and we identify the shear-flow effect on the particle size with anisotropic size modulation of this specific system. Then based on the determination of the particle size and the resultant volume fraction, we rationalize how slight decreases in the volume fraction significantly reduce the viscosity and provide a nonlinear constitutive equation. Notably, the obtained rheological predictions, including the crossover shear rate from Newtonian to non-Newtonian behavior, can be expressed only in terms of experimental observables, showing good agreement with the MD simulation results. Our perspective on the volume fraction under shear flow may provide insights into the conventional concept of free volume.

We perform the projector quantum Monte Carlo (QMC) simulation to study the trion formation and quantum phase transition in the half filled attractive SU(3) Hubbard model on a honeycomb lattice. With increasing attractive Hubbard interaction, our simulations demonstrate a continuous quantum phase transition from the semimetal to charge-density wave (CDW) at the critical coupling $U_c/t=-1.52\left(2\right)$. The critical exponents $\nu =0.82\left(3\right)$ and $\eta =0.58\left(4\right)$ determined by the QMC simulation remarkably disagree with those of the $N=3$ chiral Ising universality class suggested by the effective Gross-Neveu-Yukawa (GNY) theory, but coincide with the $N=1$ chiral Ising universality class. In the CDW phase, we show that on-site and off-site trions coexist and the off-site trion forms a local bond state. Our work not only illustrates the formation of off-site trions in two-dimensional Hubbard model but also raises doubts about the extent of applicability of GNY model on attractive SU(3) Dirac fermions.

It is commonly believed that nonuniform Berry curvature destroys the Girvin-MacDonald-Platzman algebra and as a consequence destabilizes fractional Chern insulators. In this work, we disprove this common lore by presenting a theory for all topological ideal flatbands with nonzero Chern number $\mathcal{C}$. The smooth single-particle Bloch wave function is proven to admit an exact color-entangled form as a superposition of $\mathcal{C}$ lowest Landau level type wave functions distinguished by boundary conditions. Including repulsive interactions, Abelian and non-Abelian model fractional Chern insulators of Halperin type are stabilized as exact zero-energy ground states no matter how nonuniform the Berry curvature is, as long as the quantum geometry is ideal and the repulsion is short-ranged. The key reason is the existence of an emergent Hilbert space in which Berry curvature can be exactly flattened by adjusting the wave function's normalization. In such space, the flatband-projected density operator obeys a closed Girvin-MacDonald-Platzman type algebra, making exact mapping to $\mathcal{C}$-layered Landau levels possible. In the end, we discuss applications of the theory to moiré flatband systems, with a particular focus on the fractionalized phase and the spontaneous symmetry-breaking phase recently observed in graphene-based twisted materials.

Motivated by the higher Chern bands of twisted graphene multilayers, we consider flat bands with arbitrary Chern number $C$ with ideal quantum geometry. While $C>1$ bands differ from Landau levels, we show that these bands host exact fractional Chern insulator (FCI) ground states for short-range interactions. We show how to decompose ideal higher Chern bands into separate ideal bands with Chern number 1 that are intertwined through translation and rotation symmetry. The decomposed bands admit an $\mathrm{SU}\left(C\right)$ action that combines real space and momentum space translations. Remarkably, they also allow for analytic construction of exact many-body ground states, such as generalized quantum Hall ferromagnets and FCIs, including flavor-singlet Halperin states and Laughlin ferromagnets in the limit of short-range interactions. In this limit, the $\mathrm{SU}\left(C\right)$ action is promoted to a symmetry on the ground-state subspace. While flavor singlet states are translation symmetric, the flavor ferromagnets correspond to translation broken states and admit charged skyrmion excitations corresponding to a spatially varying density wave pattern. We confirm our analytic predictions with numerical simulations of ideal bands of twisted chiral multilayers of graphene, and discuss consequences for experimentally accessible systems such as monolayer graphene twisted relative to a Bernal bilayer.

A weird electronic state accompanied with an anomalous superconducting precursor and/or exotic orders, called the pseudogap state, arises prior to a superconducting condensate in underdoped cuprates that are situated near Mott transition. Another way to make the system approach the Mott transition is the variation of bandwidth or correlation strength, which gives a new dimension to exploring this exotic state. Here we report nuclear magnetic resonance (NMR) studies on layered organic superconductors with half-filled bands whose widths are pressure tuned near the Mott transition. The system situated on the verge of the Mott transition shows a pseudogap-like anomalous suppression of spin excitations on cooling from well above the superconducting critical temperature $T_c$. The pressure variation of the NMR relaxation rate shows that the pseudogap-like behavior is rapidly suppressed by applying pressure. The NMR experiments under various magnetic fields varied up to 18 T proves the absence of symmetry breaking orders that compete with superconductivity, such as charge orders, in the metallic phase. Remarkably, the pseudogap-like behavior above $T_c$ and the superconducting condensate fade out in parallel under ascending magnetic fields with similar field-orientation dependence, indicating a superconducting precursor is the predominant origin of the pseudogap. Our further investigation of different materials, which take different “distances” from the Mott transition by chemical pressure, confirms that the superconducting precursor is not the conventional amplitude fluctuations arising from low dimensionality but unconventional preformation of Cooper pairs enhanced near the Mott transition. These findings conclude that preformed Cooper pairs persist up to twice as high as $T_c$ on the verge of the bandwidth-controlled Mott transition.

