We develop a mixed quantum-classical framework, dubbed the Moving Born-Oppenheimer Approximation (MBOA), to describe the dynamics of slow degrees of freedom (DOFs) coupled to fast ones. As in the Born-Oppenheimer Approximation (BOA), the fast degrees of freedom adiabatically follow a state that depends on the slow ones. Unlike the BOA, this state depends on both the positions and the momenta of the slow DOFs. We study several model systems: a spin-1/2 particle and a spinful molecule moving in a spatially inhomogeneous magnetic field, and a gas of fast particles coupled to a piston. The MBOA reveals rich dynamics for the slow degree of freedom, including reflection, dynamical trapping, and mass renormalization. It also significantly modifies the state of the fast DOFs. For example, the spins in the molecule are entangled and squeezed, while the gas of fast particles develops gradients that are synchronized with the motion of the piston for a long time. The MBOA can be used to describe both classical and quantum systems and has potential applications in quantum chemistry, correlated materials, atomic physics, molecular dynamics, and quantum sensing.

Recent advances in ultrafast electron emission, microscopy, and diffraction have demonstrated a remarkable ability to manipulate free electrons with quantum coherence using light beams. Here, we present a framework for exploring free electron quantum number in ultrafast electron-light interactions. We derive an explicit Jackiw-Rebbi solution for a low-energy free electron wavefunction subjected to a spatiotemporally twisted laser field, resulting in a flying topologically protected bound state with a quantum number of e/2 - termed a "half-electron". This flying bound state is dispersion-free due to its topological nature. We demonstrate the topological confinement and pair generation mechanism of half-electrons in free space, expanding their domain beyond the topological states typically found in solids and photonics. This advancement enhances our understanding of emulating exotic quantum and topological effects with low-energy free electrons.

Perhaps the simplest approach to constructing models with sub-dimensional particles or fractons is to require the conservation of dipole or higher multipole moments. We generalize this approach to allow for moments in phase space and classify all possible classical fracton models with phase-space multipole conservation laws. We focus on a new self-dual model that conserves both dipole and quadrupole moments in position and momentum; we analyze its dynamics and find quasi-periodic orbits in phase space that evade ergodic exploration of the full phase space.

Donadi and Hossenfelder claim to have constructed a novel path integral over that reproduces quantum mechanics exactly. We contend that this claim is untenable, have given merely a definition of a certain quantity (which they call a path integral) any way of actually calculating it.

We introduce a numerical method to study critical properties near classical and quantum phase transitions. Our method applies ideas of the Tensor Renormalization Group to obtain an improved action which is used to extract critical properties by performing Monte Carlo simulations on relatively small system sizes. We demonstrate this method on the XY model in three dimensions. Our method may provide a framework with which to efficiently study universal properties in a large class of phase transitions.

We show that the orbital magneto-electric effect (OME) – the generation of a steady-state orbital angular momentum density – is partly the result of a nonequilibrium dipole moment generated via Zitterbewegung and proportional to the quantum metric. For tilted massive Dirac fermions this dipole gives the only contribution to the OME in the insulating case, while the intrinsic and extrinsic OMEs occur for different electric field orientations, yielding an experimental detection method. Our results suggest quantum metric engineering as a route towards maximizing orbital torques.

We present a scenario in which a gapless extended phase serves as a "hub" connecting multiple symmetryenriched deconfined quantum critical points. As a concrete example, we construct a lattice model with Z2xZ2xZ2 symmetry for quantum spin-1/2 degrees of freedom that realizes four distinct gapful phases supporting antiferromagnetic long-range order and one extended incommensurate gapless ferromagnetic phase. The quantum phase transition between any two of the four gapped and antiferromagnetic phases goes through either a (deconfined) quantum critical point, a quantum tricritical point, or the incommensurate gapless ferromagnetic phase. In this phase diagram, it is possible to interpolate between four deconfined quantum critical points by passing through the extended gapless ferromagnetic phase. We identify the phases in the model and the nature of the transitions between them through a combination of analytical arguments and density matrix renormalization group studies.

