In this paper and its upcoming sequel, we study nonequilibrium dynamics in driven ($1+1$)-dimensional conformal field theories (CFTs) with periodic, quasiperiodic, and random driving. We study a soluble family of drives in which the Hamiltonian only involves the energy-momentum density spatially modulated at a single wavelength. The resulting time evolution is then captured by a Möbius coordinate transformation. In this paper, we establish the general framework and focus on the first two classes. In periodically driven CFTs, we generalize earlier work and study the generic features of entanglement and energy evolution in different phases, i.e., the heating and nonheating phases and the phase transition between them. In quasiperiodically driven CFTs, we mainly focus on the case of driving with a Fibonacci sequence. We find that (i) the nonheating phases form a Cantor set of measure zero; (ii) in the heating phase, the Lyapunov exponents (which characterize the growth rate of the entanglement entropy and energy) exhibit self-similarity, and can be arbitrarily small; (iii) the heating phase exhibits periodicity in the location of spatial structures at the Fibonacci times; (iv) one can find exactly the nonheating fixed point, where the entanglement entropy and energy oscillate at the Fibonacci numbers, but grow logarithmically and polynomially at the non-Fibonacci numbers; (v) for certain choices of driving Hamiltonians, the nonheating phases of the Fibonacci driving CFT can be mapped to the energy spectrum of electrons propagating in a Fibonacci quasicrystal. In addition, another quasiperiodically driven CFT with an Aubry-André–type sequence is also studied. We compare the CFT results to lattice calculations and find remarkable agreement.

We report a stable magnetic domain wall in a uniform ferromagnetic spin-1 condensate, characterized by the magnetization having a dark soliton profile with nonvanishing superfluid density. We find exact stationary solutions for a particular ratio of interaction parameters with and without magnetic fields, and develop an accurate analytic solution applicable to the whole ferromagnetic phase. In the absence of magnetic fields, this domain wall relates various distinct solitary excitations in binary condensates through $\text{SO}\left(3\right)$ spin rotations, which otherwise are unconnected. Remarkably, studying the dynamics of a quasi-two-dimensional (quasi-2D) system we show that standing wave excitations of the domain wall oscillate without decay, being stable against the snake instability. The domain wall is dynamically unstable to modes that cause the magnetization to grow perpendicularly while leaving the domain wall unchanged. Real-time dynamics in the presence of white noise reveals that this “spin twist” instability does not destroy the topological structure of the magnetic domain wall.

We investigate an electrostatically defined quantum point contact (QPC) in a high-mobility InSb two-dimensional electron gas. Well-defined conductance plateaus are observed, and the subband structure of the QPC is extracted from finite-bias measurements. The Zeeman splitting is measured in both in-plane and out-of-plane magnetic fields. We find an in-plane $g$ factor $|g_{\parallel }^{*}|\approx 40$. The out-of-plane $g$ factor is measured to be $|g_{\perp }^{*}|\approx 50$, which is close to the $g$ factor in the bulk.

Starting from the Luttinger model for the band structure of GaAs, we derive an effective theory that describes the coupling of the fractional quantum Hall (FQH) system with photons in resonant Raman scattering experiments. Our theory is applicable in the regime when the energy of the photons ${\omega }_0$ is close to the energy gap $E_G$, but $|{\omega }_0-E_G|$ is much larger than the energy scales of the quantum Hall problem. In the literature, it is often assumed that Raman scattering measures the dynamic structure factor $S(\omega ,\mathbf{k})$ of the FQH. However, in this paper, we find that the light scattering spectra measured in the experiments are proportional to the spectral densities of a pair of operators which we identified with the spin-2 components of the kinetic part of the stress tensor. In contrast with the dynamic structure factor, these spectral densities do not vanish in the long-wavelength limit $k\to 0$. We show that Raman scattering with circularly polarized light can measure the spin of the magnetoroton excitation in the FQH system. We give an explicit expression for the kinetic stress tensor that works on any Landau level and which can be used for numerical calculations of the spectral densities that enter the Raman scattering amplitudes. We propose that Raman scattering provides a way to probe the bulk of the $\nu =\frac{5}{2}$ quantum Hall state to determine its nature.

