The postulate of gauge invariance in nature does not lend itself directly to implementations of lattice gauge theories in modern setups of quantum synthetic matter. Unavoidable gauge-breaking errors in such devices require gauge invariance to be enforced for faithful quantum simulation of gauge-theory physics. This poses major experimental challenges, in large part due to the complexity of the gauge-symmetry generators. Here, we show that gauge invariance can be reliably stabilized by employing simplified local pseudogenerators designed such that within the physical sector they act identically to the actual local generator. Dynamically, they give rise to emergent exact gauge theories up to time scales polynomial and even exponential in the protection strength. This obviates the need for implementing often complex multibody full gauge symmetries, thereby further reducing experimental overhead in physical realizations. We showcase our method in the ${\mathbb{Z}}_2$ lattice gauge theory, and discuss experimental considerations for its realization in modern ultracold-atom setups.

In this paper we analyze the spectral level statistics of the one-dimensional ionic Hubbard model, the Hubbard model with an alternating on-site potential. In particular, we focus on the statistics of the gap ratios between consecutive energy levels. This quantity is often used in order to signal whether a many-body system is integrable or chaotic. A chaotic system has typically the statistics of a Gaussian ensemble of random matrices while the spectral properties of the integrable system follow a Poisson statistics. We find that whereas the Hubbard model without alternating potential is known to be integrable and its spectral properties follow a Poissonian statistics, the presence of an alternating potential causes a drastic change in the spectral properties, which resemble the one of a Gaussian ensemble of random matrices. However, to uncover this behavior one has to separately consider the blocks of all symmetries of the ionic Hubbard model.

The scaling of the entanglement entropy at a quantum critical point allows us to extract universal properties of the state, e.g., the central charge of a conformal field theory. With the rapid improvement of noisy intermediate-scale quantum (NISQ) devices, these quantum computers present themselves as a powerful tool to study critical many-body systems. We use finite-depth quantum circuits suitable for NISQ devices as a variational ansatz to represent ground states of critical, infinite systems. We find universal finite-depth scaling relations for these circuits and verify them numerically at two different critical points, i.e., the critical Ising model with an additional symmetry-preserving term and the critical XXZ model.

Vortices and black holes set the scene for many interesting dynamical processes in physics. Here, we study the dynamical instability of quantized vortices and rotational superradiance around rotating black holes, illustrating in the process that the same physics is at play in these two seemingly disparate phenomena. We also compare the instability of the vortex to the black hole bomb instability, which occurs for massive scalar fields in the Kerr spacetime. Taking inspiration from the analogy between black hole bomb modes and the hydrogen spectrum, the vortex instability is compared with nuclear resonances involved in $\alpha$ decay.

Dipole-coupled subwavelength quantum emitter arrays respond cooperatively to external light fields as they may host collective delocalized excitations (a form of excitons) with super- or subradiant character. Deeply subwavelength separations typically occur in molecular ensembles, where in addition to photon-electron interactions, electron-vibron couplings and vibrational relaxation processes play an important role. We provide analytical and numerical results on the modification of super- and subradiance in molecular rings of dipoles including excitations of the vibrational degrees of freedom. While vibrations are typically considered detrimental to coherent dynamics, we show that molecular dimers or rings can be operated as platforms for the preparation of long-lived dark superposition states aided by vibrational relaxation. In closed ring configurations, we extend previous predictions for the generation of coherent light from ideal quantum emitters to molecular emitters, quantifying the role of vibronic coupling onto the output intensity and coherence.

As an unconventional realization of topological orders with an exotic interplay of topology and geometry, fracton (topological) orders feature subextensive topological ground-state degeneracy and subdimensional excitations that are movable only within a certain subspace. It has been known, in the exactly solvable three-dimensional X-cube model that universally represents the type-I fracton orders, that mobility constraints on subdimensional excitations originate from the absence of spatially deformable stringlike operators. To unveil the interplay of topology and geometry, in this paper, we study the dynamical signature in the X-cube model in the presence of external Zeeman fields via large-scale quantum Monte Carlo simulation and stochastic analytic continuation. We compute both real-space correlation functions and dynamic structure factors of subdimensional excitations (i.e., fractons, lineons, and planons) in the fracton phase and their evolution into the trivial paramagnetic phase by increasing external fields. We find, in the fracton phase, that the correlation functions and the spectral functions show clear anisotropy exactly caused by the underlying mobility constraints. On the other hand, the external fields successfully induce quantum fluctuations and offer mobility to excitations along the subspace allowed by mobility constraints. These numerical results provide the evolution of a dynamical signature of subdimensional particles in fracton orders, indicating that the mobility constraints on local dynamical properties of subdimensional excitations are deeply related to the existence of fracton topological order. The results will also be helpful in potential experimental identifications in spectroscopy measurements such as neutron scattering and nuclear magnetic resonance.

