Phases manifesting topological patterns in functional systems, like ferroelectric and ferromagnetic vortex superlattices, can manifest intricate and apparently ungovernable behavior, typical of frustrated nonergodic states with high-dimensional energy landscapes. This is also the case for potassium-tantalate-niobate (KTN) crystals. These transparent ferroelectrics manifest remarkable but little understood metastable domain patterns at optical (micrometer and above) scales near the cubic-to-tetragonal structural phase transition. Here, we formulate the topological breakdown model based on the competition between intrinsic scales of domain-domain collinear and noncollinear interactions associated with polarization-charge screening. The model is able to explain observed KTN mesoscopic domain patterns and phase diagram as a function of temperature and external electric field. Findings include a precise set of sharp and broad percolative transitions that are experimentally verified, validating our model. Our study identifies the central role played by competing topologically protected states, identifying a fundamental link between topological protection and frustration that supports a hitherto unexplored functional nonergodic arena.

We generalize the three two-particle Bethe-Salpeter equations to ten three-particle ladders. These equations are exact and yield the exact three-particle vertex, if we knew the three-particle vertex irreducible in one of the ten channels. However, as we do not have this three-particle irreducible vertex at hand, we approximate this building block for the ladder by the sum of two-particle irreducible vertices, each connecting two fermionic lines. The comparison to the exact solution shows that this approximation is only good for rather weak interactions and even then only qualitatively—at least for the nonlinear response function analyzed.

The multipoint numerical renormalization group (mpNRG) is a powerful impurity solver that provides accurate spectral data useful for computing local, dynamic correlation functions in imaginary or real frequencies nonperturbatively across a wide range of interactions and temperatures. It gives access to a local, nonperturbative four-point vertex in imaginary and real frequencies, which can be used as input for subsequent computations such as diagrammatic extensions of dynamical mean-field theory. However, computing and manipulating the real-frequency four-point vertex on large, dense grids quickly becomes numerically challenging when the density and/or the extent of the frequency grid is increased. In this paper, we compute four-point vertices in a strongly compressed quantics tensor train format using quantics tensor cross interpolation, starting from discrete partial spectral functions obtained from mpNRG. This enables evaluations of the vertex on frequency grids with resolutions far beyond the reach of previous implementations. We benchmark this approach on the four-point vertex of the single-impurity Anderson model across a wide range of physical parameters, both in its full form and in its asymptotic decomposition. For imaginary frequencies, the full vertex can be represented to an accuracy on the order of $2\times {10}^{-3}$ with maximum bond dimensions not exceeding 120. The more complex full real-frequency vertex requires maximum bond dimensions not exceeding 170 for an accuracy of $\lesssim 2\%$. Our work marks another step toward tensor-train-based diagrammatic calculations for correlated electronic lattice models starting from a local, nonperturbative mpNRG vertex.

A Berry phase of odd multiples of $\pi$ inferred from quantum oscillations (QOs) has often been treated as evidence for nontrivial reciprocal space topology. However, disentangling the Berry phase values from the Zeeman effect and the orbital magnetic moment is often challenging. In centrosymmetric compounds, the case is simpler as the orbital magnetic moment contribution is negligible. Although the Zeeman effect can be significant, it is usually overlooked in most studies of QOs in centrosymmetric compounds. Here, we present a detailed study on the nonmagnetic centrosymmetric ${\mathrm{SrGa}}_2$ and ${\mathrm{BaGa}}_2$, which are predicted to be Dirac nodal line semimetals based on density functional theory (DFT) calculations. Evidence of the nontrivial topology is found in magnetotransport measurements. The Fermi surface topology and band structure are carefully studied through a combination of angle-dependent QOs, angle-resolved photoemission spectroscopy (ARPES), and DFT calculations, where the nodal line is observed in the vicinity of the Fermi level. Strong de Haas–van Alphen fundamental oscillations associated with higher harmonics are observed in both compounds, which are well fitted by the Lifshitz-Kosevich (LK) formula. However, even with the inclusion of higher harmonics in the fitting, we found that the Berry phases cannot be unambiguously determined when the Zeeman effect is included. We revisit the LK formula and analyze the phenomena and outcomes that were associated with the Zeeman effect in previous studies. Our experimental results confirm that ${\mathrm{SrGa}}_2$ and ${\mathrm{BaGa}}_2$ are Dirac nodal line semimetals. Additionally, we highlight the often overlooked role of spin-damping terms in Berry phase analysis.

