We consider interacting bosonic particles on a two-leg triangular ladder in the presence of an artificial gauge field. We employ density matrix renormalization group numerical simulations and analytical bosonization calculations to study the rich phase diagram of this system. We show that the interplay between the frustration induced by the triangular lattice geometry and the interactions gives rise to multiple chiral quantum phases. Phase transitions between superfluid to Mott-insulating states occur, which can have Meissner or vortex character. Furthermore, a state that explicitly breaks the symmetry between the two legs of the ladder, the biased chiral superfluid, is found for values of the flux close to $\pi$. In the regime of hard-core bosons, we show that the extension of the bond order insulator beyond the case of the fully frustrated ladder exhibits Meissner-type chiral currents. We discuss the consequences of our findings for experiments in cold atomic systems.

Elastic softening in the paraelastic phases of ${\mathrm{Ba}}_{1-x}{\mathrm{Sr}}_x{\mathrm{TiO}}_3$ is largest near the transition temperatures and decreases on heating smoothly over extended temperature ranges. Softening extends to the highest measured temperature (850 K) for Ba-rich compounds. The temperature evolution of the excess compliance of the precursor softening follows a power law $\delta S\propto |T-T_{\mathrm{C}}{|}^{-\kappa }$ with a characteristic exponent $\kappa$ ranging between 1.5 in ${\mathrm{SrTiO}}_3$ and 0.2 in ${\mathrm{BaTiO}}_3$. The latter value is below the estimated lower bounds of displacive systems with three orthogonal soft phonon branches (0.5). An alternative Vogel-Fulcher analysis shows that the softening is described by extremely low Vogel-Fulcher energies $E_a$, which increase from ${\mathrm{SrTiO}}_3$ to ${\mathrm{BaTiO}}_3$ indicating a change from a displacive to a weakly order-disorder character of the elastic precursor. Mixed crystals of ${\mathrm{Ba}}_x{\mathrm{Sr}}_{1-x}{\mathrm{TiO}}_3$ possess intermediate behavior. The amplitude of the precursor elastic softening increases continuously from ${\mathrm{SrTiO}}_3$ to ${\mathrm{BaTiO}}_3$. Using power-law fittings reveals that the elastic softening is still $33\%$ of the unsoftened Young's modulus at temperatures as high as 750 K in ${\mathrm{BaTiO}}_3$ with $\kappa \simeq$ 0.2. This proves that the high-temperature elastic properties of these materials are drastically affected by precursor softening.

Quantum transport measurements are performed in gate-defined, high-quality, two-dimensional hole and electron systems in an undoped InSb quantum well. For both polarities, the carrier systems show tunable spin-orbit interaction as extracted from weak antilocalization measurements. The effective mass of InSb holes strongly increases with carrier density as determined from the temperature dependence of Shubnikov–de Haas oscillations. Coincidence measurements in a tilted magnetic field are performed to estimate the spin susceptibility of the InSb two-dimensional hole system. The $g$ factor of the two-dimensional hole system decreases rapidly with increasing carrier density.

${\mathrm{MoS}}_2$ is an emergent van der Waals material that shows promising prospects in semiconductor industry and optoelectronic applications. However, its electronic properties are not yet fully understood. In particular, the nature of the insulating state at low carrier density deserves further investigation, as it is important for fundamental research and applications. In this study we investigate the insulating state of a dual-gated exfoliated bilayer ${\mathrm{MoS}}_2$ field-effect transistor by performing magnetotransport experiments. We observe a positive and nonsaturating magnetoresistance, in a regime where only one band contributes to electron transport. At low electron density ($\sim 1.4\times {10}^{12}{\mathrm{cm}}^{-2}$) and a perpendicular magnetic field of 7 Tesla the resistance exceeds by more than one order of magnitude the zero field resistance and exponentially drops with increasing temperature. We attribute this observation to strong electron localization. Both temperature and magnetic field dependence can, at least qualitatively, be described by the Efros-Shklovskii law, predicting the formation of a Coulomb gap in the density of states due to Coulomb interactions. However, the localization length obtained from fitting the temperature dependence exceeds by more than one order of magnitude the one obtained from the magnetic field dependence. We attribute this discrepancy to the presence of a nearby metallic gate, which provides electrostatic screening and thus reduces long-range Coulomb interactions. The result of our study suggests that the insulating state of ${\mathrm{MoS}}_2$ originates from a combination of disorder-driven electron localization and Coulomb interactions.