We propose a mechanism for light-induced unconventional superconductivity in a two-valley semiconductor with a massive Dirac-type band structure. The superconducting phase results from the out-of-equilibrium excitation of carriers in the presence of Coulomb repulsion and is stabilized by coupling the driven semiconductor to a bosonic or fermionic thermal bath. We consider a circularly polarized light pump and show that by controlling the detuning of the pump frequency relative to the band gap, different types of chiral superconductivity would be induced. The emergence of novel superconducting states, such as the chiral $p$-wave pairing, results from the Floquet engineering of the interaction. This is realized by modifying the form of the Coulomb interaction by projecting it into the states that are resonant with the pump frequency. We show that the resulting unconventional pairing in our system can host topologically protected chiral bound states. We discuss a promising experimental platform to realize our proposal and detect the signatures of the emergent superconducting state.

Many media are divided into elementary units with irregular shape and size, as exemplified by domains in magnetic materials, bubbles in foams, or cells in biological tissues. Such media are essentially characterized by geometrical disorder of their elementary units, which we term cells. Cells set a reference scale at which are often assessed parameters and fields reflecting material properties and state. Here, we consider the spectral analysis of spatially varying fields. Such analysis is difficult in geometrically disordered media, because space discretization based on standard coordinate systems is not commensurate with the natural discretization into geometrically disordered cells. Indeed, we found that two classical spectral methods, the fast Fourier transform and the graph Fourier transform, fail to reproduce all expected properties of spectra of plane waves and of white noise. We therefore built a method, which we call cellular Fourier transform (CFT), to analyze cell-scale fields, which comprise both discrete fields defined only at cell level and continuous fields smoothed out from their subcell variations. Our approach is based on the construction of a discrete operator suited to the disordered geometry and on the computation of its eigenvectors, which, respectively, play the same role as the Laplace operator and sine waves in Euclidean coordinate systems. We show that CFT has the expected behavior for sinusoidal fields and for random fields with long-range correlations. Our approach for spectral analysis is suited to any geometrically disordered material, such as a biological tissue with complex geometry, opening the path to systematic multiscale analyses of material behavior.

The La-based “214” cuprates host several symmetry-breaking phases, including superconductivity, charge and spin order in the form of stripes, and a structural orthorhombic-to-tetragonal phase transition. Therefore these materials are an ideal system to study the effects of uniaxial stress onto the various correlations that pervade the cuprate phase diagram. We report resonant x-ray scattering experiments on ${\text{La}}_{1.475}{\text{Nd}}_{0.4}{\text{Sr}}_{0.125}\text{Cu}{\text{O}}_4$(LNSCO-125) that reveal a significant response of charge stripes to uniaxial tensile stress of $\sim 0.1\mathrm{GPa}$. These effects include a reduction of the onset temperature of stripes by $\sim 50\mathrm{K}$, a 29-K reduction of the low-temperature orthorhombic-to-tetragonal transition, competition between charge order and superconductivity, and a preference for stripes to form along the direction of applied stress. Altogether, we observe a dramatic response of the electronic properties of LNSCO-125 to a modest amount of uniaxial stress.

We measure electronic transport through point contacts in a high-mobility electron gas in a Ga[Al]As heterostructure at different temperatures and bulk electron densities. The conductance through all point contacts increases with increasing temperature in a temperature window around $T\sim 10\mathrm{K}$ for all investigated electron densities and point contact widths. For high electron densities this conductance exceeds the fundamental ballistic limit (Sharvin limit). These observations are in agreement with a viscous electron transport model and previous experiments in graphene.