The fractional quantum Hall effect provides the first example of multiple quantum phases hosting quasiparticles not being fermions or bosons, but anyons. It is therefore important to investigate whether all these phases can be practical to detect these anyons. Here, we propose revisiting the intriguing physics of hole-conjugate Fractional Quantum Hall (FQH) phases with counter-propagating edge channels in the filling factor range $1/2\le \nu \le 1$ whose properties may prevent anyon interference detection. In the seminal KFP model by Kane, Fisher, and Polchinski, upstream neutral and downstream charge modes, along with random incoherent interchannel tunneling, are considered essential for explaining the observed conductance at $\nu =2/3$. In this work, we introduce a minimal model that qualitatively reproduces the edge physics of the $\nu =2/3$ FQH phase without invoking neutral and charge modes. By inserting $N$ fictive reservoirs—either Landauer reservoirs (LRs) or Energy-Preserving Reservoirs (EPRs)—along the counter-propagating channels to simulate edge channel mixing, we show that the conductance rapidly approaches the KFP fixed point of $2/3\times (e^2/h)$ for both EPRs and LRs. While LRs produce equal charge and thermal relaxation lengths, EPRs exhibit an infinite thermal relaxation length, consistent with recent observations. Our model also predicts current noise in small Hall bars that varies linearly with voltage at large bias, with an apparent Fano factor $\simeq 0.19/\sqrt{N+1}$ for $N$ LRs or an exponentially vanishing Fano factor for EPRs. Moreover, with a Quantum Point Contact at the center of the Hall bar, the model predicts the recently observed $0.5e^2/h$ conductance plateau. Finally, early experiments reporting upstream excitations are found to be conveniently explained by upstream diffusive heat flow and delta-$T$ noise, rather than by specific collective neutral modes. The results obtained in this study can be generalized to more complex hole-conjugate fractional quantum Hall phases.

The simulation of quantum many-body systems, relevant for quantum chemistry and condensed matter physics, is one of the most promising applications of near-term quantum computers before fault-tolerance. However, since the vast majority of quantum computing technologies are built around qubits and discrete gate-based operations, the translation of the physical problem into this framework is a crucial step. This translation will often be device specific, and a suboptimal implementation will be punished by the exponential compounding of errors on real devices. The importance of an efficient mapping is already revealed for models of spinful fermions in two or three dimensions, which naturally arise when the relevant physics relates to electrons. Using the most direct and well-known mapping, the Jordan-Wigner transformation, leads to a nonlocal representation of local degrees of freedom, and necessities efficient decompositions of nonlocal unitary gates into a sequence of hardware accessible local gates. In this paper, we provide a step-by-step recipe for simulating the paradigmatic two-dimensional Fermi-Hubbard model on a quantum computer using only local operations. To provide the ingredients for such a recipe, we briefly review the plethora of different approaches that have emerged recently but focus on the Derby-Klassen compact fermion mapping to make our discussion concrete. We provide a detailed recipe for an end-to-end simulation including embedding on a physical device, preparing initial states such as ground states, simulation of unitary time evolution, and measurement of observables and spectral functions. We explicitly compute the resource requirements for simulating a global quantum quench and conclude by discussing the challenges and future directions for simulating strongly correlated fermionic matter on quantum computers.

