After decades of progress and effort, obtaining a phase diagram for a strongly correlated topological system still remains a challenge. Although in principle one could turn to Wilson loops and long-range entanglement, evaluating these nonlocal observables at many points in phase space can be prohibitively costly. With growing excitement over topological quantum computation comes the need for an efficient approach for obtaining topological phase diagrams. Here we turn to machine learning using quantum loop topography (QLT), a notion we have recently introduced. Specifically, we propose a construction of QLT that is sensitive to quasiparticle statistics. We then use mutual statistics between the spinons and visons to detect a ${\mathbb{Z}}_2$ quantum spin liquid in a multiparameter phase space. We successfully obtain the quantum phase boundary between the topological and trivial phases using a simple feed-forward neural network. Furthermore, we demonstrate advantages of our approach for the evaluation of phase diagrams relating to speed and storage. Such statistics-based machine learning of topological phases opens new efficient routes to studying topological phase diagrams in strongly correlated systems.

The origin of low-energy excitations in the polycrystalline $\mathrm{E}{\mathrm{u}}_{0.42}\mathrm{S}{\mathrm{r}}_{0.58}\mathrm{Mn}{\mathrm{O}}_3$ manganite is explored by terahertz and infrared spectroscopies. The transition from the charge and/or orbital to antiferromagnetic order ($T_{\mathrm{N}}=130-140\mathrm{K}$) is seen as smooth (spread over a temperature range from 50 to 100 K) decrease of free-carrier conductivity with the activation energy change from 86 meV (high temperatures) to 0.52 meV (low temperatures). A broad relaxation is observed at around $10\mathrm{c}{\mathrm{m}}^{-1}$ which we associate with the dynamics of free charge carriers in the presence of random localizing potential. We discover an absorption resonance at $\approx 50\mathrm{c}{\mathrm{m}}^{-1}$ below $T_{\mathrm{N}}$ that is assigned to the formation of hybridized “acoustic phonon-magnon” quasiparticles.

The complex interplay of elastic and inelastic scattering amenable to different levels of approximation constitutes the major challenge for the computation and hence interpretation of TEM-based spectroscopical methods. The two major approaches to calculate inelastic scattering cross sections of fast electrons on crystals—Yoshioka-equations-based forward propagation and the reciprocal wave method—are founded in two conceptually differing schemes—a numerical forward integration of each inelastically scattered wave function, yielding the exit density matrix, and a computation of inelastic scattering matrix elements using elastically scattered initial and final states (double channeling). Here, we compare both approaches and show that the latter is computationally competitive to the former by exploiting analytical integration schemes over multiple excited states. Moreover, we show how to include full nonlocality of the inelastic scattering event, neglected in the forward propagation approaches, at no additional computing costs in the reciprocal wave method. Detailed simulations show in some cases significant errors due to the $z$-locality approximation and hence pitfalls in the interpretation of spectroscopical TEM results.

We study the quantum quench problem for a class of bosonic conformal interfaces by computing the Loschmidt echo and the bipartite fidelity. The quench can be viewed as a sudden change of boundary conditions parametrized by $\theta$ when connecting two one-dimensional critical systems. They are classified by $S\left(\theta \right)$ matrices associated with the current scattering processes on the interface. The resulting Loschmidt echo of the quench has long time algebraic decay $t^{-\alpha }$, whose exponent also appears in the finite size bipartite fidelity as $L^{-\frac{\alpha }{2}}$. We perform analytic and numerical calculations of the exponent $\alpha$, and find that it has a quadratic dependence on the change of $\theta$ if the prior and post-quench boundary conditions are of the same type of $S$, while remaining $\frac{1}{4}$ otherwise. Possible physical realizations of these interfaces include, for instance, connecting different quantum wires (Luttinger liquids), quench of the topological phase edge states, etc., and the exponent can be detected in an x-ray edge singularity-type experiment.

