In recent attempts to observe axion electrodynamics, much effort has focused on trilayer heterostructures of magnetic topological insulators, and in particular on the examination of a so-called zero Hall plateau, which has misguidedly been overstated as direct evidence of an axion insulator state. We investigate the general notion of axion insulators, which by definition must contain a nontrivial volume to host the axion term. We conduct a detailed magneto-transport analysis of Chern insulators comprising a single magnetic topological insulator layer of varying thickness as well as trilayer structures, for samples optimized to yield a perfectly quantized anomalous Hall effect. Our analysis gives evidence for a topological magneto-electric effect quantized in units of $e^2/2h$, allowing us to identify signatures of axion electrodynamics. Our observations may provide direct experimental access to electrodynamic properties of the universe beyond the traditional Maxwell equations, and challenge the hitherto proclaimed exclusive link between the observation of a zero Hall plateau and an axion insulator.

The spin-$1/2$ XXZ chain is an integrable lattice model and parts of its spin current can be protected by local conservation laws for anisotropies $-1<\mathrm{\Delta }<1$. In this case, the Drude weight $D\left(T\right)$ is nonzero at finite temperatures $T$. Here we obtain analytical results for $D\left(T\right)$ at low temperatures for zero external magnetic field and anisotropies $\mathrm{\Delta }=cos(n\pi /m)$ with $n,m$ coprime integers, using the thermodynamic Bethe ansatz. We show that to leading orders $D\left(T\right)=D\left(0\right)-a\left(\mathrm{\Delta }\right)T^{2K-2}-b_1\left(\mathrm{\Delta }\right)T^2$ where $K$ is the Luttinger parameter and the prefactor $a\left(\mathrm{\Delta }\right)$, obtained in closed form, has a fractal structure as a function of anisotropy $\mathrm{\Delta }$. The prefactor $b_1\left(\mathrm{\Delta }\right)$, on the other hand, does not have a fractal structure and can be obtained in a standard field-theoretical approach. Including both temperature corrections, we obtain an analytic result for the low-temperature asymptotics of the Drude weight in the entire regime $-1<\mathrm{\Delta }=cos(n\pi /m)<1$.

Identifying the microscopic mechanism for superconductivity in magic-angle twisted bilayer graphene (MATBG) is an outstanding open problem. While MATBG exhibits a rich phase-diagram, driven partly by the strong interactions relative to the electronic bandwidth, its single-particle properties are unique and likely play an important role in some of the phenomenological complexity. Some of the salient features include an electronic bandwidth smaller than the characteristic phonon bandwidth and a nontrivial structure of the underlying Bloch wave functions. We perform a theoretical study of the cooperative effects due to phonons and plasmons on pairing in order to disentangle the distinct role played by these modes on superconductivity. We consider a variant of MATBG with an enlarged number of fermion flavors, $N\gg 1$, where the study of pairing instabilities reduces to the conventional (weak-coupling) Eliashberg framework. In particular, we show that certain umklapp processes involving minioptical phonon modes, which arise physically as a result of the folding of the original acoustic branch of graphene due to the moiré superlattice structure, contribute significantly towards enhancing pairing. We also investigate the role played by the dynamics of the screened Coulomb interaction on pairing, which leads to an enhancement in a narrow window of fillings, and study the effect of external screening due to a metallic gate on superconductivity. At strong coupling, the dynamical pairing interaction leaves a spectral mark in the single-particle tunneling density of states. We thus predict such features will appear at specific frequencies of the umklapp phonons corresponding to the sound velocity of graphene times an integer multiple of the Brillouin zone size.

We report an infrared spectroscopy study of the axion topological insulator candidate $\mathrm{Eu}{\mathrm{In}}_2{\mathrm{As}}_2$ for which the Eu moments exhibit an A-type antiferromagnetic (AFM) order below $T_N\simeq 18\mathrm{K}$. The low-energy response is composed of a weak Drude peak at the origin with a plasma frequency of about $2000{\mathrm{cm}}^{-1}$ and a pronounced infrared-active phonon mode at $185{\mathrm{cm}}^{-1}$. The interband transitions start above $800{\mathrm{cm}}^{-1}$ and give rise to a series of weak absorption bands at 5000 and $12000{\mathrm{cm}}^{-1}$ and strong ones at 20 000, 27 500, and $32000{\mathrm{cm}}^{-1}$. The AFM transition leads to pronounced anomalies of the charge response in terms of a cusp-like maximum of the free carrier scattering rate around $T_N$ and large magnetic splittings of the interband transitions at 5000 and $12000{\mathrm{cm}}^{-1}$. The phonon mode at $185{\mathrm{cm}}^{-1}$ has also an anomalous temperature dependence around $T_N$ which suggests that it couples to the fluctuations of the Eu spins. The combined data provide evidence for a strong interaction among the charge, spin, and lattice degrees of freedom.