Rashba-type spin-orbit coupling gives rise to distinctive surface and interface phenomena, such as spin-momentum locking and spin splitting. In nonequilibrium settings, one of the key manifestations is the (Rashba-)Edelstein effect, where an electric current generates a net spin or orbital polarization perpendicular to the current direction. While the steady-state behavior of these effects is well studied, their dynamics on ultrafast timescales remain largely unexplored. In this work, we present a theoretical investigation of the ultrafast spin and orbital Edelstein effects on an Au(001) surface, triggered by excitation with a femtosecond laser pulse. These effects are intrinsic and inherently nonlinear. Using a real-space tight-binding model combined with time evolution governed by the von Neumann equation, we simulate the electron dynamics in response to the pulse. Our results reveal pronounced differences between the spin and orbital responses, offering detailed insights into their distinct temporal profiles and magnitudes. We further explore the associated charge, spin, and orbital currents, including the emergence of laser-induced spin and orbital Hall effects. Finally, we quantify the angular momentum transfer mediated by the light-matter interaction. These findings shed light on the intricate ultrafast dynamics driven by spin-orbit coupling and offer guidance for the design of next-generation spintronic and orbitronic devices.

We demonstrate longtime coherent subharmonic motion of a many-boson system subjected to an external time-periodic driving force. The underlying mechanism is exemplified numerically through analysis of a periodically driven Bose-Hubbard dimer, and clarified conceptually by semiclassical requantization of invariant tubes pertaining to the system’s mean-field description. In this way, one arrives at pre-Floquet states that relate to the actual many-body Floquet states in a manner similar to the relation of site-localized Wannier states to lattice-extended Bloch states in solid-state physics. It is argued that even high-order subharmonic response can be systematically engineered, and be observed experimentally, with weakly interacting Floquet condensates comprising a sufficiently large number of particles.

Quantum error correction protects quantum information against decoherence, provided the noise strength remains below a critical threshold. This threshold marks the critical point for the decoding phase transition. Here, we connect this transition in the toric code to a topological phase transition in disordered Majorana fermions at high temperatures. A quantum memory in the error-correctable phase is captured by the presence of a Majorana zero mode, trapped in vortex defects associated with twisted boundary conditions. These results are established by expressing the coherent information, which measures the amount of recoverable quantum information in a given noisy code, in terms of a mixed-state topological order parameter of fermions. Our work hints at a broader connection of the robustness of quantum information in stabilizer codes and mixed-state topological phase transitions in symmetry-protected fermion matter.

The presence of topological defects in apolar chiral liquid crystals causes orientational distortions, leading to nonuniform strain. This nonuniform strain generates an electric polarization response due to the flexoelectric effect, which induces an internal electric field. Associated with this electric field is an electrostatic self-energy, which has a backreaction on the director field. Calculation of this internal electric field and its resulting backreaction on the director field is complicated. We propose a method to do such, adapting a method recently developed to study the magnetostatic self-interaction effect on skyrmions in chiral ferromagnets. Bloch skyrmions in chiral magnets are solenoidal and are unaffected by the magnetostatic self-interaction. However, Bloch skyrmions in liquid crystals yield nonsolenoidal flexoelectric polarization and, thus, are affected by the electrostatic self-interaction. Additionally, as the flexoelectric coefficients are increased in strength, a transition from a hopfion to a toron is observed in three-dimensional confined systems.

Altermagnets exhibit spontaneously spin-split electronic bands in the zero spin-orbit coupling (SOC) limit arising from the presence of collinear compensated magnetic order. The distinctive magnetocrystalline symmetries of altermagnets ensure that these spin splittings have a characteristic anisotropy in crystal momentum space. These systems have attracted a great deal of interest due to their potential for applications in spintronics. In this paper, we provide a general Landau theory that encompasses all three-dimensional altermagnets where the magnetic order does not enlarge the unit cell. We identify all crystal structures that admit altermagnetism and then reduce these to a relatively small set of distinct possible Landau theories governing such systems. In the zero SOC limit, we determine the possible local multipolar orders that are tied to the spin splitting of the band structure. We make precise the connection between altermagnetism as defined at zero SOC (“ideal” altermagnets) and the effects of weak SOC. In particular, we examine which response functions allowed by symmetry when SOC is present are guaranteed by the spin-orbit free theory and spell out the distinctive properties of altermagnets in comparison with conventional collinear antiferromagnets. Finally, we show how these ideas can be applied by considering a number of altermagnetic candidate materials.

