We present a first-principles approach for the computation of the magnetic Gibbs free energy of materials using magnetically constrained supercell calculations. Our approach is based on an adiabatic approximation of slowly varying local moment orientations, the so-called finite-temperature disordered local moment picture. It describes magnetic phase transitions and how electronic and/or magnetostructural mechanisms generate a discontinuous (first-order) character. We demonstrate that the statistical mechanics of the local moment orientations can be described by an affordable number of supercell calculations containing noncollinear magnetic configurations. The applicability of our approach is illustrated by firstly studying the ferromagnetic state in bcc Fe. We then investigate the temperature-dependent properties of a triangular antiferromagnetic state stabilizing in two antiperovskite systems ${\mathrm{Mn}}_{3}A\text{N}$ ($A=\text{Ga}$, Ni). Our calculations provide the negative thermal expansion of these materials as well as the ab initio origin of the discontinuous character of the phase transitions, electronic and/or magnetostructural, in good agreement with experiment.

We introduce the dissipation-assisted operator evolution (DAOE) method for calculating transport properties of strongly interacting lattice systems in the high temperature regime. DAOE is based on evolving observables in the Heisenberg picture and applying an artificial dissipation acting on long operators. We represent the observable as a matrix product operator and show that the dissipation leads to a decay of operator entanglement, allowing us to follow the dynamics to long times. We test this scheme by calculating spin and energy diffusion constants in a variety of physical models. By gradually weakening the dissipation, we are able to consistently extrapolate our results to the case of zero dissipation, thus estimating the physical diffusion constant with high precision.

We investigate the rich quantum phase diagram of Wegner's theory of discrete Ising gauge fields interacting with $U\left(1\right)$ symmetric single-component fermion matter hopping on a two-dimensional square lattice. In particular limits, the model reduces to (i) pure ${\mathbb{Z}}_2$ even and odd gauge theories, (ii) free fermions in a static background of deconfined ${\mathbb{Z}}_2$ gauge fields, and (iii) the kinetic Rokhsar-Kivelson quantum dimer model at a generic dimer filling. We develop a local transformation that maps the lattice gauge theory onto a model of ${\mathbb{Z}}_2$ gauge-invariant spin $1/2$ degrees of freedom. Using the mapping, we perform numerical density matrix renormalization group calculations that corroborate our understanding of the limits identified above. Moreover, in the absence of the magnetic plaquette term, we reveal signatures of topologically ordered Dirac semimetal and staggered Mott insulator phases at half filling. At strong coupling, the lattice gauge theory displays fracton phenomenology with isolated fermions being completely frozen and dimers exhibiting restricted mobility. In that limit, we predict that in the ground state, dimers form compact clusters, whose hopping is suppressed exponentially in their size. We determine the band structure of the smallest clusters numerically using exact diagonalization. The rich phenomenology discussed in this paper can be probed in analog and digital quantum simulators of discrete gauge theories and in Kitaev spin-orbital liquids.

Machine-learned force fields (MLFFs) are increasingly used to accelerate first-principles simulations of many materials properties. However, MLFFs are generally trained from density functional theory (DFT) data and thus suffer from the same limitations as DFT. To achieve more predictive accuracy, MLFFs based on higher levels of theory are required, but the training becomes exceptionally arduous. Here, we present an approach to generate MLFFs with beyond DFT accuracy which combines an efficient on-the-fly active learning method and $\mathrm{\Delta }$-machine learning. Using this approach, we generate an MLFF for zirconia based on the random phase approximation (RPA). Specifically, an MLFF trained on the fly during DFT-based molecular dynamics simulations is corrected by another MLFF that is trained on the differences between RPA and DFT calculated energies, forces, and stress tensors. We show that owing to the relatively smooth nature of these differences, the expensive RPA calculations can be performed only on a small number of representative structures of small unit cells selected by rank compression of the kernel matrix. This dramatically reduces the computational cost and allows one to generate an MLFF fully capable of reproducing high-level quantum-mechanical calculations beyond DFT. We carefully validate our approach and demonstrate its success in studying the phase transitions of zirconia. These results open the way to many-body calculations of finite-temperature properties of materials.

