We investigate the ground-state properties of quantum particles interacting via a long-range repulsive potential ${\mathcal{V}}_{\sigma }(x)\sim 1/|x{|}^{1+\sigma }$ ($-1<\sigma$) or ${\mathcal{V}}_{\sigma }(x)\sim -|x{|}^{-1-\sigma }$ ($-2\le \sigma <-1$) that interpolates between the Coulomb potential ${\mathcal{V}}_0(x)$ and the linearly confining potential ${\mathcal{V}}_{-2}(x)$ of the Schwinger model. In the absence of disorder the ground state is a Wigner crystal when $\sigma \le 0$. Using bosonization and the nonperturbative functional renormalization group we show that any amount of disorder suppresses the Wigner crystallization when $-3/2<\sigma \le 0$; the ground state is then a Mott glass, i.e., a state that has a vanishing compressibility and a gapless optical conductivity. For $\sigma <-3/2$ the ground state remains a Wigner crystal.

The realization of interacting topological states of matter such as fractional Chern insulators (FCIs) in cold atom systems has recently come within experimental reach due to the engineering of optical lattices with synthetic gauge fields providing the required topological band structures. However, detecting their occurrence might prove difficult since transport measurements akin to those in solid state systems are challenging to perform in cold atom setups and alternatives have to be found. We show that for a $\nu =1/2$ FCI state realized in the lowest band of a Harper-Hofstadter model of interacting bosons confined by a harmonic trapping potential, the fractionally quantized Hall conductivity ${\sigma }_{xy}$ can be accurately determined by the displacement of the atomic cloud under the action of a constant force which provides a suitable experimentally measurable signal for detecting the topological nature of the state. Using matrix-product state algorithms, we show that, in both cylinder and square geometries, the movement of the particle cloud in time under the application of a constant force field on top of the confining potential is proportional to ${\sigma }_{xy}$ for an extended range of field strengths.

The quest for non-Abelian quasiparticles has inspired decades of experimental and theoretical efforts, where the scarcity of direct probes poses a key challenge. Among their clearest signatures is a thermal Hall conductance with quantized half-integer value in units of ${\kappa }_0={\pi }^2{k}_B^{2}T/3h$ ($T$ is temperature, $h$ the Planck constant, $k_B$ the Boltzmann constant). Such values were recently observed in a quantum-Hall system and a magnetic insulator. We show that nontopological “thermal metal” phases that form due to quenched disorder may disguise as non-Abelian phases by well approximating the trademark quantized thermal Hall response. Remarkably, the quantization here improves with temperature, in contrast to fully gapped systems. We provide numerical evidence for this effect and discuss its possible implications for the aforementioned experiments.

The temperature dependence of the superfluid density ${\rho }_s(T)$ has been measured for a series of ultrathin MBE-grown ${\mathrm{DyBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7\text{−}\delta }$ superconducting (SC) films by submillimeter wave interferometry combined with time-domain terahertz spectroscopy and IR ellipsometry. We find that all films 10 u.c. and thicker show the same universal temperature dependence of ${\rho }_s(T)$, which follows the critical behavior characteristic of single crystal ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7\text{−}\delta }$ as $T$ approaches $T_c$. In 7 u.c. thick films, ${\rho }_s(T)$ declines steeply upon approaching $T_c$, as expected for the Berezinskii-Kosterlitz-Thouless vortex unbinding transition. Our analysis provides evidence for a sharply defined 4 u.c. non-SC interfacial layer, leaving a quasi-2D SC layer on top. We propose that the SC state in this interfacial layer is suppressed by competing (possibly charge) order.

We show that when the time reversal symmetry is broken in a multicomponent superconducting condensate without inversion symmetry the resulting Bogoliubov quasiparticles generically exhibit mini-Bogoliubov-Fermi (BF) surfaces, for small superconducting order parameter. The absence of inversion symmetry makes the BF surfaces stable with respect to weak perturbations. With sufficient increase of the order parameter, however, the Bogoliubov-Fermi surface may disappear through a Lifshitz transition, and the spectrum this way become fully gapped. Our demonstration is based on the computation of the effective Hamiltonian for the bands near the normal Fermi surface by the integration over high-energy states. Exceptions to the rule, and experimental consequences are briefly discussed.