Despite much anticipation of valleytronics as a candidate to replace the aging complementary metal-oxide-semiconductor (CMOS) based information processing, its progress is severely hindered by the lack of practical ways to manipulate valley polarization all electrically in an electrostatic setting. Here, we propose a class of all-electric-controlled valley filter, valve, and logic gate based on the valley-contrasting transport in a merging Dirac cones system. The central mechanism of these devices lies on the pseudospin-assisted quantum tunneling which effectively quenches the transport of one valley when its pseudospin configuration mismatches that of a gate-controlled scattering region. The valley polarization can be abruptly switched into different states and remains stable over semi-infinite gate-voltage windows. Colossal tunneling valley-pseudomagnetoresistance ratio of over $10000$% can be achieved in a valley-valve setup. We further propose a valleytronic-based logic gate capable of covering all 16 types of two-input Boolean logics. Remarkably, the valley degree of freedom can be harnessed to resurrect logical reversibility in two-input universal Boolean gate. The ($2+1$) polarization states (two distinct valleys plus a null polarization) reestablish one-to-one input-to-output mapping, a crucial requirement for logical reversibility, and significantly reduce the complexity of reversible circuits. Our results suggest that the synergy of valleytronics and digital logics may provide new paradigms for valleytronic-based information processing and reversible computing.

In Liu et al. [Phys. Rev. B 87, 235306 (2013)], the authors obtain that the cross coupling between vector gauge field and chiral gauge field can lead to the anomaly of vector current. We demonstrate that this anomaly is not a physical effect. On one hand, it can be regulated out by the proper regulation. On the other hand, it leads to unjustifiable results, the breaking of the vector gauge symmetry and the ambiguous boundary current. Moreover, the effects associated with anomaly of vector current are understood by random phase approximation (RPA) in the paper we comment on. We point out that the RPA cannot describe the effects resulting from the quantum anomaly.

Recently, in their Comment, Zhang et al. question our results of anomaly equations. In this Reply, we provide detailed derivation of anomaly equations from microscopic models and explain the reason why we respectfully disagree with the derivation and argument in the Comment.

Although many works have been devoted to the order-disorder transition in carbon-supersaturated α-Fe, all seem to have overlooked the temperature hysteresis phenomenon occurring around the critical temperature. It is shown, from a mean-field model based on the elasticity theory of point defects, that the origin of the temperature hysteresis is thermodynamic. As a consequence, both the critical temperature and carbon concentration for the order-disorder transition can be defined upon heating and cooling. The results obtained were successfully compared to molecular dynamics simulations, and are evidence that the transition is of first order and that linear elasticity is the predominant source of the thermodynamics of the Fe-C solid solutions.

We numerically construct translationally invariant quasiconserved operators with maximum range $M$, which best commute with a nonintegrable quantum spin chain Hamiltonian, up to $M=12$. In the large coupling limit, we find that the residual norm of the commutator of the quasiconserved operator decays exponentially with its maximum range $M$ at small $M$, and turns into a slower decay at larger $M$. This quasiconserved operator can be understood as a dressed total “spin-$z$” operator, by comparing with the perturbative Schrieffer-Wolff construction developed to high order reaching essentially the same maximum range. We also examine the operator inverse participation ratio of the operator, which suggests its localization in the operator Hilbert space. The operator also shows an almost exponentially decaying profile at short distance, while the long-distance behavior is not clear due to limitations of our numerical calculation. Further dynamical simulation confirms that the prethermalization-equilibrated values are described by a generalized Gibbs ensemble that includes such quasiconserved operator.