Evaluations of the orbital Hall effect (OHE) have retained only interband matrix elements of the position operator. Here, we evaluate the OHE including all matrix elements of the position operator, including the technically challenging intraband elements. We recover previous results and find quantum corrections due to the noncommutativity of the position and velocity operators and interband matrix elements of the orbital angular momentum. The quantum corrections dominate the OHE responses of the topological antiferromagnet CuMnAs and of massive Dirac fermions.

The in-plane and out-of-plane superconducting stiffness of La_{1.83}Sr_{0.17}CuO_4La1.83Sr0.17CuO4 rings appear to vanish at different transition temperatures, which contradicts thermodynamical expectation. In addition, we observe a surprisingly strong dependence of the out-of-plane stiffness transition on sample width. With evidence from Monte Carlo simulations, this effect is explained by very small ratio \alphaα of inter-plane over intra-plane Josephson couplings. For three dimensional rings of millimeter dimensions, a crossover from layered three dimensional to quasi one dimensional behavior occurs at temperatures near the thermodynamic transition temperature {T_{c}}Tc, and the out-of-plane stiffness appears to vanish below {T_{c}}Tc by a temperature shift of order \alpha L_a/{\xi^{\parallel}}αLa/ξ∥, where L_a/{\xi^{\parallel}}La/ξ∥ is the sample’s width over coherence length. Including the effects of layer-correlated disorder, the measured temperature shifts can be fit by a value of \alpha=4.1× 10^{-5}α=4.1×10−5, near {T_{c}}Tc, which is significantly lower than its previously measured value near zero temperature.

A computational phase transition in a classical or quantum system is a non-analytic change in behavior of an order parameter which can only be observed with the assistance of a nontrivial classical computation. Such phase transitions, and the computational observables which detect them, play a crucial role in the optimal decoding of quantum error-correcting codes and in the scalable detection of measurement-induced phenomena. In this work we show that computational phase transitions and observables can also provide important physical insight on the phase diagram of a classical statistical physics system, specifically in the context of the dislocation-mediated melting of a two-dimensional antiferromagnetic (AF) crystal. In the solid phase, elementary dislocations disrupt the bipartiteness of the underlying square lattice, and as a result, pairs of dislocations are linearly confined by string-like AF domain walls. It has previously been argued that a novel AF tetratic phase can arise when double dislocations proliferate while elementary dislocations remain bound. However, since elementary dislocations carry AF Ising gauge flux, no local order parameter can distinguish between AF and paramagnetic (PM) tetratic regimes, and consequently there is no thermodynamic phase transition separating the two regimes. Nonetheless, we demonstrate that it is possible to algorithmically construct a staggered magnetization which distinguishes the AF and PM tetratic regimes by "pairing" dislocations, which requires an increasingly nontrivial classical computation as elementary dislocation pairs increase in density and unbind. We discuss both algorithm-dependent and "intrinsic" algorithm-independent computational phase transitions in this setting, the latter of which includes a transition in one's ability to consistently sort atoms into two sublattices to construct a well-defined staggered magnetization.

We generalize the recent work of Shibata and Katsura [Phys. Rev. B 99, 174303 (2019)], who considered a S = 12 chain with alternating XX and YY couplings in the presence of dephasing, the dynamics of which are described by the GKLS master equation. Their model is equivalent to a non -Hermitian system described by the Kitaev formulation [Kitaev, Ann. Phys. 321, 2 (2006)] in terms of a single Majorana species hopping on a two -leg ladder in the presence of a nondynamical Z2 gauge field. Our generalization involves Dirac gamma matrix "spin" operators on the square lattice and maps onto a non -Hermitian square lattice bilayer which is also Kitaev solvable. We describe the exponentially many nonequilibrium steady states in this model. We identify how the spin degrees of freedom can be accounted for in the two-dimensional model in terms of the gauge -invariant quantities and then proceed to study the Liouvillian spectrum. We use simulated annealing to estimate the Liouvillian gap and the first decay modes for large system sizes. We observe a transition in the first decay modes, similar to that in the work of Shibata and Katsura. The results we obtain are compared to the results we obtained from a perturbative analysis for small and large values of the dissipation strength.