${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ (MBT) materials are promising antiferromagnetic topological insulators in which field-driven ferromagnetism is predicted to cause a transition between axion insulator and Weyl semimetallic states. However, the presence of antiferromagnetic coupling between Mn/Bi antisite defects and the main Mn layer can reduce the low-field magnetization, and it has been shown that such defects are more prevalent in the structurally identical magnetic insulator ${\mathrm{MnSb}}_2{\mathrm{Te}}_4$ (MST). We use high-field magnetization measurements to show that the magnetization of MBT and MST occur in stages and full saturation requires fields of $\sim 60$ T. As a consequence, the low-field magnetization plateau state in MBT, where many determinations of the quantum anomalous Hall state are studied, actually consists of ferrimagnetic septuple blocks containing both uniform and staggered magnetization components.

Random measurements have been shown to induce a phase transition in an extended quantum system evolving under chaotic unitary dynamics, when the strength of measurements exceeds a threshold value. Below this threshold, a steady state with a subthermal volume law entanglement emerges, which is resistant to the disentangling action of measurements, suggesting a connection to quantum error-correcting codes. We quantify these notions by identifying a power-law decay of the mutual information $I(\left\{x\right\}:\overline{A})\propto x^{-3/2}$ in the volume-law-entangled phase, between a qudit located a distance $x$ from the boundary of a region $A$, and the complement $\overline{A}$, which implies that a measurement of this qudit will retrieve very little information about $\overline{A}$. We also find a universal logarithmic contribution to the volume law entanglement entropy $S^{\left(2\right)}\left(A\right)=\kappa L_A+\frac{3}{2}log{L}_A$ which is intimately related to the first observation. We obtain these results by relating the entanglement dynamics to the imaginary time evolution of an Ising model, to which we apply field-theoretic and matrix-product-state techniques. Finally, exploiting the error-correction viewpoint, we assume that the volume-law state is an encoding of a Page state in a quantum error-correcting code to obtain a bound on the critical measurement strength $p_c$ as a function of the qudit dimension $d$: $p_{c}log\left[(d^2-1)\left(p_c^{-1}-1\right)\right]\le log\left[(1-p_c)d\right]$. The bound is saturated at $p_c(d\to \infty )=1/2$ and provides a reasonable estimate for the qubit transition: $p_c(d=2)\le 0.1893$.

Several efforts have been made to polarize the nearby nuclear environment of nitrogen-vacancy (NV) centers for quantum metrology and quantum information applications. Different methods showed different nuclear spin polarization efficiencies and rely on electronic spin polarization associated to the NV center, which in turn crucially depends on the intersystem crossing. Recently, the rates involved in the intersystem crossing have been measured leading to different transition rate models. Here, we consider the effect of these rates on several nuclear polarization methods based on the level anticrossing, and precession of the nuclear population while the electronic spin is in the $m_s=0$ and $m_s=1$ spin states. We show that the nuclear polarization depends on the power of optical excitation used to polarize the electronic spin. The degree of nuclear spin polarization is different for each transition rate model. Therefore, the results presented here are relevant for validating these models and for polarizing nuclear spins. Furthermore, we analyze the performance of each method by considering the nuclear position relative to the symmetry axis of the NV center.

Nonlinear Drude weight (NLDW) is a generalization of the linear Drude weight, which characterizes the nonlinear transport in quantum many-body systems. We investigate these weights for the spin-$\frac{1}{2}$ XXZ chain in the critical regime. The effects of the Dzyaloshinskii-Moriya interaction and an external magnetic field are also studied. Solving the Bethe equations numerically, we obtain these weights for very large system sizes and identify parameter regimes where the weights diverge in the thermodynamic limit. These divergences appear in all the orders studied in this Letter and can be regarded as a generic feature of the NLDWs. We study the origin of these divergences and reveal that they result from nonanalytic finite-size corrections to the ground-state energy. Furthermore, we compute closed-form expressions for several weights in the thermodynamic limit and find excellent agreement with the numerical results.