We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner by constructing an appropriate open quantum system. We focus on the quantum steady states of such models for both fermionic and bosonic systems. Surprisingly, key features and spatial structures in the steady state cannot be simply understood from the non-Hermitian Hamiltonian alone. Using the 1D Hatano-Nelson model as a paradigmatic example, we show that the steady state has a marked sensitivity to boundary conditions. In particular, the open boundary system can exhibit a large macroscopic length scale, despite having no corresponding long timescale. These effects persist in more general models and are distinct from the localization physics associated with the non-Hermitian skin effect. Further, particle statistics play an unexpected role: The steady-state density profile is dramatically different for fermions versus bosons. Our paper highlights the key role of fluctuations in quantum realizations of non-Hermitian dynamics and provides a starting point for future work on engineered steady states of open quantum systems.

Spin waves have risen as promising candidate information carriers for the next generation of information technologies. Recent experimental demonstrations of their detection using electron spins in diamond pave the way towards studying the back-action of a controllable paramagnetic spin bath on the spin waves. Here, we present a macroscopic quantum theory describing the interaction between spin waves and paramagnetic spins. As a case study, we consider an ensemble of nitrogen-vacancy spins in diamond in the vicinity of an yttrium-iron-garnet thin film. We show how the back-action of the ensemble results in strong and tuneable modifications of the spin wave spectrum and propagation properties. These modifications include the full suppression of spin wave propagation and, in a different parameter regime, the enhancement of their propagation length by $\sim 50\%$ for modes near resonance with the NV transition frequency. Furthermore, we show how the spin wave thermal fluctuations—even down to the quantum magnonic ground state—induce a measurable frequency shift of the paramagnetic spins in the bath. This shift results in a thermal dispersion force that can be measured optically and/or mechanically with a diamond mechanical resonator. In addition, we use our theory to compute the spin wave-mediated interaction between the spins in the bath. We show that all the above effects are measurable by state-of-the-art experiments. Our results provide the theoretical foundation for describing hybrid quantum systems of spin waves and spin baths and establish the potential of quantum spins as active control, sensing, and interfacing tools for spintronics.

Through advanced experimental techniques on ${\mathrm{CrI}}_3$ single crystals, we derive a pressure-temperature phase diagram. We find that $T_c$ increases to $\sim 66$ K with pressure up to $\sim 3$ GPa followed by a decrease to $\sim 10$ K at 21.2 GPa. The experimental results are reproduced by theoretical calculations based on density functional theory where electron-electron interactions are treated by a static on-site Hubbard $U$ on Cr $3d$ orbitals. The origin of the pressure-induced reduction of the ordering temperature is associated with a decrease in the calculated bond angle, from ${95}^{\circ }$ at ambient pressure to $\sim {85}^{\circ }$ at 25 GPa. Above 22 GPa, experiment and theory jointly point to the idea that the ferromagnetically ordered state is destroyed, giving rise first to a complex, unknown magnetic configuration, and at sufficiently high pressures a pure antiferromagnetic configuration. This sequence of transitions in the magnetism is accompanied by a well-detected pressure-induced semiconductor-to-metal phase transition that is revealed by both high-pressure resistivity measurements and ab initio theory.

