Fermion sampling is to generate probability distribution of a many-body Slater-determinant wave function, which is termed “determinantal point process” in statistical analysis. For its inherently embedded Pauli exclusion principle, its application reaches beyond simulating fermionic quantum many-body physics to constructing machine learning models for diversified datasets. Here we propose a fermion sampling algorithm, which has a polynomial time complexity—quadratic in the fermion number and linear in the system size. This algorithm is about $100\%$ more efficient in computation time than the best known algorithms. In sampling the corresponding marginal distribution, our algorithm has a more drastic improvement, achieving a scaling advantage. We demonstrate its power on several test applications, including sampling fermions in a many-body system and a machine learning task of text summarization, and confirm its improved computation efficiency over other methods by counting floating-point operations.

The kagome magnet ${\mathrm{TbMn}}_6{\mathrm{Sn}}_6$ is a new type of topological material that is known to support exotic quantum magnetic states. Experimental work has identified that ${\mathrm{TbMn}}_6{\mathrm{Sn}}_6$ hosts Dirac electronic states that could lead to topological and Chern quantum phases, but the optical response of the Dirac fermions of ${\mathrm{TbMn}}_6{\mathrm{Sn}}_6$ and its properties remain to be explored. Here, we perform an optical spectroscopy measurement combined with first-principles calculations on a single-crystal sample of ${\mathrm{TbMn}}_6{\mathrm{Sn}}_6$ to investigate the associated exotic phenomena. ${\mathrm{TbMn}}_6{\mathrm{Sn}}_6$ exhibits frequency-independent optical conductivity spectra in a broad range from 1800 to 3000 ${\mathrm{cm}}^{-1}$ (220–370 meV) in experiments. The theoretical band structures and optical conductivity spectra are calculated with several shifted Fermi energies to compare with the experiment. The theoretical spectra with a 0.56 eV shift for Fermi energy are well consistent with our experimental results. In addition, massive quasi-two-dimensional (quasi-2D) Dirac bands, which have a linear band dispersion in the $k_x\text{−}{k}_y$ plane and no band dispersion along the $k_z$ direction, exist close to the shifted Fermi energy. According to a tight-binding model analysis, the quasi-2D Dirac bands give rise to a flat optical conductivity, while its value is smaller than (about one tenth of) that from the calculations and experiments. It indicates that the other trivial bands also contribute to the flat optical conductivity.

We study the formation of exciton-polariton condensates in potlike traps created by optical pumping in a planar microcavity with embedded quantum wells. The trap is formed by a repulsive reservoir of incoherent excitons excited by a ring-shaped nonresonant laser beam. Polariton condensates confined in a trapping potential are subject to spatial confinement leading to energy quantization. We reveal experimentally the discrete spectrum of polariton eigenstates in an optical trap that can be characterized by a pair of quantum numbers, azimuthal and radial quantum numbers, that correspond to the number of nodes of a condensate wave function in the corresponding directions. The occupation numbers of the eigenstates of a polariton condensate are determined by the overlap integral of the condensate wave function and the exciton reservoir spatial density distribution. The nonresonant pumping scheme enables engineering the shape and size of the trap, that allows to selectively excite specific superpositions of the eigenstates of a polariton condensate in each experiment. We demonstrate both single- and multiple-mode polariton lasing in an optical trap.

We report an experimental and theoretical study of the electron-phonon coupling for $\alpha \text{−}\mathrm{Sn}/\mathrm{Ge}\left(111\right)$, a prototypical triangular lattice surface, closely related to $\mathrm{Sn}/\mathrm{Si}\left(111\right)\text{−}(\sqrt{3}\times \sqrt{3})$, where recent experimental evidence has found superconductivity [X. Wu et al., Phys. Rev. Lett. 125, 117001 (2020)]. We concentrate our study on the ($3\times 3$) phase of $\alpha \text{−}\mathrm{Sn}/\mathrm{Ge}\left(111\right)$ that appears between 150 and 120 K and has a well-known geometry with a half-filled electronic band around the Fermi energy. We show that this surface presents a giant electron-phonon interaction that can be considered at least partially responsible for the different phases that this system shows at very low temperature. Our theoretical results indicate that indeed the electron-phonon interaction in $\alpha \text{−}\mathrm{Sn}/\mathrm{Ge}\left(111\right)\text{−}(3\times 3)$ is unusually large, since we find that $\lambda$, the electron mass enhancement for the half-filled band, is $\lambda =1.3$. This result is in good agreement with the experimental value obtained from high-resolution angle-resolved photoemission spectroscopy measurements, which yield $\lambda =1.45\pm 0.1$.