${}^{139}\mathrm{La}$ nuclear magnetic resonance (NMR) measurements under pressure ($p=0–2.64$ GPa) have been carried out to investigate the static and dynamic magnetic properties of the itinerant ferromagnet ${\mathrm{LaCrGe}}_3$. ${}^{139}\mathrm{La}$-NMR spectra for all measured pressures in the ferromagnetically ordered state show a large shift due to the internal field induction $|B_{\mathrm{int}}|\sim 4$ T at the La site produced by Cr ordered moments. The change in $B_{\mathrm{int}}$ by less than 5% with $p$ up to 2.64 GPa indicates that the Cr $3d$ moments are robust under pressure. The temperature dependence of NMR shift and $B_{\mathrm{int}}$ suggest that the ferromagnetic order develops below $\sim 50$ K under higher pressures in a magnetic field of $\sim 7.2$ T. Based on the analysis of NMR data using the self-consistent-renormalization (SCR) theory, the spin fluctuations in the paramagnetic state well above $T_{\mathrm{C}}$ are revealed to be three-dimensional ferromagnetic throughout the measured $p$ region.

Nuclear magnetism in $n$-doped semiconductors with a positive hyperfine constant is revisited. Two kinds of nuclear magnetic ordering can be induced by resident electrons in a deeply cooled nuclear spin system. At positive nuclear spin temperature below a critical value, randomly oriented nuclear spin polarons similar to that predicted by Merkulov [Phys. Solid State 40, 930 (1998)] should emerge. These polarons are oriented randomly, and within each polaron, nuclear and electron spins are aligned antiferromagnetically. At negative nuclear spin temperature below a critical value, we predict another type of magnetic ordering—a dynamically induced nuclear ferromagnet. This is a long-range ferromagnetically ordered state involving both electrons and nuclei. It can form if electron spin relaxation is dominated by the hyperfine coupling, rather than by the spin-orbit interaction. Application of the theory to the $n$-doped GaAs suggests that ferromagnetic order may be reached at experimentally achievable nuclear spin temperature ${\mathrm{\Theta }}_{\text{N}}\approx -0.5\mu \mathrm{K}$ and lattice temperature $T_{\text{L}}\approx 5\mathrm{K}$.

${\mathrm{CeCd}}_3{\mathrm{As}}_3$ is a rare-earth triangular-lattice antiferromagnet with large interlayer separation. Our field-dependent heat capacity measurements at dilution fridge temperatures allow us to trace the field evolution of the spin-excitation gaps throughout the antiferromagnetic and paramagnetic regions. The distinct gap evolution places strong constraints on the microscopic pseudospin model, which, in return, yields a close quantitative description of the gap behavior. This analysis provides crucial insights into the nature of the magnetic state of ${\mathrm{CeCd}}_3{\mathrm{As}}_3$, with a certainty regarding its stripe order and low-energy model parameters that sets a compelling paradigm for exploring and understanding the rapidly growing family of the rare-earth-based triangular-lattice systems.

Variational wave functions and Green's functions are two important paradigms for solving quantum Hamiltonians, each having their own advantages. Here we detail the variational discrete action theory (VDAT), which exploits the advantages of both paradigms in order to approximately solve the ground state of quantum Hamiltonians. VDAT consists of two central components: the sequential product density matrix (SPD) ansatz and a discrete action associated with the SPD. The SPD is a variational ansatz inspired by the Trotter decomposition and characterized by an integer $\mathcal{N}$, recovering many well-known variational wave functions, in addition to the exact solution for $\mathcal{N}=\infty$. The discrete action describes all dynamical information of an effective integer time evolution with respect to the SPD. We generalize the path integral to our integer time formalism, which converts a dynamic correlation function in integer time to a static correlation function in a compound space. We also generalize the usual many-body Green's function formalism to integer time, which results in analogous but distinct mathematical structures, yielding integer time versions of the generating functional, Dyson equation, and Bethe-Salpeter equation. We prove that the SPD can be exactly evaluated in the multiband Anderson impurity model (AIM) by summing a finite number of diagrams. For the multiband Hubbard model, we prove that the self-consistent canonical discrete action approximation (SCDA), which is the integer time analog of the dynamical mean-field theory, exactly evaluates the SPD for $d=\infty$. VDAT within the SCDA provides an efficient yet reliable method for capturing the local physics of quantum lattice models, which will have broad applications for strongly correlated electron materials. More generally, VDAT should find applications in various many-body problems in physics.