The ultrafast dynamics of magnetic order in a ferromagnet are governed by the interplay between electronic, magnetic, and lattice degrees of freedom. In order to obtain a microscopic understanding of ultrafast demagnetization, information on the response of all three subsystems is required. A consistent description of demagnetization and microscopic energy flow, however, is still missing. Here, we combine a femtosecond electron diffraction study of the ultrafast lattice response of nickel to laser excitation with ab initio calculations of the electron-phonon interaction and energy-conserving atomistic spin dynamics simulations. Our model is in agreement with the observed lattice dynamics and previously reported electron and magnetization dynamics. Our approach reveals that the spin system is the dominating heat sink in the initial few hundred femtoseconds and implies a transient nonthermal state of the spins. Our results provide a clear picture of the microscopic energy flow between electronic, magnetic, and lattice degrees of freedom on ultrafast timescales and constitute a foundation for theoretical descriptions of demagnetization that are consistent with the dynamics of all three subsystems.

We address the long-standing question of the nature of oxygen vacancies in strontium titanate, using a combination of density functional theory and dynamical mean-field theory ($\mathrm{DFT}+\mathrm{DMFT}$) to investigate in particular the effect of vacancy-site correlations on the electronic properties. Our approach uses a minimal low-energy electronic subspace including the $\mathrm{Ti}-t_{2g}$ orbitals plus an additional vacancy-centered Wannier function, and it provides an intuitive and physically transparent framework to study the effect of the local electron-electron interactions on the excess charge introduced by the oxygen vacancies. We estimate the strength of the screened interaction parameters using the constrained random phase approximation, and we find a sizable Hubbard $U$ parameter for the vacancy orbital. Our main finding, which reconciles previous experimental and computational results, is that the ground state is either a state with double occupation of the localized defect state or a state with a singly occupied vacancy and one electron transferred to the conduction band. The balance between these two competing states is determined by the strength of the interaction both on the vacancy and the Ti sites, and on the Ti-Ti distance across the vacancy. Finally, we contrast the case of vacancy doping in $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ with doping via La substitution, and we show that the latter is well described by a simple rigid-band picture.

The phenomenon of dielectric friction predicts slowing down of rotational and translational diffusion of a dipolar tracer in a polar medium due to retarded response of the medium polarization. This problem is studied here by numerical simulations in which the dipole moment of the tracer (solute) is continuously increased. The rotational time of the solute increases linearly with its squared dipole moment. A more pronounced effect of the solute dipole is found on the relaxation time of the electric field of the medium acting on the dipole: We report two orders of magnitude retardation for the electric field dynamics. With this strong retardation, classical theories of dielectric friction fail to describe slowing down of rotational diffusion. This failure is traced back to the breakdown of additivity between friction produced by van der Waals and electrostatic forces and torques. In contrast to the neglect of their correlations by traditional models, electrostatic and van der Waals forces and torques are strongly correlated. Electrostatic interactions bring to linear transport coefficients a number of features typically associated with the dynamics of low-temperature and supercooled liquids. The translational diffusion coefficient becomes strongly anisotropic in the solute's body frame, which translates to non-Gaussian translational dynamics. The Stokes-Einstein-Debye relation connecting the translational and rotational single-particle dynamics deviates from the hydrodynamic limit in linear proportion to the squared solute dipole. It is also found to increase with lowering temperature in qualitative agreement with phenomenology of supercooled liquids.

We describe a mechanism by which the longitudinal thermal conductivity ${\kappa }_{xx}$, measured in an in-plane magnetic field, oscillates as a function of field angle in layered nodal superconductors. These oscillations occur when the spin-orbit splitting at the nodes is larger than the nodal scattering rate, and are complementary to vortex-induced oscillations identified previously. In sufficiently anisotropic materials, the spin-orbit mechanism may be dominant. As a particular application, we focus on the cuprate high-temperature superconductor ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$. This material belongs to the class of Rashba bilayers, in which individual ${\mathrm{CuO}}_2$ layers lack inversion symmetry although the crystal itself is globally centrosymmetric. We show that spin-orbit coupling endows ${\kappa }_{xx}/T$ with a characteristic dependence on magnetic field angle that should be easily detected experimentally, and argue that for underdoped samples the spin-orbit contribution is larger than the vortex contribution. A key advantage of the magnetothermal conductivity is that it is a bulk probe of spin-orbit physics, and therefore not sensitive to inversion breaking at surfaces.

