We theoretically investigate non-Hermitian $p$-wave Fermi superfluidity in one-dimensional spin-polarized Fermi gases which is relevant to recent ultracold atomic experiments. Considering an imaginary atom-dimer coupling responsible for the three-body recombination process in the Lindblad formalism, we discuss the stability of the superfluid state against the atomic loss effect. Within the two-channel non-Hermitian BCS-Eagles-Leggett theory, the atomic loss is characterized by the product of the imaginary atom-dimer coupling and the $p$-wave effective range. Our results indicate that for a given imaginary atom-dimer coupling, a smaller magnitude of the effective ranges of $p$-wave interaction is crucial for reaching the non-Hermitian $p$-wave Fermi superfluid state. Moreover, our theoretical framework for many-body systems with the three-body loss, which is inevitable in ultracold atoms, would promote further progress in non-Hermitian cold-atomic physics.

Anomalous Floquet topological superconductivity with chirality can be achieved by applying a dc-bias voltage across the Josephson junction with a sandwiched magnetic topological insulator (TI), in which the intrinsic Josephson phase provides a time-dependent periodic driving [R.-X. Zhang and S. Das Sarma, Phys. Rev. Lett. 127, 067001 (2021)]. In this work, we remove the bias voltage and connect the magnetic TI to an external AC voltage source to modulate the chemical potential, thus bringing about an explicit-time Floquet periodic driving. In the context of the driving, the system is similarly found to convert into a two-dimensional anomalous Floquet topological superconductor with chirality. By tuning the AC voltage source's frequency, we obtain a rich variety of novel Floquet topological superconducting phases with chirality. Particularly, by manipulating such static parameters as Zeeman field and superconducting pairing potential, a series of topological superconducting phase transitions are also exhibited, accompanied by exotic Floquet topological superconducting phases with chirality.

The electromagnetic Casimir effect has a fermionic counterpart in topological insulators: Zero-point fluctuations of a massless Dirac fermion field mediate a force between magnetic scatterers. The Casimir force is insensitive to disorder that preserves the topological protection of an unpaired Dirac cone. The protection may be broken if the Dirac equation is discretized, and an exponential suppression of the Casimir effect will result if a gap opens at the Dirac point. Here, we show how this lattice artifact may be avoided, by applying a recently developed local discretization of the Euclidean action that does not suffer from the fermion-doubling obstruction of local discretizations of the Hamiltonian.

A hallmark of glasses is an excess of low-frequency, nonphononic vibrations. It is manifested as a terahertz peak—the boson peak—in the ratio of the vibrational density of state (VDoS) and Debye's VDoS of phonons. Here, using experimental data, extensive computer simulations, and a mean-field model, we show that the nonphononic part of the VDoS itself features both a universal power-law tail and a peak at higher frequencies, entirely accounted for by quasilocalized nonphononic vibrations, whose existence and spectra power-law tail were recently established in computer glasses. We rationalize the variation of the peak's frequency and magnitude with glasses' thermal history, which is much weaker than the variation of the tail and may follow an opposite trend, and show that the peak's modes are composed of many spatially coupled quasilocalized nonphononic vibrations. Our results shed light on the origin, nature, and properties of the boson peak in glasses.

We study the entanglement spectra of surface states of symmetry-protected topological phases. The topological bulk imprints the surface with an anomaly that does not permit it to form a trivial “vacuum” state that is gapped, unfractionalized, and symmetry preserving. Any surface wave function encodes the topology of the underlying bulk in addition to a specific surface phase. We show that the real-space entanglement spectrum of such surface wave functions are dominated by the bulk topology and do not readily permit identifying the surface phase. We thus use a modified form of entanglement spectra that incorporates the anomaly and argue that they correspond to physical edge states between different surface states. We support these arguments by explicit analytical and numerical calculations for free and interacting surfaces of three-dimensional topological insulators of electrons.

The construction of optimally localized Wannier functions (and Wannier functions in general) for a Chern insulator has been considered to be impossible owing to the fact that the second moment of such functions is generally infinite. In this article, we propose a solution to this problem in the case of a single band isolated from the rest of the band structure. We accomplish this by drawing an analogy between the minimization of the variance and the minimization of the electrostatic energy of a periodic array of point charges in a smooth neutralizing background. In doing so, we obtain a natural regularization of the diverging variance and this leads to an analytical solution to the minimization problem. We demonstrate our results numerically for a particular model system. Furthermore, we show how the optimally localized Wannier functions provide a natural way of evaluating the electric polarization for a Chern insulator.