Running quantum algorithms on real hardware is essential for understanding their strengths and limitations, especially in the noisy intermediate scale quantum (NISQ) era. Herein we focus on the practical aspect of quantum computational calculations of solid-state crystalline materials based on theory developed in our group by using real quantum hardware with a noise mitigation technique referred to as partition-measurement symmetry verification, which performs postselection of shot counts based on $Z_2$ and $U_1$ symmetry verification. We select two periodic systems with different levels of complexity for these calculations. One of them is the distorted hydrogen chain as an example of very simple systems, and the other one is iron crystal in the bcc and fcc phases as it is considered to be inaccessible by using classical computational wave-function methods. The ground-state energies are evaluated based on the translational quantum subspace expansion method for the hydrogen chain, and periodic boundary condition adapted variational quantum eigensolver for our iron models. By applying these techniques for the simplest two-qubit iron model systems, the correlation energies obtained by the hardware calculations agree with those of the state-vector simulations within $\sim 5$ kJ/mol. Although the quantum computational resources used for those experiments are still limited, the techniques applied to obtain our simplified models will be applicable in essentially the same manner to more complicated cases as quantum hardware matures.

Constructing new topological phases is very important in both Hermitian and non-Hermitian systems because of their potential applications. Here we propose theoretically and demonstrate a general scheme experimentally to construct $N\mathrm{th}$ power root topological phases. Such a scheme is not only suitable for Hermitian systems, but also non-Hermitian systems. It is found that the robust degree of edge state in the Hermitian system becomes stronger and stronger with the increase of $N$. It tends to be a strongly surface localized form when $N$ is large enough. In the non-Hermitian system, the skin effect becomes more apparent, and it approaches the ideal situation with the increase of $N$. This means that edge states and skin effects can be observed by taking different $N$. This scheme has been proved experimentally by designing circuits. Our work opens up a way to engineer topological states according to the requirements, which is very important for developing topologically protected devices, such as topology sensing, switches, and so on.

Theoretical studies of magnets have traditionally concentrated on either classical spins, or the extreme quantum limit of spin-1/2. However, magnets built of spin-1 moments are also intrinsically interesting, not least because they can support quadrupole, as well as dipole moments, on a single site. For this reason, spin-1 models have been extensively studied as prototypes for quadrupolar (spin-nematic) order in magnetic insulators, and Fe-based superconductors. At the same time, because of the presence of quadrupoles, the classical limit of a spin-1 moment is not an $O\left(3\right)$ vector, a fact, which must be taken into account in describing their properties. In this article we develop a method to simulate spin-1 magnets based on a $u\left(3\right)$ algebra, which treats both dipole and quadrupole moments on equal footing. This approach is amenable to both classical and quantum calculations, and we develop the techniques needed to calculate thermodynamic properties through Monte Carlo simulations and classical low-temperature expansion, and dynamical properties, through “molecular dynamics” simulations and a multiple-boson expansion. As a case study, we present detailed analytic and numerical results for the thermodynamic properties of ferroquadrupolar order on the triangular lattice, and its associated dynamics. At low temperatures, we show that it is possible to “correct” for the effects of classical statistics in simulations, and extrapolate to the zero-temperature quantum results found in flavour-wave theory.

In recent years, strong-field physics in condensed matter was pioneered as a potential approach for controlling material properties through laser dressing, as well as for ultrafast spectroscopy via nonlinear light-matter interactions (e.g., harmonic generation). A potential controversy arising from these advancements is that it is sometimes vague which band picture should be used to interpret strong-field experiments: The field-free bands, the adiabatic (instantaneous) field-dressed bands, Floquet bands, or some other intermediate picture. Here, we try to resolve this issue by performing theoretical experiments of time- and angle-resolved photoelectron spectroscopy (Tr-ARPES) for a strong-field laser-pumped solid, which should give access to the actual observable bands of the irradiated material. To our surprise, we find that the adiabatic band picture survives quite well up to high field intensities ($\sim {10}^{12}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$) and in a wide frequency range (driving wavelengths of 4000 to 800 nm, with Keldysh parameters ranging up to $\sim 7$). We conclude that, to first order, the adiabatic instantaneous bands should be the standard blueprint for interpreting ultrafast electron dynamics in solids when the field is highly off resonant with characteristic energy scales of the material. We then discuss weaker effects of modifications of the bands beyond this picture that are nonadiabatic, showing that by using bichromatic fields the deviations from the standard picture can be probed with enhanced sensitivity. In this paper, we outline a clear band picture for the physics of strong-field interactions in solids, which should be useful for designing and analyzing strong-field experimental observables and to formulate simpler semi-empirical models.