Spin-memory loss (SML) of electrons traversing ferromagnetic-metal/heavy-metal (FM/HM), FM/normal-metal (FM/NM), and HM/NM interfaces is a fundamental phenomenon that must be invoked to explain consistently large numbers of spintronic experiments. However, its strength extracted by fitting experimental data to phenomenological semiclassical theory, which replaces each interface by a fictitious bulk diffusive layer, is poorly understood from a microscopic quantum framework and/or materials properties. Here we describe an ensemble of flowing spin quantum states using spin-density matrix, so that SML is measured like any decoherence process by the decay of its off-diagonal elements or, equivalently, by the reduction of the magnitude of polarization vector. By combining this framework with density functional theory, we examine how all three components of the polarization vector change at Co/Ta, Co/Pt, Co/Cu, Pt/Cu, and Pt/Au interfaces embedded within Cu/FM/HM/Cu vertical heterostructures. In addition, we use ab initio Green's functions to compute spectral functions and spin textures over FM, HM, and NM monolayers around these interfaces which quantify interfacial spin-orbit coupling and explain the microscopic origin of SML in long-standing puzzles, such as why it is nonzero at the Co/Cu interface; why it is very large at the Pt/Cu interface; and why it occurs even in the absence of disorder, intermixing and magnons at the interface.

We study a frustrated spin-$\frac{1}{2}{J}_1\text{−}{J}_2\text{−}{J}_3\text{−}{J}_1^{\perp }$ Heisenberg antiferromagnet on an $AA$-stacked bilayer honeycomb lattice. In each layer we consider nearest-neighbor (NN), next-nearest-neighbor, and next-next-nearest-neighbor antiferromagnetic (AFM) exchange couplings $J_1,J_2$, and $J_3$, respectively. The two layers are coupled with an AFM NN exchange coupling $J_1^{\perp }\equiv \delta J_1$. The model is studied for arbitrary values of $\delta$ along the line $J_3=J_2\equiv \alpha J_1$ that includes the most highly frustrated point at $\alpha =\frac{1}{2}$, where the classical ground state is macroscopically degenerate. The coupled cluster method is used at high orders of approximation to calculate the magnetic order parameter and the triplet spin gap. We are thereby able to give an accurate description of the quantum phase diagram of the model in the $\alpha \delta$ plane in the window $0\le \alpha \le 1,0\le \delta \le 1$. This includes two AFM phases with Néel and striped order, and an intermediate gapped paramagnetic phase that exhibits various forms of valence-bond crystalline order. We obtain accurate estimations of the two phase boundaries, $\delta ={\delta }_{c_i}\left(\alpha \right)$, or equivalently, $\alpha ={\alpha }_{c_i}\left(\delta \right)$, with $i=1$ (Néel) and 2 (striped). The two boundaries exhibit an “avoided crossing” behavior with both curves being re-entrant. Thus, in this $\alpha \delta$ window, Néel order exists only for values of $\delta$ in the range ${\delta }_{c_1}^{<}\left(\alpha \right)<\delta <{\delta }_{c_1}^{>}\left(\alpha \right)$, with ${\delta }_{c_1}^{<}\left(\alpha \right)=0$ for $\alpha <{\alpha }_{c_1}\left(0\right)\approx 0.46\left(2\right)$ and ${\delta }_{c_1}^{<}\left(\alpha \right)>0$ for ${\alpha }_{c_1}\left(0\right)<\alpha <{\alpha }_1^{>}\approx 0.49\left(1\right)$, and striped order similarly exists only for values of $\delta$ in the range ${\delta }_{c_2}^{<}\left(\alpha \right)<\delta <{\delta }_{c_2}^{>}\left(\alpha \right)$, with ${\delta }_{c_2}^{<}\left(\alpha \right)=0$ for $\alpha >{\alpha }_{c_2}\left(0\right)\approx 0.600\left(5\right)$ and ${\delta }_{c_2}^{<}\left(\alpha \right)>0$ for ${\alpha }_{c_2}\left(0\right)>\alpha >{\alpha }_2^{<}\approx 0.56\left(1\right)$.