Orbitronics harnesses non-equilibrium densities and flows of electrons orbital angular momentum (OAM). Although the OAM must be long lived to be useful in information processing, the mechanisms leading to OAM non-conservation remain unknown. Here we show that an electric field induces an intrinsic torque on the OAM mediated by the quantum metric tensor, without spin-orbit coupling or magnetic fields. The torque vanishes in pseudospin-1/2 systems with particle-hole symmetry but is nonzero in the presence of nontrivial textures. We discuss implications for topological materials and strategies for experimental observation.

We propose a synthetic dimension for ultrafast free electrons based on the discrete energy sidebands in photon-induced near-field electron microscopy (PINEM). The PINEM synthetic dimension can offer a powerful way to coherently shape or modulate free-electron wavefunctions in systems such as ultrafast transmission electron microscopes, dielectric laser accelerators, and quantum free-electron lasers. As examples of this paradigm, we demonstrate Bloch oscillations, diffraction management, and linear optics effects such as Talbot self-imaging in the PINEM lattice. These effects show the potential of PINEM synthetic dimensions as a novel quantum simulation platform.

Time crystals are systems that spontaneously break time-translation symmetry, exhibiting repeating patterns in time. Recent work has shown that non-Hermitian Floquet systems can host a time crystalline phase with quasi-long-range order. In this work, we investigate the effect of introducing a non-integrable interaction term into this non-Hermitian time crystal model. Using a combination of numerical TEBD simulations, mean-field analysis, and perturbation theory, we find that the interaction term has two notable effects. First, it induces a shift in the phase diagram, moving the boundaries between different phases. Second, a sufficiently strong interaction induces an unexpected symmetry-breaking transition, which is not captured by the mean-field approach. Within average Hamiltonian theory, we trace this back to a ferromagnetic transition in the anisotropic non-Hermitian XXZ model. Our results demonstrate that the interplay between non-Hermitian dynamics and many-body interactions can lead to novel symmetry breaking.

The in-plane and out-of-plane superconducting stiffness appear to vanish at different transition temperatures, which contradicts thermodynamical expectation. In addition, we observe a surprisingly strong dependence of the out-of-plane stiffness transition on sample width. With evidence from Monte Carlo simulations, this effect is explained by a crossover from three dimensions into quasi one dimensional behavior of the finite sample. Due to an essential singularity at the thermodynamic transition temperature $T_c$, the out-of-plane stiffness appears to vanish below $T_c$ by an amount which is proportional to the inverse width. A fit of our prediction to the data is used to determine the value of the anisotropy parameter. Analogy to studies of helium superfluids in nanopores is made.

We generalize the recent work of Shibata and Katsura, who considered a S=1/2 chain with alternating XX and YY couplings in the presence of dephasing, the dynamics of which are described by the GKLS master equation. Their model is equivalent to a non-Hermitian system described by the Kitaev formulation in terms of a single Majorana species hopping on a two-leg ladder in the presence of a nondynamical Z_2 gauge field. Our generalization involves Dirac gamma matrix `spin' operators on the square lattice, and maps onto a non-Hermitian square lattice bilayer which is also Kitaev-solvable. We describe the exponentially many non-equilibrium steady states in this model. We identify how the spin degrees of freedom can be accounted for in the 2d model in terms of the gauge-invariant quantities and then proceed to study the Liouvillian spectrum. We use a genetic algorithm to estimate the Liouvillian gap and the first decay modes for large system sizes. We observe a transition in the first decay modes, similar to that found by Shibata and Katsura. The results we obtain are consistent with a perturbative analysis for small and large values of the dissipation strength.

Band-touching Weyl points in Weyl semimetals give rise to many novel characteristics, one of which the presence of surface Fermi-arc states that is topologically protected. The number of such states can be computed by the Chern numbers at different momentum slices, which fluctuates with changing momentum and depends on the distribution of Weyl points in the Brillouin zone. For realistic systems, it may be difficult to locate the momenta at which these Weyl points and Fermi-arc states appear. Therefore, we extend the analysis of a parametric random matrix model proposed by Walker and Wilkinson to find the statistics of their distributions. Our numerical data shows that Weyl points with opposite polarities are short range correlated, and the Chern number fluctuation only grows linearly for a limited momentum difference before it saturates. We also find that the saturation value scales with the total number of bands. We then compute the short-range correlation length from perturbation theory, and derive the dependence of the Chern number fluctuation on the momentum difference, showing that the saturation results from the short-range correlation.