Identifying entanglement-based order parameters characterizing topological systems, in particular topological superconductors and topological insulators, has remained a major challenge for the physics of quantum matter in the last two decades. Here we show that the end-to-end, long-distance, bipartite squashed entanglement between the edges of a many-body system, defined in terms of the edge-to-edge quantum conditional mutual information, is the natural nonlocal order parameter for topological superconductors in one dimension as well as in quasi-one-dimensional geometries. For the Kitaev chain in the entire topological phase, the edge squashed entanglement is quantized to $ln\left(2\right)/2$, half the maximal Bell-state entanglement, and vanishes in the trivial phase. Such a topological squashed entanglement exhibits the correct scaling at the quantum phase transition, is stable in the presence of interactions, and is robust against disorder and local perturbations. Edge quantum conditional mutual information and edge squashed entanglement defined with respect to different multipartitions discriminate topological superconductors from symmetry breaking magnets, as shown by comparing the fermionic Kitaev chain and the spin-1/2 Ising model in transverse field. For systems featuring multiple topological phases with different numbers of edge modes, like the quasi-1D Kitaev ladder, topological squashed entanglement counts the number of Majorana excitations and distinguishes the different topological phases of the system. In fact, we show that the edge quantum conditional mutual information and the edge squashed entanglement remain valid detectors of topological superconductivity even for systems, like the Kitaev tie with long-range hopping, featuring geometrical frustration and a suppressed bulk-edge correspondence.

Out-of-equilibrium systems exhibit various dynamic phases with different degrees of order. A moving smectic phase with transverse periodicity is one of the ordered states, which is theoretically expected to be generic to driven two-dimensional systems. However, a comprehensive dynamic phase diagram, including the moving smectic phase, has not been obtained because of lack of suitable experimental methods. Here we study dynamic phases of driven vortex matter in an amorphous ${\mathrm{Mo}}_x{\mathrm{Ge}}_{1-x}$ film by using two-step measurements of transient voltage in response to mutually perpendicular driving currents. We find dynamic orderings from the plastic flow to the anisotropic smectic flow and from the anisotropic smectic flow to the isotropic moving Bragg glass as a function of the current. Convincing evidence of the moving smectic phase is obtained from the first transverse mode locking (ML) with signals larger than those of longitudinal ML, indicating the higher transverse order than the longitudinal one. Transverse ML developed here is useful to detect the anisotropic periodicity in driven media.

As a powerful tool, pressure can effectively tune the electronic structure of elements, such as gold (Au), to react with other elements and form a material that is inaccessible at atmospheric pressure. However, current knowledge shows that Au cannot form stable compounds with nitrogen (N) even under extreme compression, and it is thus of fundamental interest to hunt stable compounds with Au-N bonds in the fields of physics and chemistry. Here, we perform extensive swarm-intelligence structure searching simulations on the Au-N system under high pressure by introducing the additional element of lithium (Li). Remarkably, a variety of ternary Au-N-Li structures with archetypal Au-N bonds features are proposed to be stable under high pressure, becoming an example of stable compounds with Au-N bonds, where Li plays a key role in providing electrons and improving the stability of the Au-N system. These results establish the theoretical stability of the compressed ternary Au-N-Li system, and more importantly, highlight the importance of lithium as the electron donor in tuning the structures of Au-bearing compounds.

The construction and classification of crystalline symmetry protected topological (SPT) phases in interacting bosonic and fermionic systems have been intensively studied in the past few years. Crystalline SPT phases are not only of conceptual importance, but also provide us great opportunities towards experimental realization since space group symmetries naturally exist for any realistic material. In this paper, we systematically classify the crystalline topological superconductors (TSC) and topological insulators (TI) in 2D interacting fermionic systems by using an explicit real-space construction. In particular, we discover an intriguing fermionic crystalline topological superconductor that can only be realized in interacting fermionic systems (i.e., not in free-fermion or interacting bosonic systems). Moreover, we also verify the recently conjectured crystalline equivalence principle for generic 2D interacting fermionic systems.

We develop the Landau-Zener transfer matrix theory for the instantaneous Floquet states (IFSs) for quantum systems driven by a strong pulse laser. Applying this theory to the pulse excitation probability in two-level quantum systems, we show unexpectedly good quantitative agreement for few-cycle pulses. This approach enables us to qualitatively understand the probability's peculiar behaviors as quantum path interference between IFSs. We also study the pulse-width dependence, finding that this Floquet-state interpretation remains useful for shorter pulses down to two-cycle ones in the present model. These results imply that the Floquet theory is meaningful in experimental few-cycle lasers if applied appropriately in the sense of IFSs.

It is not widely appreciated that an acoustic wave can “jump” or “tunnel” across a vacuum gap between two piezoelectric solids, nor has the general case been formulated or studied in detail. Here, we remedy that situation, by presenting a general formalism and approach to study such an acoustic tunneling effect between two arbitrarily oriented anisotropic piezoelectric semi-infinite crystals. The approach allows one to solve for the reflection and transmission coefficients of all the partial-wave modes, and is amenable to practical numerical or even analytical implementation, as we demonstrate by a few chosen examples. The formalism can be used in the future for quantitative studies of the tunneling effect in connection not only with the manipulation of acoustic waves, but with many other areas of physics of vibrations such as heat transport, for example.