We investigate a well-studied system of a quantum dot coupled to a Coulomb box and leads, realizing a spin-flavor Kondo model. It exhibits a recently discovered non-Fermi liquid (NFL) behavior with emergent SO(5) symmetry. Here, through a detailed bosonization and refermionization solution, we push forward our previous work and provide a consistent and complete description of the various exotic properties and phase diagram. A unique NFL phase emerges from the presence of an uncoupled Majorana fermion from the flavor sector, whereas Fermi liquid-like susceptibilities result from the gapping out of a pair of Majorana fermions from the spin and flavor sectors. Other properties, such as a $T^{3/2}$ scaling of the conductance, stability under channel or spin-symmetry breaking, and a reappearance of NFL behavior upon breaking the particle-hole symmetry, are all accounted for by a renormalization group treatment of the refermionized Majorana model.

The Higgs amplitude mode is a collective excitation studied and observed in a broad class of matter, including superconductors, charge density waves, antiferromagnets, ${}^3\mathrm{He} p$-wave superfluid, and ultracold atomic condensates. In all the observations reported thus far, the amplitude mode was excited by perturbing the condensate out of equilibrium. Studying an exciton-polariton condensate, here, we report the observation of this amplitude mode purely driven by intrinsic quantum fluctuations without such perturbations. By using an ultrahigh quality microcavity and a Raman spectrometer to maximally reject photoluminescence (PL) from the condensate, we observe weak but distinct PL at energies below the condensate emission. We identify this as the so-called ghost branches of the amplitude mode arising from quantum depletion of the condensate into this mode. These energies, as well as the overall structure of the PL spectra, are in good agreement with our theoretical analysis.

In $\alpha \text{−}{\mathrm{RuCl}}_3$, an external magnetic field applied within the honeycomb plane can induce a transition from a magnetically ordered state to a disordered state that is potentially related to the Kitaev quantum spin liquid. In zero field, single crystals with minimal stacking faults display a low-temperature state with in-plane zigzag antiferromagnetic order and a three-layer periodicity in the direction perpendicular to the honeycomb planes. Here, we present angle-dependent magnetization, ac susceptibility, and thermal transport data that demonstrate the presence of an additional intermediate-field ordered state at fields below the transition to the disordered phase. Neutron-diffraction results show that the magnetic structure in this phase is characterized by a six-layer periodicity in the direction perpendicular to the honeycomb planes. Theoretically, the intermediate ordered phase can be accounted for by including spin-anisotropic couplings between the layers in a three-dimensional spin model. Together, this demonstrates the importance of interlayer exchange interactions in $\alpha \text{−}{\mathrm{RuCl}}_3$.

We study the stability of topological crystalline superconductors in the symmetry class DIIIR and in two-dimensional space when perturbed by quartic contact interactions. It is known that no less than eight copies of helical pairs of Majorana edge modes can be gapped out by an appropriate interaction without spontaneously breaking any one of the protecting symmetries. Hence, the noninteracting classification $\mathbb{Z}$ reduces to ${\mathbb{Z}}_8$ when these interactions are present. It is also known that the stability when there are less than eight modes can be understood in terms of the presence of topological obstructions in the low-energy bosonic effective theories, which prevent opening of a gap. Here, we investigate the stability of the edge theories with four, two, and one edge modes, respectively. We give an analytical derivation of the topological term for the first case, because of which the edge theory remains gapless. For two edge modes, we employ bosonization methods to derive an effective bosonic action. When gapped, this bosonic theory is necessarily associated to the spontaneous symmetry breaking of either one of time-reversal or reflection symmetry whenever translation symmetry remains on the boundary. For one edge mode, stability is explicitly established in the Majorana representation of the edge theory.