Electronically driven nematic order breaks the rotational symmetry of a system, e.g., through a Pomeranchuk instability of the Fermi surface, with a concomitant distortion of the lattice. As a result, in a metal, the nematic collective mode interacts with two different sets of gapless excitations: the particle-hole excitations of the metal and the lattice fluctuations that become soft at the induced structural transition, namely, the transverse acoustic phonons. However, the dynamics of these hybridized collective modes formed by the transverse acoustic phonons and the metallic electronic nematic fluctuations has remained largely unexplored. Here, we address this problem by developing a formalism in which the nematoelastic coupling is obtained microscopically from the direct coupling between electrons and transverse acoustic phonons enabled by impurities present in the crystal. We then demonstrate the emergence of hybrid nematoelastic modes that mix the characteristics of the transverse phonons and of the nematic fluctuations. Near the nematic quantum critical point in a metal, two massless modes emerge with intertwined dynamic behaviors, implying that neither mode dominates the response of the system. We systematically study the nontrivial dependence of these collective modes on the longitudinal and transverse momenta, revealing a rich landscape of underdamped and overdamped modes as the proximity to the quantum critical point and the strength of the electron-phonon coupling are changed. Since dynamics play an important role for determining superconducting instabilities, our results have implications for the study of pairing mediated by electronic nematic fluctuations.

Thermal radiation features of dynamical axion insulators, which are characterized by an antiferromagnetic order with simultaneously broken time-reversal and space-inversion symmetries, are investigated. Planck's radiation law is shown to exhibit remarkable anisotropic behavior as a result of the strong dispersion caused by the light-matter interaction. A crossover scenario at low temperature is identified and an associated phase highly populated by slow thermal photons is revealed. We show that the asymmetry degree of the heat radiation and its angular distribution can be controlled via a magnetic field, paving the way toward a directional-tunable mechanism for thermal quantum manipulation and storage. Analogies are drawn with the expected behavior of blackbody radiation in the core of neutron stars.

In active matter, such as the Vicsek model of flocking, particles possess an internal degree of freedom, such as their director, which is subject to interaction with other particles, provided they are within a certain range. In an effort to understand better the interplay between spatial and internal degrees of freedom, we study numerically a variation of the $q=2$ Potts model on and off the lattice, where particles are additionally subject to Brownian motion. The lack of a feedback of the internal degrees of freedom to the spatial degrees of freedom renders this model generically nonequilibrium. We confirm previous work that showed that the static exponents of the phase transition are unaffected by the diffusion. In contrast to previous work, we show that the formation of ordered clusters is not undermined by diffusion, but should rather be thought of as an effective form of interaction. We demonstrate how our numerical findings can be understood on the basis of the well-established Model A, B and C: Off lattice, the Brownian $q=2$ Potts model is Model C. On the lattice, it is Model A with an additional (irrelevant, conserved) Model B noise.