We investigate the interplay between unitary and nonunitary dynamics after a quantum quench in a noninteracting fermionic chain. In particular, we consider the effect of localized loss processes, for which fermions are added and removed incoherently at the center of the chain. We focus on the hydrodynamic limit of large distances from the localized losses and of long times, with their ratio being fixed. In this limit, the localized losses gives rise to an effective imaginary delta potential (nonunitary impurity), and the time-evolution of the local correlation functions admits a simple hydrodynamic description in terms of the fermionic occupations in the initial state and the reflection and transmission amplitudes of the impurity. We derive this hydrodynamic framework from the ab initio calculation of the microscopic dynamics. This allows us to analytically characterize the effect of losses for several theoretically relevant initial states, such as a uniform Fermi sea, homogeneous product states, or the inhomogeneous state obtained by joining two Fermi seas. In this latter setting, when both gain and loss processes are present, we observe the emergence of exotic nonequilibrium steady states with stepwise uniform density profiles. In all instances, for strong loss and gain rates the coherent dynamics of the system is arrested, which is a manifestation of the celebrated quantum Zeno effect.

We present the derivation and code implementation of a first-principles methodology to calculate the lattice-mediated contributions to the bulk flexoelectric tensor. The approach is based on our recent analytical long-wavelength extension of density-functional perturbation theory [M. Royo and M. Stengel, Phys. Rev. X 9, 021050 (2019)], and avoids the cumbersome numerical derivatives with respect to the wave vector that were adopted in previous implementations. To substantiate our results, we revisit and numerically validate the sum rules that relate flexoelectricity and uniform elasticity by generalizing them to regimes where finite forces and stresses are present. We also revisit the definition of the elastic tensor under stress, especially in regards to the existing linear-response implementation. We demonstrate the performance of our method by applying it to representative cubic crystals and to the tetragonal low-temperature polymorph of ${\mathrm{SrTiO}}_3$, obtaining excellent agreement with the available literature data.

The electric or magnetic control of band splitting in ferroelectric or ferromagnetic materials is one of the central themes in the context of spin orbitronics. The conventional controllable splitting patterns can be mainly categorized into three types including Rashba-, Dresselhaus-, and Zeeman-type spin splittings, which originate from either a spin-orbit interaction or magnetic exchange interaction. The discovery of new patterns of controllable band splittings and understanding their mechanisms are important not only from a fundamental perspective, but also for practical applications in the design of spin-orbitronic devices. Here, by first-principles calculations and a symmetry analysis, we identify the existence of a band splitting pattern in $Pnma$ ferromagnetic ${\mathrm{YTiO}}_3$ that is controllable by a magnetic field. In sharp contrast to the conventional band splitting patterns (e.g., Rashba-, Dresselhaus-, and Zeeman-type splittings), the mechanism of our pattern is ascribed to the electrons' orbital degree of freedom. Such a mechanism can be generalized to various ferromagnets adopting the $Pnma$ symmetry. We hope that our research will create another avenue for controlling band splittings and provide an alternative route towards designing magnetically based spin-orbitronic devices.

We investigate the strongly anisotropic near-surface electronic band structure of Ag(110) by multidimensional momentum microscopy within the energy-momentum space of the Brillouin zone accessible to multiphoton photoemission (mPP). The momentum imaging of the near-surface band structure reveals an unexpected plethora of energy-momentum mPP features arising from surface-surface, surface-bulk, and bulk-bulk optical transitions. The nonlinear excitation enables the imaging of the surface and bulk bands over a wider energy-momentum range than is available to linear photoemission spectroscopy. The mPP spectra record the unusual in-surface-plane responses involving resonances with the known Shockley surface states of Ag(110) at the $\overline{Y}$ point, as well as the strongly anisotropic surface state in a minigap at the $\overline{\mathrm{\Gamma }}$ point, which mediates the plasmonic photoemission of Ag(110). In addition, image potential surface states and resonances of Ag(110) appear with different contrast that is defined by their parallel momentum-dependent projections onto the projected bands and gaps, the resonance conditions from the lower surface and bulk bands, as well as the order of the nonlinear photoemission process.