Lattice generalizations of fractional quantum Hall (FQH) systems, called fractional Chern insulators (FCIs), have been extensively investigated in strongly correlated systems. Despite many efforts, previous studies have not revealed all of the guiding principles for the FCI search. In this paper, we investigate a relationship between the topological band structure in the two-particle problem and the FCI ground states in the many-body problem. We first formulate the two-particle problem of a bosonic on-site interaction projected onto the lowest band of a given tight-binding Hamiltonian. We introduce a reduced Hamiltonian whose eigenvalues correspond to the two-particle bound-state energies. By using the reduced Hamiltonian, we define the two-particle Chern number and numerically check the bulk-boundary correspondence that is predicted by the two-particle Chern number. We then propose that a nontrivial two-particle Chern number of dominant bands roughly indicates the presence of bosonic FCI ground states at filling factor $\nu =1/2$. We numerically investigate this relationship in several tight-binding models with Chern bands and find that it holds well in most of the cases, albeit two-band models being exceptions. Although the two-particle topology is neither a necessary nor a sufficient condition for the FCI state as other indicators in previous studies, our numerical results indicate that the two-particle topology characterizes the degree of similarity to the FQH systems.

We present a method to determine the model Hamiltonians to treat rare-earth multiplets in solids from the results of the quasiparticle self-consistent GW (QSGW) method. We apply the method to trivalent Eu compounds ${\mathrm{EuCl}}_3$, EuN, and Eu-doped GaN after examining free rare-earth ions. We solve the model Hamiltonian by the exact diagonalization. Our results justify applying the Dieke diagram to ions in solid, while its limitation is clarified. In particular, we show that the crystal fields cause sizable breaking of the Russell-Saunders coupling.

Some correlated materials display an insulator-to-metal transition as the temperature is increased. In most cases, this transition can also be induced electrically, resulting in volatile resistive switching due to the formation of a conducting filament. While this phenomenon has attracted much attention due to potential applications, many fundamental questions remain unaddressed. One of them is its characteristic lengths: What sets the size of these filaments, and how does this impact resistive switching properties? Here, we use a combination of wide-field and scattering-type scanning near-field optical microscopies to characterize filament formation in ${\mathrm{NdNiO}}_3$ and ${\mathrm{SmNiO}}_3$ thin films. We find a clear trend: Smaller filaments increase the current density, yielding sharper switching and a larger resistive drop. With the aid of numerical simulations, we discuss the parameters controlling the filament width and, hence, the switching properties.

We investigate the emergence of topological valley Hall and kink states in a two-dimensional topolectrical (TE) model as a result of broken chiral and reflection symmetries. The TE system consists of two segments hosting distinct topological states with opposite (similar) signs of the valley Hall index, and separated by a heterojunction to exhibit valley kink (Chern insulating) phases at the interface. In the practical circuit, the valley Hall index can be flipped between the two segments by modulating the on-site potential on the sublattice nodes of the respective segments. The presence of grounding connections in the circuit array subsequently leads to the emergence of gapped and gapless valley and kink states in the admittance spectra. These topological modes can be detected electrically by the impedance readouts of the system, which can be correlated to its admittance spectra. Finally, we confirm the robustness of the valley Hall and kink states via realistic LTspice simulation, taking into account the tolerance windows and parasitic effects inherent in circuit components. Our study demonstrates the applicability of TE circuit networks as a platform to realize and tune valley-dependent and kink topological phenomena.

Gapless fracton phases are characterized by the conservation of certain charges and their higher moments. These charges generically couple to higher rank gauge fields. In this paper we study systems conserving charge and dipole moment, and construct the corresponding gauge fields propagating in arbitrary curved backgrounds. The relation between the symmetries of these class of systems and spacetime transformations is discussed. In fact, we argue that higher rank symmetric gauge theories are closer to gravitational fields than to a standard gauge theory.

We report the observation of graphene doped up to the Lifshitz transition obtained solely by the intercalation of Erbium atoms. ARPES measurements show that a wide flat band is generated around the $M$ point of the Brillouin zone. We propose that this is the effect of an induced spin-orbit coupling. Scanning Tunneling Microscopy (STM) experiments reveal a longrange ordered hexagonal superstructure: we argue that this reflects the ordering of the intercalated Er atoms acting as impurities. This system provides a playground to study the interaction between a magnetic order and a divergent density of states at the Fermi level.

We perform nonperturbative calculations of light-field driven valley-polarization process in monolayer ${\mathrm{MoS}}_2$ which has additional Rashba spin-orbit couplings (SOCs). The ultrafast electron dynamics is simulated within the independent particle picture by solving density-matrix equations in the basis of linear combination of atomic orbitals, where tight-binding (TB) models including both intrinsic atomic and Rashba SOCs are used to calculate relevant matrix elements. We demonstrate that the Rashba-type SOCs can be manifested by suboptical-cycle control of valley selectivity excitations, in particular necessary via using few-cycle linearly polarized pulse with controlled carrier-envelope phase (CEP). This procedure will lead to a CEP-dependent valley Hall conductivity (VHC), which exhibits an important phase shift among different Rashba coupling strengths. The additional analysis shows that this phase shift is mainly determined by the $d_z^2$-orbital TB Rashba parameter from Mo atom and originates from contribution of conduction bands to VHC, where the Berry curvature modified by Rashba SOC plays a crucial role. Moreover, we also provide a qualitative interpretation on the Rashba-dependent VHC in terms of suboptical-cycle Landau-Zener-Stückelberg interference. Our results suggest a feasible approach for probing Rashba SOCs in hexagonal two-dimensional materials, and might pave the way of achieving more controls in the future valleytronics application.