We study the quench dynamics of non-Hermitian topological models with non-Hermitian skin effects. Adopting the non-Bloch band theory and projecting quench dynamics onto the generalized Brillouin zone, we find that emergent topological structures, in the form of dynamic skyrmions, exist in the generalized momentum-time domain, and are correlated with the non-Bloch topological invariants of the static Hamiltonians. The skyrmion structures anchor on the fixed points of dynamics whose existence is conditional on the coincidence of generalized Brillouin zones of the pre- and post-quench Hamiltonians. Global features of dynamic skyrmions, however, persist well beyond such a condition, constituting signatures for a general dynamic detection scheme of non-Bloch topology in the presence of non-Hermitian skin effects. Applying our theory to an experimentally relevant, nonunitary quantum walk, we explicitly demonstrate how the non-Bloch topological invariants can be revealed through the non-Bloch quench dynamics.

Given a class of $q$-local Hamiltonians, is it possible to find a simple variational state whose energy is a finite fraction of the ground-state energy in the thermodynamic limit? Whereas product states often provide an affirmative answer in the case of bosonic (or qubit) models, we show that Gaussian states fail dramatically in the fermionic case, such as for the Sachdev-Ye-Kitaev (SYK) models. This prompts us to propose a new class of wave functions for SYK models inspired by the variational coupled cluster algorithm. We introduce a static “(0+0)-dimensional” large-$N$ field theory to study the energy, two-point correlators, and entanglement properties of these states. Most importantly, we demonstrate a finite disorder-averaged approximation ratio of $r\approx 0.62$ between the variational and ground-state energy of the SYK model for $q=4$. Moreover, the variational states provide an exact description of spontaneous symmetry breaking in a related two-flavor SYK model.

Kitaev materials are promising materials for hosting quantum spin liquids and investigating the interplay of topological and symmetry-breaking phases. We use an unsupervised and interpretable machine-learning method, the tensorial-kernel support vector machine, to study the honeycomb Kitaev-$\mathrm{\Gamma }$ model in a magnetic field. Our machine learns the global classical phase diagram and the associated analytical order parameters, including several distinct spin liquids, two exotic $S_3$ magnets, and two modulated $S_3\times Z_3$ magnets. We find that the extension of Kitaev spin liquids and a field-induced suppression of magnetic order already occur in the large-$S$ limit, implying that critical parts of the physics of Kitaev materials can be understood at the classical level. Moreover, the two $S_3\times Z_3$ orders are induced by competition between Kitaev and $\mathrm{\Gamma }$ spin liquids and feature a different type of spin-lattice entangled modulation, which requires a matrix description instead of scalar phase factors. Our work provides a direct instance of a machine detecting new phases and paves the way towards the development of automated tools to explore unsolved problems in many-body physics.

Interacting single-level quantum dots connected to BCS superconducting leads represent a well-controllable system to study the interplay between the correlation effects and the electron pairing that can result in a $0-\pi$ (singlet-doublet) quantum phase transition (QPT). The physics of this system can be well described by the impurity Anderson model. We present an analysis of the statistics of the perturbation expansion order of the continuous-time hybridization expansion quantum Monte Carlo algorithm in the vicinity of such a first-order impurity QPT. By calculating the moments of the histograms of the expansion order which deviate from the ideal Gaussian shape, we provide an insight into the thermodynamic mixing of the two phases at low but finite temperatures, which is reflected in the bimodal nature of the histograms.