The anomalous surface states of symmetry protected topological (SPT) phases are usually thought to be only possible in conjunction with the higher-dimensional topological bulk. However, it has recently been realized that a class of anomalous SPT surface states can be realized in the same dimension if symmetries are allowed to act in a nonlocal fashion. An example is the particle-hole symmetric half-filled Landau level, which effectively realizes the anomalous surface state of a $3d$ chiral topological insulator (class AIII). A dual description in terms of Dirac composite fermions has also been discussed. Here we explore generalizations of these constructions to multicomponent quantum Hall states. Our results include a duality mapping of the bilayer case to composite bosons with Kramers degeneracy and the possibility of a particle-hole symmetric integer quantum Hall state when the number of components is a multiple of eight. Next, we make a further extension by half-filling other classes of topological bands and imposing particle-hole symmetry. When applied to time-reversal invariant topological insulators, we realize a different chiral class (CII) topological surface state. Notably, half-filling a $3d$ TI band allows for the realization of the surface of the otherwise inaccessible $4d$ topological insulator, which supports an anomalous $3d$ Dirac cone. Surface topological orders equivalent to the $3d$ Dirac cone (from the global anomaly standpoint) are constructed and connections to Witten's SU(2) anomaly are made. These observations may also be useful for numerical simulations of topological surface states and of Dirac fermions without fermion doubling.

Analytical formulation of subcycle modulation (SCM) of dielectrics including electron excitation is presented. The SCM is sensitive to not only the time-resolved dynamical Franz-Keldysh effect (Tr-DFKE) [T. Otobe et al., Phys. Rev. B 93, 045124 (2016)], which is the nonlinear response without the electron excitation, but also the excited electrons. The excited electrons enhance the modulation with even harmonics of pump laser frequency, and generate the odd-harmonics components. The new aspect of SCM is a consequence of (i) the interference between the electrons excited by the pump laser and those excited by the probe-pulse laser and (ii) oscillation of the generated wave packed by the pump laser. When the probe- and pump-pulse polarizations are parallel, the enhancement of the even harmonics and the generation of the odd-harmonics modulation appear. However, if the polarizations are orthogonal, the effect arising from the electron excitations becomes weak. By comparing the parabolic and cosine band models, I found that the electrons under the intense laser field move as quasifree particles.

Weyl semimetals possess low-energy excitations which act as monopoles of Berry curvature in momentum space. These emergent monopoles are at the heart of the many novel transport properties that Weyl semimetals exhibit. The singular nature of the Berry curvature around the nodal points in Weyl semimetals allows for the possibility of large anomalous transport coefficients in zero applied magnetic field. Recently, a new class, termed type-II Weyl semimetals, has been demonstrated in a variety of materials, where the Weyl nodes are tilted. We present here a theoretical study of anomalous transport in this new class of Weyl semimetals. We find that the parameter governing the tilt of these type-II Weyl points is intimately related to the zero-field transverse transport properties. We also find that the temperature dependence of the chemical potential plays an important role in determining how the transport coefficients can effectively probe the Berry curvature of the type-II Weyl points. In particular, we find that the transverse thermoelectric transport coefficient $L_{xy}^{ET}$ is strongly enhanced with the tilt of the type-II Weyl nodes and with increasing temperature. We also discuss the experimental implications of our work for time-reversal breaking type-II Weyl semimetals.

We present results of ${}^{23}\mathrm{Na}$ and ${}^{19}\mathrm{F}$ nuclear magnetic resonance (NMR) measurements on ${\mathrm{NaCaCo}}_2{\mathrm{F}}_7$, a frustrated pyrochlore magnet with a Curie-Weiss temperature ${\mathrm{\Theta }}_{\mathrm{CW}}\approx -140$ K and intrinsic bond disorder. Below 3.6 K both the ${}^{23}\mathrm{Na}$ and ${}^{19}\mathrm{F}$ spectra broaden substantially in comparison to higher temperatures accompanied by a considerable reduction (80%) of the NMR signal intensity: This proves a broad quasistatic field distribution. The ${}^{19}\mathrm{F}$ spin-lattice relaxation rate ${}^{19}(1/T_1$) exhibits a peak at 2.9 K already starting to develop below 10 K. We attribute the spin freezing to the presence of bond disorder. This is corroborated by large-scale Monte Carlo simulations of a classical bond-disordered XY model on the pyrochlore lattice. The low freezing temperature, together with the very short magnetic correlation length not captured by the simulations, suggests that quantum effects play a decisive role in ${\mathrm{NaCaCo}}_2{\mathrm{F}}_7$.