It is shown that the equation of motion of the one-particle Green function of an interacting many-electron system is governed by a multiplicative time-dependent exchange-correlation potential, which is the Coulomb potential of a time-dependent exchange-correlation hole. This exchange-correlation hole fulfills a sum rule, a generalization of the well-known sum rule of the static exchange-correlation hole. It is envisaged that the proposed formalism may provide an alternative route for calculating the Green function by finding a suitable approximation for the exchange-correlation hole or potential based on, e.g., a local-density approximation.

${\mathrm{Ca}}_3{\mathrm{Co}}_2{\mathrm{O}}_6$ is a frustrated magnet consisting of a triangular arrangement of chains of Ising spins. It shows regular magnetization steps versus magnetic field every 1.2 T that are metastable with very slow dynamics. This has puzzled the community for many years and given rise to numerous potential theories. Here we approach the problem by seeking the elusive magnetic equilibrium state at $T=2$ K. To this end, we explore two approaches: (1) bypassing the slow dynamics produced by changing fields by instead field-cooling directly to the target temperature and (2) quantum annealing in transverse magnetic fields. While we observe no measurable effect of the quantum annealing in fields up to 7 T, which is likely due to the large Ising anisotropy of Co spins in this material, we find that for the field cooling in longitudinal fields we achieve the predicted equilibrium 1/3 magnetization. We perform Monte Carlo simulations of the ground state phase diagram and we also simulate the quantum annealing process and find good agreement between experiment and theory. Thus we present an investigation of the elusive ground state properties of the canonical frustrated triangular system ${\mathrm{Ca}}_3{\mathrm{Co}}_2{\mathrm{O}}_6$.

Many-body localized (MBL) phases of disordered quantum many-particle systems have a number of unique properties, including failure to act as a thermal bath and protection of quantum coherence. Studying MBL is complicated by the effects of rare ergodic regions, necessitating large system sizes and averaging over many disorder configurations. Here, building on the Feynman-Vernon theory of quantum baths, we characterize the quantum noise that a disordered spin system exerts on its parts via an influence matrix (IM). In this approach, disorder averaging is implemented exactly, and the thermodynamic-limit IM obeys a self-consistency equation. Viewed as a wave function in the space of trajectories of an individual spin, the IM exhibits slow scaling of temporal entanglement in the MBL phase. This enables efficient matrix-product-states computations to obtain temporal correlations, providing a benchmark for quantum simulations of nonequilibrium matter. The IM quantum noise formulation provides an alternative starting point for novel rigorous studies of MBL.

Time-reversal symmetry breaking (TRSB) in ${\mathrm{UTe}}_2$ was inferred from observations of a spontaneous Kerr response in the superconducting state after cooling in zero magnetic field, while a finite $c$-axis magnetic field training was further used to determine the nature of the nonunitary composite order parameter of this material. Here, we present an extensive study of the magnetic-field-trained Kerr effect, which unveils a unique critical state of pinned “ferromagnetic vortices.” We show that a remanent Kerr signal appears following the removal of a training magnetic field, which reflects the response to the TRSB order parameter and the external magnetic field through the paramagnetic susceptibility. This unambiguously demonstrates the importance of the magnetic fluctuations and their intimate relation to the composite order parameter. Focusing the beam on the center of the sample, we are able to accurately determine the maximum field that is screened by the critical state and the respective critical current. Measurements in the presence of magnetic field show the tendency of the superconductor to produce shielding currents that oppose the increase in vortex-induced magnetization due to the diverging paramagnetic susceptibility.

While the chiral linear Luttinger liquid is integrable via bosonization, its nonlinear counterpart does not admit for an analytic solution. In this work, we find a subextensive number of exact eigenstates for a large family of density-density interaction terms. These states are embedded in a continuum of strongly correlated excited states. The real-space entanglement entropy of some exact states scales logarithmically with system size while that of others has volume-law scaling. We introduce momentum-space entanglement as an unambiguous differentiator between these exact states and the remaining excited states. With regard to momentum space, the exact states behave as bona fide quantum many-body scars: they exhibit identically zero momentum-space entanglement, while typical eigenstates behave thermally. We corroborate this finding by a level statistics analysis. Furthermore, we detail the general formalism for systematically finding all interaction terms and associated exact states, and present a number of infinite exact state sequences extending to arbitrarily high energies. Unlike many previous examples of quantum many-body scars, the exact states uncovered here do not lie at equidistant energies and do not follow from a special operator algebra. Instead, they are uniquely enabled by the interplay of Fermi statistics and chirality.