Recent experiments have tuned the monolayer $1{\mathrm{T}}^{\prime }\text{−}{\mathrm{WTe}}_2$ to be superconducting by electrostatic gating. Here, we theoretically study the phonon-mediated superconductivity in monolayer $1{\mathrm{T}}^{\prime }\text{−}{\mathrm{WTe}}_2$ via charge doping. We reveal that the emergence of soft-mode phonons with specific momentum is crucial to give rise to the superconductivity in the electron-doping regime, whereas no such soft-mode phonons and no superconductivity emerge in the hole-doping regime. We also find a superconducting dome, which can be attributed to the change of Fermi surface nesting conditions with electron doping. By taking into account the experimentally established strong anisotropy of temperature-dependent upper critical field $H_{c2}$ between the in-plane and out-of-plane directions, we show that the superconducting state probably has the unconventional equal-spin-triplet pairing in the $A_u$ channel of the $C_{2h}$ point group. Our studies provide a promising understanding to the doping dependent superconductivity and strong anisotropy of $H_{c2}$ in monolayer $1{\mathrm{T}}^{\prime }\text{−}{\mathrm{WTe}}_2$, and can be extended to understand the superconductivity in other gated transition metal dichalcogenides.

Motivated by recent progress on synthesizing two-dimensional magnetic van der Waals systems, we propose a setup for detecting the topological Berezinskii-Kosterlitz-Thouless phase transition in spin-transport experiments on such structures. We demonstrate that the spatial correlations of injected spin currents into a pair of metallic leads can be used to measure the predicted universal jump of $2/\pi$ in the ferromagnet spin stiffness as well as its predicted universal square root dependence on temperature as the transition is approached from below. Our setup provides a simple route to measuring this topological phase transition in two-dimensional magnetic systems, something which up to now has proven elusive. It is hoped that this will encourage experimental efforts to investigate critical phenomena beyond the standard Ginzburg-Landau paradigm in low-dimensional magnetic systems with no local order parameter.

We study nonlinear response in quantum spin systems near infinite-randomness critical points. Nonlinear dynamical probes, such as two-dimensional (2D) coherent spectroscopy, can diagnose the nearly localized character of excitations in such systems. We present exact results for nonlinear response in the 1D random transverse-field Ising model, from which we extract information about critical behavior that is absent in linear response. Our analysis yields exact scaling forms for the distribution functions of relaxation times that result from realistic channels for dissipation in random magnets. We argue that our results capture the scaling of relaxation times and nonlinear response in generic random quantum magnets in any spatial dimension.

We combine the anisotropy of magnetic interactions and the point symmetry of finite solids in the study of dipolar clusters as new basic units for multiferroics metamaterials. The Hamiltonian of magnetic dipoles with an easy axis at the vertices of polygons and polyhedra, maps exactly into a Hamiltonian with symmetric and antisymmetric exchange couplings. The last one gives rise to a Dzyaloshinskii-Moriya contribution responsible for the magnetic modes of the systems and their symmetry groups, which coincide with those of a particle in a crystal field with spin-orbit interaction. We find that the clusters carry spin current and that they manifest the magnetoelectric effect. We expect our results to pave the way for the rational design of magnetoelectric devices at room temperature.

Microswimmers typically move near walls, which can strongly influence their motion. However, direct experimental measurements of swimmer-wall separation remain elusive to date. Here, we determine this separation for model catalytic microswimmers from the height dependence of the passive component of their mean-squared displacement. We find that swimmers exhibit “ypsotaxis,” a tendency to assume a fixed height above the wall for a range of salt concentrations, swimmer surface charges, and swimmer sizes. Our findings indicate that ypsotaxis is activity induced, posing restrictions on future modeling of their still-debated propulsion mechanism.