We construct a three-dimensional second-order topological insulator with gapless helical hinge states from an array of weakly tunnel-coupled Rashba nanowires. For suitably chosen interwire tunnelings, we demonstrate that the system has a fully gapped bulk as well as fully gapped surfaces, but hosts a Kramers pair of gapless helical hinge states propagating along a path of hinges that is determined by the hierarchy of interwire tunnelings and the boundary termination of the system. Furthermore, the coupled-wires approach allows us to incorporate electron-electron interactions into our description. At suitable filling factors of the individual wires, we show that sufficiently strong electron-electron interactions can drive the system into a fractional second-order topological insulator phase with hinge states carrying only a fraction $e/p$ of the electronic charge $e$ for an odd integer $p$.

In this Letter, we study the superconductivity and non-Fermi liquid transport behavior in a doped valence bond solid insulator using sign-problem-free quantum Monte Carlo simulation. We show superconductivity emerges as a function of doping. For a wide temperature range above the superconducting $T_c$, a pseudogap exists. Moreover, close to the valence bond solid to semimetal quantum critical point at half filling, we observe linear temperature resistivity when doping is nonzero.

We present a systematic method to automatically generate symmetry-adapted magnetic structures for a given crystal structure and general propagation vector $\mathit{k}$ as an efficient approach of the analysis of complex modulated magnetic structures. The method is developed as an extension of the generation scheme based on the multipole expansion, which was demonstrated only for the propagation vector $\mathit{k}=\mathit{0}$ [M.-T. Suzuki et al., Phys. Rev. B 99, 174407 (2019)]. The symmetry-adapted magnetic structures characterized with an ordering vector $\mathit{k}$ are obtained by mapping the multipole magnetic alignments on a virtual cluster to the periodic crystal structure with the phase factor for the wave vector $\mathit{k}$. This method provides all magnetic bases compatible with irreducible representations under a $\mathit{k}$ group for a given crystal structure and wave vector $\mathit{k}$. Multiple-$\mathit{k}$ magnetic structures are derived from a superposition of single-$\mathit{k}$ magnetic bases related to the space group symmetry. We apply the scheme to deduce the magnetic structures of $\alpha$-Mn and $\mathrm{Co}{M}_3{\mathrm{S}}_6$ ($M=\mathrm{Nb}$, Ta), in which the large anomalous Hall effect has recently been observed in antiferromagnetic phases, and identify the magnetic structures inducing anomalous Hall effect without net magnetization. The physical phenomena originating from emergent multipoles in the ordered phases are also discussed based on the Landau theory.

Interfacial Rashba-type spin-orbit coupling is an attractive effect to provide spin-orbit torques without the presence of heavy metals. In this work, we report the experimental observation of the Rashba-Edelstein magnetoresistance in the Cr/YIG heterostructure, which can indicate the presence of the interfacial spin-orbit coupling. By comparing the angular-dependent magnetoresistance of the Cr/YIG and the Cr/Cu/YIG heterostructures, we identify that the magnetoresistance in the Cr/YIG heterostructure is superimposed with two parts: the Rashba-Edelstein magnetoresistance induced by the interfacial spin-orbit coupling and the anisotropic magnetoresistance induced by the magnetic proximity effect. The Rashba-Edelstein magnetoresistance shows a nonsaturated external field dependence, which can be attributed to the Hanle magnetoresistance and the interfacial antiferromagnetic ordering of the Cr layer. Our findings show an approach to obtain spin-orbit torques via the interfacial spin-orbit coupling for YIG-based devices. Furthermore, our findings also provide an understanding of the multiple couplings at the $3d$-metal/YIG interface.