A quantum system of interacting particles under the effect of a static external potential is hereby described as kicked when that potential suddenly starts moving with a constant velocity $\mathbf{v}$. If initially in a stationary state, the excess energy at any time after the kick equals $\mathbf{v}·\langle \mathbf{P}\rangle \left(t\right)$, with $\mathbf{P}$ being the total momentum of the system. If the system is finite and remains bound, the long-time average of the excess energy tends to $M{v}^2$, with $M$ the system’s total mass, or a related expression if there is particle emission. $M{v}^2$ is twice what expected from an infinitely smooth onset of motion, and any monotonic onset is expected to increase the average energy to a value within both limits. In a macroscopic system, a particle flow emerges countering the potential’s motion when the particles stay partially behind. For charged particles, the described kinetic kick is equivalent to the kick given by the infinitely short electric-field pulse $\mathcal{E}=\frac{m}{q}\mathbf{v}\delta \left(t\right)$ to the system at rest, useful as a formal limit in ultrafast phenomena. A linear-response analysis of low-$v$ countercurrents in kicked metals shows that the coefficient of the linear term in $v$ is the Drude weight. Nonlinear in $v$ countercurrents are expected for insulators through the electron-hole excitations induced by the kick, going as $v^3$ at low $v$ for centrosymmetric ones. First-principles calculations for simple solids are used to ratify those predictions, although the findings apply more generally to systems such as Mott insulators or cold lattices of bosons or fermions.

We investigate the impact of disorder in the form of impurity scattering on a generalized version of the circular photogalvanic effect (CPGE) in Weyl semimetals where the frequency detuning between the two orthogonally polarized beams is nonzero. Considering a minimal model with two Weyl nodes at different energies, we employ the self-consistent Born approximation to unravel the dependence of the associated two-point retarded Green's function on the strength of intra- and internode scattering, frequency detuning, and energy difference between the two Weyl nodes. In the case of intranode scattering only, the second-order current density acquires Drude-like features, which we elucidate further by introducing an effective scattering strength. The Drude-like theory can even describe the second-order response in the presence of strong internode scattering, provided the latter has a linear interdependence with the intranode scattering. By properly adjusting the frequency detuning, we also find the real part of the two-point retarded Green's function to be reminiscent of a “quantized CPGE”-like form, although the imaginary part of the latter function is in general finite, and the second-order current density oscillates with time due to the finite frequency detuning. We finally conclude with an outlook on possible experimental consequences.

We implement the Gutzwiller wave function for attractive SU(3) fermion systems on a quantum computer using a quantum-classical hybrid scheme based on the discrete Hubbard-Stratonovich transformation. In this approach, the nonunitary Gutzwiller operator is decomposed into a linear combination of unitaries constructed from two-qubit fermionic Givens-rotation gates, whose rotation angles are dictated by the auxiliary fields. We develop and reformulate two complementary methods to perform the sum over these auxiliary fields. In the first method, the Gutzwiller wave function is probabilistically prepared on the register qubits by projectively postselecting the desired state via measurements of ancilla qubits. We analyze the success rate both analytically and numerically as a function of the Gutzwiller variational parameter $g$ for the Fermi-sea and BCS-like trial states at half filling. The success rate is found to decay exponentially for small $\left|g\right|$, but remains finite in the $\left|g\right|\to \infty$ limit, with increasing $\left|g\right|$. In the second method, we employ importance sampling to address the Gutzwiller variational problem, where the central objective is to estimate the expectation values of observables. We demonstrate the proposed scheme by calculating the energy and triple occupancy of the attractive SU(3) Hubbard model in the framework of digital quantum simulation. Moreover, we present experimental results obtained on a trapped-ion quantum computer for the two-site attractive SU(3) Hubbard model, showing good agreement with exact values within statistical errors.

Using the Dirac string formalism for monopoles, we expose an extensive analogy between magnetic monopole excitations in the dumbbell model of spin ice and those of the vacuum. In both cases, the Dirac strings are defined in the space-time of monopole trajectories, which are simulated in spin ice using transition graphs between initial and final configurations. The Stanford experiment for Dirac monopole detection is reconstructed in spin ice using the fragmentation procedure. The setup is then extended to simulate magnetic noise experiments using stochastic dynamics. It is shown that the noise from the monopoles and their constraining strings can be separated and that the correlated signal over long times comes largely from the constraining strings rather than from the monopoles themselves.