Active materials, composed of internally driven particles, have properties that are qualitatively distinct from matter at thermal equilibrium. However, the most spectacular departures from equilibrium phase behavior are thought to be confined to systems with polar or nematic asymmetry. In this Letter, we show that such departures are also displayed by more symmetric phases such as hexatics if, in addition, the constituent particles have chiral asymmetry. We show that chiral active hexatics whose rotation rate does not depend on density have giant number fluctuations. If the rotation rate depends on density, the giant number fluctuations are suppressed due to a novel orientation-density sound mode with a linear dispersion which propagates even in the overdamped limit. However, we demonstrate that beyond a finite but large length scale, a chirality and activity-induced relevant nonlinearity invalidates the predictions of the linear theory and destroys the hexatic order. In addition, we show that activity modifies the interactions between defects in the active chiral hexatic phase, making them nonmutual. Finally, to demonstrate the generality of a chiral active hexatic phase we show that it results from the melting of chiral active crystals in finite systems.

We consider the problem of encoding pairwise correlations between coupled dynamical systems in a low-dimensional latent space based on few distinct observations. We use variational autoencoders (VAEs) to embed temporal correlations between coupled nonlinear oscillators that model brain states in the wake-sleep cycle into a two-dimensional manifold. Training a VAE with samples generated using two different parameter combinations results in an embedding that encodes the repertoire of collective dynamics, as well as the topology of the underlying connectivity network. We first follow this approach to infer the trajectory of brain states measured from wakefulness to deep sleep from the two end points of this trajectory; then, we show that the same architecture was capable of representing the pairwise correlations of generic Landau-Stuart oscillators coupled by complex network topology.

We present a class of Hamiltonians $H$ for which a sector of the Hilbert space invariant under a Lie group $G$, which is not a symmetry of $H$, possesses the essential properties of many-body scar states. These include the absence of thermalization and the “revivals” of special initial states in time evolution. A particular class of examples concerns interacting spin-$1/2$ fermions on a lattice consisting of $N$ sites (it includes deformations of the Fermi-Hubbard model as special cases), and we show that it contains two families of $N+1$ scar states. One of these families, which was found in recent literature, comprises the well-known $\eta$-pairing states. We find another family of scar states that is $\mathrm{U}(N)$ invariant. Both families and most of the group-invariant scar states produced by our construction, in general, give rise to the off-diagonal long range order, which survives at high temperatures and is insensitive to the details of the dynamics. Such states could be used for reliable quantum information processing because the information is stored nonlocally and thus cannot be easily erased by local perturbations. In contrast, other scar states we find are product states, which could be easily prepared experimentally. The dimension of scar subspace is directly controlled by the choice of group $G$ and can be made exponentially large.

We study scalar fields in a black hole background and show that, when the scalar is suitably coupled to curvature, rapid rotation can induce a tachyonic instability. This instability, which is the hallmark of spontaneous scalarization in the linearized regime, is expected to be quenched by nonlinearities and endow the black hole with scalar hair. Hence, our results demonstrate the existence of a broad class of theories that share the same stationary black hole solutions with general relativity at low spins, but which exhibit black hole hair at sufficiently high spins ($a/M\gtrsim 0.5$). This result has clear implications for tests of general relativity and the nature of black holes with gravitational and electromagnetic observations.

A number of approaches to four-dimensional quantum gravity, such as loop quantum gravity and holography, situate areas as their fundamental variables. However, this choice of kinematics can easily lead to gravitational dynamics peaked on flat spacetimes. We show that this is due to how regions are glued in the gravitational path integral via a discrete spin foam model. We introduce a family of “effective” spin foam models that incorporate a quantum area spectrum, impose gluing constraints as strongly as possible, and leverage the discrete general relativity action to specify amplitudes. These effective spin foam models avoid flatness in a restricted regime of the parameter space.