We study the plasma branch of an homogeneous three-dimensional electron gas in an $s$-wave superconducting state. Although a sum rule guarantees that the departure of the plasma branch always coincides with the plasma frequency ${\omega }_p$, the dispersion and lifetime of plasmons is strongly affected by the presence of the pair condensate, especially when ${\omega }_p$ is close to the pair-breaking threshold $2\mathrm{\Delta }$. When ${\omega }_p$ is between $1.7\mathrm{\Delta }$ and $2\mathrm{\Delta }$, the level repulsion is strong enough to give the plasma branch an anomalous, downward dispersion and a dispersion minimum strictly lower than ${\omega }_p$. Then for ${\omega }_p>2\mathrm{\Delta }$, plasmons damp out in pair-breaking excitations, acquiring a small damping rate at zero temperature, which we compute in a non-perturbative way. Finally, the density-density response function displays a resonance near $2\mathrm{\Delta }$ (not to be confused with the amplitude mode), which can beat with the main plasma resonance, and subsists for ${\omega }_p$ large compared to $\mathrm{\Delta }$, thereby distinguishing charged from neutral condensates.

Based on a weak coupling calculation, we show that an accidental degeneracy appears between even- and odd-parity superconductivity in the quasi-one-dimensional (1D) limit of the repulsive Hubbard model on the square lattice. We propose that this effect could be at play on the quasi-1D orbitals Ru $d_{zx}$ and $d_{zy}$ of ${\text{Sr}}_2{\text{RuO}}_4$, leading to a gap of the form ${\mathrm{\Delta }}_{\text{even}}+i{\mathrm{\Delta }}_{\text{odd}}$ which could help reconcile several experimental results.

We put the density of states (DoS) approach to Monte Carlo (MC) simulations under a stress test by applying it to a physical problem with the worst possible sign problem: the real-time evolution of a nonintegrable quantum spin chain. Benchmarks against numerical exact diagonalization and stochastic reweighting are presented. Both MC methods, the DoS approach and reweighting, allow for simulations of spin chains as long as $L=40$, far beyond exact diagonalizability, though only for short evolution times $t\lesssim 1$. We identify discontinuities of the DoS as one of the key problems in the MC simulations and propose calculating some of the dominant contributions analytically, increasing the precision of our simulations by several orders of magnitude. Even after these improvements, the DoS is found highly nonsmooth, and therefore, the DoS approach cannot outperform reweighting. We prove this implication theoretically and provide numerical evidence, concluding that the DoS approach is not well suited for quantum real-time simulations with discrete degrees of freedom.

We study the cubic fixed point for $N=3$ and 4 by using finite-size scaling applied to data obtained from Monte Carlo simulations of the $N$-component ${\varphi }^4$ model on the simple cubic lattice. We generalize the idea of improved models to a two-parameter family of models. The two-parameter space is scanned for the point, where the amplitudes of the two leading corrections to scaling vanish. To this end, a dimensionless quantity is introduced that monitors the breaking of the $O\left(N\right)$ invariance. For $N=4$, we determine the correction exponents ${\omega }_1=0.763\left(24\right)$ and ${\omega }_2=0.082\left(5\right)$. In the case of $N=3$, we obtain $Y_4=0.0142\left(6\right)$ for the renormalization group exponent of the cubic perturbation at the $O\left(3\right)$-invariant fixed point, while the correction exponent ${\omega }_2=0.0133\left(8\right)$ at the cubic fixed point. Simulations close to the improved point result in the estimates $\nu =0.7202\left(7\right)$ and $\eta =0.0371\left(2\right)$ of the critical exponents of the cubic fixed point for $N=4$. For $N=3$, at the cubic fixed point, the $O\left(3\right)$ symmetry is only mildly broken and the critical exponents differ only by little from those of the $O\left(3\right)$-invariant fixed point. We find $-0.00001⪅{\eta }_{\text{cubic}}-{\eta }_{O\left(3\right)}⪅0.00007$ and ${\nu }_{\text{cubic}}-{\nu }_{O\left(3\right)}=-0.00061\left(10\right)$.