We explore the nonunitary dynamics of $(2+1)$-dimensional free fermions and show that the obtained steady state is critical regardless the strength of the nonunitary evolution. Numerical results indicate that the entanglement entropy has a logarithmic violation of the area law and the mutual information between two distant regions decays as a power-law function. In particular, we provide an interpretation of these scaling behaviors in terms of a simple quasiparticle pair picture. In addition, we study the dynamics of the correlation function and demonstrate that this system has dynamical exponent $z=1$. We further demonstrate the dynamics of the correlation function can be well captured by a classical nonlinear master equation. Our method opens a door to a vast number of nonunitary random dynamics in free fermions and can be generalized to any dimensions.

Gapped graphene has been proposed to be a good platform to observe the valley Hall effect, a transport phenomenon involving the flow of electrons that are characterized by different valley indices. In the present work, we show that this phenomenon is better described as an instance of the orbital Hall effect (OHE), where the ambiguous “valley” indices are replaced by a physical quantity, the orbital magnetic moment, which can be defined uniformly over the entire Brillouin zone. This description removes the arbitrariness in the choice of arbitrary cutoff for the valley-restricted integrals in the valley Hall conductivity, as the conductivity in the OHE is now defined as the Brillouin zone integral of a new quantity, called the orbital Berry curvature. This reformulation in terms of OHE provides a direct explanation to the accumulated opposite orbital moments at the edges of the sample, observed in previous Kerr rotation measurements.

We study generalized spin waves in graphene under a strong magnetic field when the Landau-level filling factor is $\nu =\pm 1$. In this case, the ground state is a particular SU(4) quantum Hall ferromagnet, in which not only the physical spin is fully polarized but also the pseudospin associated with the valley degree of freedom. The nature of the ground state and the spin-valley polarization depend on explicit symmetry-breaking terms that are also reflected in the generalized spin-wave spectrum. In addition to pure spin waves, one encounters valley-pseudospin waves as well as more exotic entanglement waves that have a mixed spin-valley character. Most saliently, the SU(4) symmetry-breaking terms not only yield gaps in the spectra, but also under certain circumstances, namely, in the case of residual ground-state symmetries, render the originally quadratic (in the wave vector) spin-wave dispersion linear.

We investigate the twisted bilayer graphene (TBG) model of Bistritzer and MacDonald (BM) [Bistritzer and MacDonald, Proc. Natl. Acad. Sci. 108, 12233 (2011)] to obtain an analytic understanding of its energetics and wave functions needed for many-body calculations. We provide an approximation scheme for the wave functions of the BM model, which first elucidates why the BM $K_M$-point centered original calculation containing only four plane waves provides a good analytical value for the first magic angle (${\theta }_M\approx 1^{\circ }$). The approximation scheme also elucidates why most of the many-body matrix elements in the Coulomb Hamiltonian projected to the active bands can be neglected. By applying our approximation scheme at the first magic angle to a ${\mathrm{\Gamma }}_M$-point centered model of six plane waves, we analytically understand the reason for the small ${\mathrm{\Gamma }}_M$-point gap between the active and passive bands in the isotropic limit $w_0=w_1$. Furthermore, we analytically calculate the group velocities of the passive bands in the isotropic limit, and show that they are almost doubly degenerate, even away from the ${\mathrm{\Gamma }}_M$ point, where no symmetry forces them to be. Furthermore, moving away from the ${\mathrm{\Gamma }}_M$ and $K_M$ points, we provide an explicit analytical perturbative understanding as to why the TBG bands are flat at the first magic angle, despite the first magic angle is defined by only requiring a vanishing $K_M$-point Dirac velocity. We derive analytically a connected “magic manifold” $w_1=2\sqrt{1+w_0^2}-\sqrt{2+3w_0^2}$, on which the bands remain extremely flat as $w_0$ is tuned between the isotropic ($w_0=w_1$) and chiral ($w_0=0$) limits. We analytically show why going away from the isotropic limit by making $w_0$ less (but not larger) than $w_1$ increases the ${\mathrm{\Gamma }}_M$-point gap between the active and the passive bands. Finally, by perturbation theory, we provide an analytic ${\mathrm{\Gamma }}_M$ point $k·p$ two-band model that reproduces the TBG band structure and eigenstates within a certain $w_0,w_1$ parameter range. Further refinement of this model are discussed, which suggest a possible faithful representation of the TBG bands by a two-band ${\mathrm{\Gamma }}_M$ point $k·p$ model in the full $w_0,w_1$ parameter range.