Inspired by the persistent thermal Hall effects at finite temperatures in various quantum paramagnets, we explore the origin of the thermal Hall effects from the perspective of the upper branch parts by invoking dispersive and twisted crystal field excitations. It is shown that the upper branches of the local energy levels could hybridize and form dispersive bands. The observation is that, upon time-reversal symmetry breaking by the magnetic fields, these upper branch bands could acquire a Berry curvature distribution and contribute to the thermal Hall effect even in the paramagnetic regime. As a proof of principle, we consider the setting on kagomé lattice with one ground-state singlet and an excited doublet, and show this is indeed possible. We expect this effect to be universal and that it has no strong connection with the underlying lattice. Although the thermal Hall signal can be contributed from other sources such as phonons and their scattering in the actual materials, we discuss the application to the relevant quantum materials.

We present a ${}^{31}\mathrm{P}$ NMR investigation of $\mathrm{BaCdVO}{\left({\mathrm{PO}}_4\right)}_2$ focusing on the nearly saturated regime between ${\mu }_0{H}_{c1}=4.05\mathrm{T}$ and ${\mu }_0{H}_{c2}=6.5\mathrm{T}$, which used to be considered a promising candidate for a spin-nematic phase. NMR spectra establish the absence of any dipolar order there, whereas the weak field dependence of the magnetization above $H_{c1}$ is accounted for by Dzyaloshinskii-Moriya interaction terms. The low-energy spin dynamics (fluctuations), measured by the nuclear spin-lattice relaxation rate $T_1^{-1}$, confirms the continuity of this phase and the absence of any low-temperature phase transition. Unexpectedly, the spin dynamics above $H_{c1}$ is largely dominated by two-magnon processes, which is expected above the saturation field of a spin-nematic phase, but not inside. This shows that $\mathrm{BaCdVO}{\left({\mathrm{PO}}_4\right)}_2$ is indeed close to a spin-nematic instability; however, this phase is not stabilized. We thus confirm recent theoretical predictions that the spin-nematic phase can be stabilized, at most, in an extremely narrow field range close to saturation or is rather narrowly avoided [Jiang et al., Phys. Rev. Lett. 130, 116701 (2023)].

Quantum many-body scars (QMBSs) are a novel paradigm for the violation of the eigenstate thermalization hypothesis—Hamiltonians of these systems exhibit mid-spectrum eigenstates that are equidistant in energy and which possess low entanglement and evade thermalization for long times. We present a novel approach to understanding the anomalous dynamical behavior in these systems. Specifically, we postulate that QMBS Hamiltonians $H$ can generically be partitioned into a set of terms $O_a$ which do not commute over the entire Hilbert space, but commute to all orders within the subspace of scar states. All states in the scar subspace thus evolve according to a “broken unitary” $U_s\left(t\right)={\prod }_a{e}^{-i{O}_{a}t}$, where $H={\sum }_a{O}_a$, which provides a simple interpretation of the anomalous dynamical features exhibited by quantum scars; they evolve in time according to a simpler unitary operator allowing for revivals. It is found that the observed dynamical decoupling is often a direct consequence of simple local conditions, which when satisfied lead to recurring aspects of QMBSs, including equidistant eigenvalues, many-body revivals, and sub-volume-law entanglement entropy. Two classes of scar models emerge in this picture—those with a finite set of $O_a$, as pertaining of, for instance, scars in the AKLT model, and those with an extensive set of such operators, such as eta pairing scar states in the Hubbard model. Besides discussing how many well-known scar models fit into the above picture, we show how the broken unitary formalism captures many known scar construction methods, known in the literature and generalizes others such as quasiparticles matrix product state (MPS) based methods, and the Shiraishi-Mori approach.