An indispensable step to understand collective magnetic phenomena in rare-earth compounds is the determination of spatially anisotropic single-ion properties resulting from spin-orbit coupling and crystal field (CF). The CF Hamiltonian has a discrete energy spectrum—accessible to spectroscopic probes such as neutron scattering—controlled by a number of independent parameters reflecting the point symmetry of the magnetic sites. Determining these parameters in low-symmetry systems is often challenging. Here, we describe a general method to analyze CF excitation spectra using adjustable effective point-charges. We benchmark our method to existing neutron-scattering measurements on pyrochlore rare-earth oxides and obtain a universal point-charge model that describes a large family of related materials. We adapt this model to the newly discovered tripod kagome magnets ($R_3{\mathrm{Mg}}_2{\mathrm{Sb}}_3{\mathrm{O}}_{14}, R$ = Tb, Ho, Er, Yb) for which we report broadband inelastic neutron-scattering spectra. Analysis of these data using adjustable point-charges yields the CF wave functions for each compound. From this, we calculate thermomagnetic properties that accurately reflect our measurements on powder samples and predict the effective gyromagnetic tensor for pseudospin degrees of freedom—a crucial step to understand the exotic collective properties of these kagome magnets at low temperature. We present further applications of our method to other tripod kagome materials and triangular rare-earth compounds $R{\mathrm{MgGaO}}_4$ ($R$ =Yb, Tm). Overall, this study establishes a widely applicable methodology to predict CF and single-ion properties of rare-earth compounds based on interpretable and adjustable models of effective point charges.

We develop a nonperturbative approach to the bulk polarization of crystalline electric insulators in $d\ge 1$ dimensions. Formally, we define polarization via the response to background fluxes of both charge and lattice translation symmetries. In this approach, the bulk polarization is related to properties of magnetic monopoles under translation symmetries. Specifically, in 2D, the monopole is a source of $2\pi$ flux, and the polarization is determined by the crystal momentum of the $2\pi$ flux. In 3D, the polarization is determined by the projective representation of translation symmetries on Dirac monopoles. Our approach also leads to a concrete scheme to calculate polarization in 2D, which in principle can be applied even to strongly interacting systems. For open boundary conditions, the bulk polarization leads to an altered boundary Luttinger theorem (constraining the Fermi surface of surface states) and also to modified Lieb-Schultz-Mattis theorems on the boundary, which we derive.

Majorana corner modes appearing in two-dimensional second-order topological superconductors have great potential applications for fault-tolerant topological quantum computations. We demonstrate that in the presence of an in-plane magnetic field, two-dimensional ($s+p$)-wave superconductors host Majorana corner modes, whose location can be manipulated by the direction of the magnetic field. In addition, we discuss the effects of edge imperfections on the Majorana corner modes. We describe how different edge shapes and edge disorder affect the number and controllability of the Majorana corner modes, which is of relevance for the implementation of topological quantum computations. We also discuss tunneling spectroscopy in the presence of the Majorana corner modes, where a lead wire is attached to the corner of the noncentrosymmetric superconductor. The zero-bias differential conductance shows a distinct periodicity with respect to the direction of the magnetic field, which demonstrates the excellent controllability of the Majorana corner modes in this setup. Our results lay the theoretical groundwork for observing and tuning Majorana corner modes in experiments on ($s+p$)-wave superconductors.

Simulating quantum circuits with classical computers requires resources growing exponentially in terms of system size. Real quantum computer with noise, however, may be simulated polynomially with various methods considering different noise models. In this work, we simulate random quantum circuits in one dimension with matrix product density operators (MPDOs), for different noise models such as dephasing, depolarizing, and amplitude damping. We show that the method based on matrix product states (MPSs) fails to approximate the noisy output quantum states for any of the noise models considered, while the MPDO method approximates them well. Compared with the method of matrix product operators (MPOs), the MPDO method reflects a clear physical picture of noise (with inner indices taking care of the noise simulation) and quantum entanglement (with bond indices taking care of two-qubit gate simulation). Consequently, in case of weak system noise, the resource cost of the MPDO will be significantly less than that of the MPO due to a relatively small inner dimension needed for the simulation. In case of strong system noise, a relatively small bond dimension may be sufficient to simulate the noisy circuits, indicating a regime that the noise is large enough for an “easy” classical simulation, which is further supported by a comparison with the experimental results on an IBM cloud device. Moreover, we propose a more effective tensor updates scheme with optimal truncations for both the inner and the bond dimensions, performed after each layer of the circuit, which enjoys a canonical form of the MPDO for improving simulation accuracy. With truncated inner dimension to a maximum value $\kappa$ and bond dimension to a maximum value $\chi$, the cost of our simulation scales as $\sim ND{\kappa }^3{\chi }^3$, for an $N$-qubit circuit with depth $D$.