We investigate the influence of the temporal variations of various medium parameters on the propagation of Dirac-type waves in materials where the quasiparticles are described by a generalized version of the pseudospin-1/2 Dirac equation. Our considerations also include the propagation of electromagnetic waves in metamaterials with the Dirac-type dispersion. We focus on the variations of the scalar and vector potentials, mass, Fermi velocity, and tilt velocity describing the Dirac cone tilt. We derive the scattering coefficients associated with the temporal interfaces and slabs analytically and find that the temporal scattering is caused by the changes of the mass, Fermi velocity, and vector potential, but does not arise from the changes of the scalar potential and tilt velocity. We also explore the conditions under which the temporal Brewster effect and total interband transition occur and calculate the change in total wave energy. We examine bilayer Dirac temporal crystals where parameters switch between two different sets of values periodically and prove that these systems do not have momentum gaps. Finally, we assess the potential for observing these temporal scattering effects in experiments.

We report the magnetization, ac susceptibility, and specific heat of optically float-zoned single crystals of ${\mathrm{CePdAl}}_3$. In comparison to the properties of polycrystalline ${\mathrm{CePdAl}}_3$ reported in the literature, which displays a tetragonal crystal structure and no long-range magnetic order, our single crystals exhibit an orthorhombic structure ($Cmcm$) and antiferromagnetic order below a Néel temperature $T_1=5.6$ K. The specific heat at zero field shows two anomalies, namely, a broad transition at $T_1=5.6$ K followed by a $\lambda$-anomaly at $T_2=5.4$ K. A conservative estimate of the Sommerfeld coefficient of the electronic specific heat, $\gamma =121\mathrm{mJ}{\mathrm{K}}^{-2}{\mathrm{mol}}^{-1}$, indicates a moderately enhanced heavy-fermion ground state. A twin microstructure evolves in the family of planes spanned by the basal plane lattice vectors ${\mathbf{a}}_{\mathrm{o}}$ and ${\mathbf{c}}_{\mathrm{o}}$ , with the magnetic hard axis ${\mathbf{b}}_{\mathrm{o}}$ common to all twins. The antiferromagnetic state is characterized by a strong a${}_{\mathrm{o}}$, c${}_{\mathrm{o}}$ easy-plane magnetic anisotropy where the a${}_{\mathrm{o}}$ direction is the easy axis in the easy plane. A spin-flop transition induced under magnetic field along the easy directions, results in complex magnetic phase diagrams. Taken together, our results reveal a high sensitivity of the magnetic and electronic properties of ${\mathrm{CePdAl}}_3$ to its structural modifications.

We present a unified treatment of the Aharonov-Bohm (AB) effect for two-dimensional multiband electronic systems possessing isotropic band structures. We propose an integral representation of the AB scattering state of an electron scattered by an infinitely thin solenoid. Moreover, we derive the asymptotic form of the AB scattering state and obtain the differential cross section from that. We found a remarkable result, namely, that this cross section is the same for all isotropic systems and agrees with that obtained first by Aharonov and Bohm for spinless free-particle systems. To demonstrate the generality of our theory, we consider several specific multiband systems relevant to condensed matter physics.

It is well known that two-dimensional fermionic systems with a nonzero Chern number must break the time-reversal symmetry, manifested by the appearance of chiral edge modes on an open boundary. Such an incompatibility between topology and symmetry can occur more generally. We will refer to this phenomenon as enforced symmetry breaking (ESB) by topological orders. In this work, we systematically study ESB of a finite symmetry group $G_f$ by fermionic invertible topological orders. Mathematically, the group $G_f$ is a central extension over a bosonic symmetry group $G$ by the fermion parity group ${\mathbb{Z}}_2^f$, characterized by a 2-cocycle $\lambda \in {\mathcal{H}}^2(G,{\mathbb{Z}}_2)$. For given $G$ and $\lambda$, we are able to obtain a series of criteria on the existence or nonexistence of ESB by the corresponding fermionic invertible topological orders. For 2D systems, we define a set of physical quantities to describe symmetry-enriched invertible topological orders and derive obstruction functions using both fermionic and bosonic languages. The study in the bosonic language is performed after gauging the fermion parity, and we find that some obstruction functions are consequences of conditional anomalies of the bosonic symmetry-enriched topological states, with the conditions inherited from the original fermionic system. The obstruction functions are crucial components of the ESB criteria that we derive. With these criteria, we discover many new ESB examples, e.g., we find that the quaternion group $Q_8$ is incompatible with two copies of $p+ip$ superconductors. We also obtain explicit results on the ESB phenomena of the continuous group ${\mathrm{SU}}_f\left(N\right)$ by 2D invertible topological orders through a different argument.

We have performed micro-/nanofocused angle-resolved photoemission spectroscopy (ARPES) on cleaved single-crystal surfaces of bismuth to clarify the spatially resolved electronic states. While the dominant area of the cleaved surface was found to display the well-known Rashba-spin-split surface state with the (111)-surface origin, the steplike region with a typical width of $\sim 10\text{–}20$ $\mu \mathrm{m}$ shows distinctly different band structure and fermiology originating from the hard-to-cleave (100) surface. This unexpected mixture of the (100)-derived electronic states in a tiny area of the cleaved (111) surface is attributed to the crystal planes separated by a twin boundary, as supported by laser microscopy and electron backscatter diffraction measurements. The present study paves a pathway toward investigating electronic states associated with inhomogeneities and coexisting phases of hard-to-cleave crystal planes and complex materials by spatially resolved ARPES, making this technique a powerful method to investigate the interplay between local electronic states and crystal structures when combined with structural characterization techniques.