Magnetic frustration can lead to peculiar magnetic orderings that break a discrete symmetry of the lattice in addition to the fundamental magnetic symmetries (i.e., spin rotation invariance and time-reversal symmetry). In this work, we focus on frustrated quantum magnets and study the nature of the quantum phase transition between a paramagnet and a magnetically ordered state with broken threefold (${\mathbb{Z}}_3$) crystal rotation symmetry. We show that the transition can occur in two stages, giving rise to an intermediate nematic phase in which rotation symmetry is broken but the system remains magnetically disordered. Since the nematic transition is described by the three-state Potts model, the intermediate phase is a ${\mathbb{Z}}_3$ Potts-nematic phase. Our prediction of the existence of a Potts-nematic phase is based on an analysis of bound states formed from two-magnon excitations in the paramagnet, which become gapless while single-magnon excitations remain gapped. By considering three different lattice models, we demonstrate a generic instability towards two-magnon bound state formation in the Potts-nematic channel. We present both numerical results and a general analytical perturbative formula for the bound state binding energy similar to BCS theory. We further discuss a number of different materials that realize key features of the model considered, and thus provide promising venues for possible experimental observation.

In the field of ergodicity-breaking phases, it has been recognized that quantum avalanches can destabilize many-body localization at a wide range of disorder strengths. This has in particular been demonstrated by the numerical study of a toy model, sometimes simply called the “avalanche model” or the “quantum sun model” [Phys. Rev. Lett. 129, 060602 (2022)], which consists of an ergodic seed coupled to a perfectly localized material. In this paper, we connect this toy model to a well-studied model in random matrix theory, the ultrametric ensemble. We conjecture that the models share the following features. (1) The location of the critical point may be predicted sharply by analytics. (2) On the localized site, both models exhibit Fock space localization. (3) There is a manifold of critical points. On the critical manifold, the eigenvectors exhibit nontrivial multifractal behavior that can be tuned by moving on the manifold. (4) The spectral statistics at criticality is intermediate between Poisson statistics and random matrix statistics, also tunable on the critical manifold. We confirm numerically these properties.

In this paper we study metastable states in single- and two-component dipolar Bose-Einstein condensates. We show that this system supports a rich variety of states that are remarkably stable despite not being ground states. In a parameter region where striped phases are ground states, we find such metastable states that are energetically favorable compared to triangular and honeycomb lattices. Among these metastable states we report a peculiar ring-lattice state, which is led by the competition between triangular and honeycomb symmetries and rarely seen in other systems. In the case of dipolar mixtures we show that via tuning the miscibility these states can be stabilized in a broader domain by utilizing interspecies interactions.

Entanglement forging based variational algorithms leverage the bipartition of quantum systems for addressing ground-state problems. The primary limitation of these approaches lies in the exponential summation required over the numerous potential basis states, or bitstrings, when performing the Schmidt decomposition of the whole system. To overcome this challenge, we propose a method for entanglement forging employing generative neural networks to identify the most pertinent bitstrings, eliminating the need for the exponential sum. Through empirical demonstrations on systems of increasing complexity, we show that the proposed algorithm achieves comparable or superior performance compared to the existing standard implementation of entanglement forging. Moreover, by controlling the amount of required resources, this scheme can be applied to larger as well as non-permutation-invariant systems, where the latter constraint is associated with the Heisenberg forging procedure. We substantiate our findings through numerical simulations conducted on spin models exhibiting one-dimensional rings, two-dimensional triangular lattice topologies, and nuclear shell model configurations.

In superconducting systems in which inversion and time-reversal symmetry are simultaneously broken the critical current for positive and negative current bias can be different. For superconducting systems formed by Josephson junctions (JJs) this effect is termed Josephson diode effect. In this paper, we study the Josephson diode effect for a superconducting quantum interference device (SQUID) formed by a topological JJ with a $4\pi$-periodic current-phase relationship and a topologically trivial JJ. We show how the fractional Josephson effect manifests in the Josephson diode effect with the application of a magnetic field and how tuning properties of the trivial SQUID arm can lead to diode polarity switching. We then investigate the ac response and show that the polarity of the diode effect can be tuned by varying the ac power and discuss differences between the ac diode effect of asymmetric SQUIDs with no topological JJ and SQUIDs in which one JJ is topological.

Quantized adiabatic transport can occur when a system is slowly modulated over time. In most realizations, however, the efficiency of such transport is reduced by unwanted dissipation, back-scattering, and nonadiabatic effects. In this paper, we realize a topological adiabatic pump in an electrical circuit network that supports remarkably stable and long-lasting pumping of a voltage signal. We further characterize the topology of our system by deducing the Chern number from the measured edge band structure. To achieve this, the experimental setup makes use of active circuit elements that act as time-variable voltage-controlled inductors.