We have investigated the optical properties of thin films of topological insulators ${\mathrm{Bi}}_2{\mathrm{Te}}_3$, ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, and their alloys ${\mathrm{Bi}}_2{\left({\mathrm{Te}}_{1-x}{\mathrm{Se}}_x\right)}_3$ on ${\mathrm{BaF}}_2$ substrates by a combination of infrared ellipsometry and reflectivity in the energy range from 0.06 to 6.5 eV. For the onset of interband absorption in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, after the correction for the Burstein-Moss effect, we find the value of the direct band gap of $215\pm 10$ meV at 10 K. Our data support the picture that ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ has a direct band gap located at the $\mathrm{\Gamma }$ point in the Brillouin zone and that the valence band reaches up to the Dirac point and has the shape of a downward-oriented paraboloid, i.e., without a camel-back structure. In ${\mathrm{Bi}}_2{\mathrm{Te}}_3$, the onset of strong direct interband absorption at 10 K is at a similar energy of about 200 meV, with a weaker additional feature at about 170 meV. Our data support the recent $GW$ band-structure calculations suggesting that the direct interband transition does not occur at the $\mathrm{\Gamma }$ point but near the $Z\text{−}F$ line of the Brillouin zone. In the ${\mathrm{Bi}}_2{\left({\mathrm{Te}}_{1-x}{\mathrm{Se}}_x\right)}_3$ alloy, the energy of the onset of direct interband transitions exhibits a maximum near $x=0.3$ (i.e., the composition of ${\mathrm{Bi}}_2{\mathrm{Te}}_2\mathrm{Se}$), suggesting that the crossover of the direct interband transitions between the two points in the Brillouin zone occurs close to this composition.

Low-dimensional electron systems often show a delicate interplay between electron-phonon and electron-electron interactions, giving rise to interesting quantum phases such as the charge density wave (CDW) and magnetism. Using the density-functional theory (DFT) calculations with the semilocal and hybrid exchange-correlation functionals as well as the exact-exchange plus correlation in the random-phase approximation (EX + cRPA), we systematically investigate the ground state of the metallic atom wires containing dangling-bond (DB) electrons, fabricated by partially hydrogenating the GaN($10\overline{1}0$) and ZnO($10\overline{1}0$) surfaces. We find that the CDW or antiferromagnetic (AFM) order has an electronic energy gain due to a band-gap opening, thereby being more stabilized compared to the metallic state. Our semilocal DFT calculation predicts that both DB wires in GaN($10\overline{1}0$) and ZnO($10\overline{1}0$) have the same CDW ground state, whereas the hybrid DFT and EX + cRPA calculations predict the AFM ground state for the former DB wire and the CDW ground state for the latter one. It is revealed that more localized Ga DB electrons in GaN($10\overline{1}0$) prefer the AFM order, while less localized Zn DB electrons in ZnO($10\overline{1}0$) the CDW formation. Our findings demonstrate that the drastically different ground states are competing in the DB wires created on the two representative compound semiconductor surfaces.

We theoretically study the quantum measurement of a double quantum dot coupled to environments by Bloch equations with an additional vector. Using a quantum point contact as a detector, we accurately calculate the current, the Fano factor, and the waiting time, respectively, to characterize the dynamical properties in two kinds of environments. In the dissipative case, the asymmetrical Fano factor is enhanced with the increase in deocoherence rates and suppressed as the growth of relaxation rates, and the super-Poissonian noise is mainly due to the effects of a dynamical channel blockade and quantum coherence. In the pure dephasing case, the symmetrical Fano factor is magnified, which can be attributed to the quantum Zeno effect. Moreover, we show that the distribution of the average waiting time exhibits good agreement with the variation tendency of the current. Our paper provides an effective method in handling quantum measurement.