Computationally intractable tasks are often encountered in physics and optimization. They usually comprise a cost function to be optimized over a so-called feasible set, which is specified by a set of constraints. This may yield, in general, to difficult and nonconvex optimization tasks. A number of standard methods are used to tackle such problems: variational approaches focus on parametrizing a subclass of solutions within the feasible set. In contrast, relaxation techniques have been proposed to approximate it from outside, thus complementing the variational approach to provide ultimate bounds to the global optimal solution. In this paper, we propose a novel approach combining the power of relaxation techniques with deep reinforcement learning in order to find the best possible bounds within a limited computational budget. We illustrate the viability of the method in two paradigmatic problems in quantum physics and quantum information processing: finding the ground state energy of many-body quantum systems, and building energy-based entanglement witnesses of quantum local Hamiltonians. We benchmark our approach against other classical optimization algorithms such as breadth-first search or Monte Carlo, and we characterize the effect of transfer learning. We find the latter may be indicative of phase transitions with a completely autonomous approach. Finally, we provide tools to tackle other common applications in the field of quantum information processing with our method.

We study a three-dimensional (3D) classical Ising model that is exactly solvable when some coupling constants take certain imaginary values. The solution combines and generalizes the Onsager-Kaufman solution [L. Onsager, Phys. Rev. 65, 117 (1944); B. Kaufman, Phys. Rev. 76, 1232 (1949)] of the 2D Ising model and the solution of Kitaev's honeycomb model [A. Kitaev, Ann. Phys, 321, 2 (2006)], leading to a three-parameter phase diagram with a third-order phase transition between two distinct phases. Interestingly, the phases of this model are distinguished by topological features: the expectation value of a certain family of loop observables depend only on the topology of the loop (whether the loop is contractible), and are quantized at rational values that differ in the two phases. We show that a related exactly solvable 3D classical statistical model with real coupling constants also shows the topological features of one of these phases. Furthermore, even in the model with complex parameters, the partition function has some physical relevance, as it can be interpreted as the transition amplitude of a quantum dynamical process and may shed light on dynamical quantum phase transitions.

Quasiperiodic behavior is mostly known to occur in systems with enforced quasiperiodicity or randomness, in either the lattice structure or the potential, as well as in periodically driven systems. Here, we present instead a rarer setting where quasiperiodic behavior emerges in clean, nondriven lattice systems. We illustrate this through two examples of experimental relevance, namely an infinite tight-binding chain with a gated segment, and a hopping particle coupled to static Ising degrees of freedom. We show how the quasiperiodic behavior manifests in the number of states that are localized by the geometry of the system, with corresponding effects on transport and hybridization properties.

Experimental progress in qubit manufacturing calls for the development of new theoretical tools to analyze quantum data. We show how an unsupervised machine-learning technique can be used to understand short-range entangled many-qubit systems using data of local measurements. The method successfully constructs the phase diagram of a cluster-state model and detects the respective order parameters of its phases, including string order parameters. For the toric code subject to external magnetic fields, the machine identifies the explicit forms of its two stabilizers. Prior information of the underlying Hamiltonian or the quantum states is not needed; instead, the machine outputs their characteristic observables. Our work opens the door for a first-principles application of hybrid algorithms that aim at strong interpretability without supervision.

To define the topology of driven systems, recent works have proposed synthetic dimensions as a way to uncover the underlying parameter space of topological invariants. Using time as a synthetic dimension, together with a momentum dimension, gives access to a synthetic two-dimensional ($2\mathrm{D}$) Chern number. It is, however, still unclear how the synthetic 2D Chern number is related to the Chern number that is defined from a parametric variable that evolves with time. Here we show that in periodically driven systems in the adiabatic limit, the synthetic $2\mathrm{D}$ Chern number is a multiple of the Chern number defined from the parametric variable. The synthetic 2D Chern number can thus be engineered via how the parametric variable evolves in its own space. We justify our claims by investigating Thouless pumping in two one-dimensional ($1\mathrm{D}$) tight-binding models, a three-site chain model, and a two-$1\mathrm{D}$-sliding-chains model. The present findings could be extended to higher dimensions and other periodically driven configurations.

Dirac semimetals feature Dirac cones with topologically nontrivial states in the bulk that are protected by crystalline symmetries. They attract considerable attention due to rich quantum states and properties of interest, such as high Fermi velocities, mobility, and small effective masses. Here, we show that a ternary intermetallic BaAuSb crystal hosts both trivial and nontrivial topological Dirac states in the bulk. The nontrivial Fermi-surface pocket at the Brillouin zone center is characterized with only a few hundredths of a bare electron mass and with very high mobility. All parts of the Fermi surface detected by quantum oscillations, topologically trivial or nontrivial, have carriers with unusually high Fermi velocities and small masses. These conducting states may be coupled with magnetic moments in materials where Ba is replaced by magnetic rare-earth atoms.