We use the Lindblad equation method to investigate the onset of a mobility edge and the topological phase transition in the disordered SSH chain connected to two external baths in the large bias limit. From the scaling properties of the nonequilibrium stationary current flowing across the system, we recover the localization/delocalization in the disordered chain. To probe the topological phase transition in the presence of disorder, we use the even-odd differential occupancy as a means to discriminate topologically trivial from topologically nontrival phases in the out-of-equilibrium system. Eventually, we argue how to generalize our method to other systems undergoing a topological phase transition in the presence of disorder.

Nonlinear optical responses, such as shift current and second-harmonic generation (SHG), of topological semimetals have been subjects of great interest because the momentum-space topological structures near Weyl or Dirac points lead to unusually large responses. This is especially important for technological applications as the shift current and SHG are often used for solar cell and frequency-changing applications for lasers, respectively. We demonstrate that nodal line semimetals can offer even larger responses at low frequencies. For example, we show that a large SHG response arises at finite doping when an external dc electric field is applied to break the inversion symmetry of an otherwise inversion-symmetric model of a nodal line semimetal. Furthermore, we introduce a model with intrinsically broken inversion symmetry, where both the shift current and SHG are singular in a range of parameters.

We report dissipative dynamics of two valley excitons residing in the $K$ and $K^{\prime }$ valleys of a bare ${\mathrm{WSe}}_2$ monolayer and the one being integrated into a bimodal optical cavity. In the former, only when the exciton-field detunings in the $K$ and $K^{\prime }$ valleys are rigorously equal (resonant detuning) can partially entangled stationary states be created. Otherwise, the concurrence of exciton qubits turns to zero. Remarkably, in the latter (the ${\mathrm{WSe}}_2$ monolayer in a bimodal optical cavity), the transfers of entanglement from one subsystem (exciton/light) to the other (light/exciton) take place. Hence a finite stationary concurrence of exciton qubits is always generated, independent of whether the exciton-field detuning in two valleys is resonant or nonresonant. In addition, it can even reach as high as 1 (maximally entangled state of two valley excitons). Since there no real system which has a strictly resonant detuning, an immersion of the ${\mathrm{WSe}}_2$ monolayer in a bimodal optical cavity provides an opportunity to overcome the challenge facing by the bare ${\mathrm{WSe}}_2$, opening a novel realm of potential qubits.

I investigate the tunneling decay rate of a polaritonic system formed by a strong coupling between a vacuum cavity mode and $N$ metastable systems. Using a simple model potential, I find the instanton solutions controlling the low-temperature tunneling rate. The resulting rate modification due to the cavity is proportional to the mean of the second power of the light-matter coupling. No collective effect that would enhance the rates by a factor of $\sqrt{N}$ is present, which is in line with the results in the thermal activation regime.

Tuning dimensionality in van der Waals materials with finite interlayer coupling has introduced various electronic phase transitions by conventional mechanical exfoliation. Particularly when the electronic order is tied to the modulation of the interlayer coupling, such dimensional tunability has a strong impact on its stability and properties, which has rarely been investigated experimentally. Here, we demonstrate a dimensional crossover of charge order in ${\mathrm{IrTe}}_2$ from genuine two- to quasi-three-dimensions using low-temperature scanning tunneling microscopy and spectroscopy. Employing atomically thin ${\mathrm{IrTe}}_2$ flakes ranging from monolayer to multilayer, we observe a gradual phase transition of charge order and exponential decay of Coulomb gap with increasing thickness. Moreover, we find a suppression of the density of states emerging at an abrupt lateral interface between two and three dimensions. These findings are attributed to the interplay between the strongly coupled layers and substrate-driven perturbation, which can provide a new insight into the dimensional crossover of strongly coupled layered materials with hidden electronic phases.

We present a first-principles methodology to calculate spin-dependent plasma frequency. Electronic structure and plasma frequency of nine metals (Al, Au, Ag, Cu, Pd, Pt, Na, Fe, and Co) are studied using density-functional theory in an all-electron full-potential framework. The results are compared to pseudopotential approaches and experiments. We find a significant difference between the spin-up and spin-down contributions to plasma frequency. Thus, spin-polarization effects are important for understanding optical properties of metals. Spin-orbit coupling inclusion affects plasma frequency since it contains an interaction term between spin-up and spin-down electrons.