We present a minimal theory of superconductivity enhancement in ferroelectric-type materials. Simple expressions for the optical mode responsible for the soft mode transition are assumed. A key role is played by the anharmonic phonon damping which is modulated by an external control parameter (electron doping or mechanical strain) causing the appearance of the soft mode. It is shown that the enhancement in the superconducting critical temperature $T_c$ upon approaching the ferroelectric transition from either side is due to the Stokes electron-phonon scattering processes promoted by strong phonon damping effects.

We report a Raman scattering study of nematic degrees of freedom in the iron-based superconductor parent compound $\mathrm{Ba}{\mathrm{Fe}}_2{\mathrm{As}}_2$ under tunable uniaxial strain. We demonstrate that the polarization resolved arsenic (As) phonon intensity can be used to monitor the nematic order parameter as a function of both temperature and strain. At low temperature in the nematic ordered phase, we use it to track the continuous and reversible orientation of nematic domains under variable strain. At higher temperatures, the evolution of the As phonon intensity under strain reflects an enhanced nematic susceptibility close to the nematic transition $T_S$. Its temperature dependence under strong strain qualitatively follows the expected behavior of an Ising order parameter under a symmetry-breaking field. Our elasto-Raman study illustrates the interest of combining selective anisotropic strain with a symmetry-resolved probe like Raman scattering. Elasto-Raman scattering can be applied to a wide variety of quantum materials where uniaxial strain tunes electronic orders.

Recently, evidence has emerged for a field-induced even- to odd-parity superconducting phase transition in $\mathrm{Ce}{\mathrm{Rh}}_2{\mathrm{As}}_2$ [S. Khim et al., Science 373, 1012 (2021)]. Here we argue that the $P4/nmm$ nonsymmorphic crystal structure of $\mathrm{Ce}{\mathrm{Rh}}_2{\mathrm{As}}_2$ plays a key role in enabling this transition by ensuring large spin-orbit interactions near the Brillouin zone boundaries, which naturally leads to the required near-degeneracy of the even- and odd-parity channels. We further comment on the relevance of our theory to FeSe, which crystallizes in the same structure.

Spatially indirect excitons with displaced wave functions of electrons and holes play a pivotal role in a large portfolio of fascinating physical phenomena and emerging optoelectronic applications, such as valleytronics, exciton spin Hall effect, excitonic integrated circuit, and high-temperature superfluidity. Here, we uncover three types of spatially indirect excitons (including their phonon replicas) and their quantum-confined Stark effects in hexagonal boron nitride encapsulated bilayer $\mathrm{W}{\mathrm{Se}}_2$ by performing electric field-tunable photoluminescence measurements. Because of different out-of-plane electric dipole moments, the energy order between the three types of spatially indirect excitons can be switched by a vertical electric field. Remarkably, we demonstrate, assisted by first-principles calculations, that the observed spatially indirect excitons in bilayer $\mathrm{W}{\mathrm{Se}}_2$ are also momentum indirect, involving electrons and holes from Λ and $K$/Γ valleys in the Brillouin zone, respectively. This is in contrast to the previously reported spatially indirect excitons with electrons and holes localized in the same valley. Furthermore, we find that the spatially indirect intervalley excitons in bilayer $\mathrm{W}{\mathrm{Se}}_2$ can exhibit considerable, doping-sensitive circular polarization. The spatially indirect excitons with momentum-dark nature and highly tunable circular polarization may provide a firm basis for the understanding and engineering of technological applications in photonics and optoelectronics.