The PH-Pfaffian (particle-hole Pfaffian) topological order has been proposed as a candidate order for the $\nu =5/2$ quantum Hall effect. The PH-Pfaffian liquid is known to be the ground state in several coupled wire and coupled stripe constructions. No translationally and rotationally invariant models with the PH-Pfaffian ground state have been identified so far. By employing anyon condensation on top of a topological order, allowed in an isotropic system, we argue that the PH-Pfaffian order is possible in the presence of rotational and translational symmetries.

Ortho-para conversion of molecularly chemisorbed ${\mathrm{H}}_2$ on a Pd(210) surface at a surface temperature of 50 K is reported. A combination of a pulsed molecular beam, photostimulated desorption, and resonance-enhanced multiphoton ionization techniques was used for probing the change in the rotational states of molecularly chemisorbed ${\mathrm{H}}_2$ on the surface. Our result shows that fast ortho-para conversion of chemisorbed ${\mathrm{H}}_2$ occurs. The conversion time was experimentally determined to be about 2 s, which is in good agreement with a previous theoretical calculation. This agreement supports that the ortho-para conversion mechanism of the molecularly chemisorbed ${\mathrm{H}}_2$ on Pd(210) is a two-step process based on the hyperfine-Coulomb excitation.

Van Hove points are special points in the energy dispersion, where the density of states exhibits analytic singularities. When a Van Hove point is close to the Fermi level, tendencies towards density wave orders, Pomeranchuk orders, and superconductivity can all be enhanced, often in more than one channel, leading to a competition between different orders and unconventional ground states. Here we consider the effects from higher-order Van Hove points, around which the dispersion is flatter than near a conventional Van Hove point, and the density of states has a power-law divergence. We argue that such points are present in intercalated graphene and other materials. We use an effective low-energy model for electrons near higher-order Van Hove points and analyze the competition between different ordering tendencies using an unbiased renormalization-group approach. For purely repulsive interactions, we find that two key competitors are ferromagnetism and chiral superconductivity. For a small attractive interaction, we find an unconventional spin Pomeranchuk order, in wich the spin oder parameter winds around the Fermi surface. The supermetal state, predicted for a single higher-order Van Hove point, is an unstable fixed point in our case.

We study the quench dynamics of a topologically trivial one-dimensional gapless wire following its sudden coupling to topological bound states. We find that as the bound states leak into and propagate through the wire, signatures of their topological nature survive and remain measurable over a long lifetime. Thus, the quench dynamically induces topological properties in the gapless wire. Specifically, we study a gapless wire coupled to fractionally charged solitons or Majorana fermions, and we characterize the dynamically induced topology in the wire, in the presence of coupling to the bath, disorder, and short-range interactions, by analytical and numerical calculations of the dynamics of fractional charge, fermion parity, entanglement entropy, and fractional exchange statistics. In a dual effective description, this phenomenon is described by correlators of boundary changing operators, which, remarkably, generate topologically nontrivial monodromies in the gapless wire, both for Abelian and non-Abelian quantum statistics of the bound states.

We propose an approach to study the ground state of quantum many-body systems in which tensor network states, specifically projected entangled pair states (PEPSs), and Green's function Monte Carlo (GFMC) are combined. PEPSs, by design, encode the area law which governs the scaling of entanglement entropy in quantum systems with short-range interactions but are hindered by the high computational complexity scaling with bond dimension $D$. GFMC is a highly efficient method, but it usually suffers from the infamous negative sign problem which can be avoided by the fixed-node approximation in which a guiding wave function is utilized to modify the sampling process. The trade-off for the absence of the negative sign problem is the introduction of systematic error by the guiding wave function. In this work, we combine these two methods, PEPS and GFMC, to take advantage of both of them. PEPSs are very accurate variational wave functions, while at the same time, only contractions of the single-layer tensor network are necessary in GFMC, which reduces the cost substantially. Moreover, energy obtained in GFMC is guaranteed to be variational and lower than the variational energy of the guiding PEPS wave function. Benchmark results of the $J_1-J_2$ Heisenberg model on the square lattice are provided.

Macroscopic two-dimensional (2D) sonic crystals with inversion symmetry are studied to reveal higher-order topological physics in classical wave systems. By tuning a single geometry parameter, the band topology of the bulk and the edges can be controlled simultaneously. The bulk band gap forms an acoustic analog of topological crystalline insulators with edge states which are gapped due to symmetry reduction on the edges. In the presence of mirror symmetry, the band topology of the edge states can be characterized by the Zak phase, illustrating the band topology in a hierarchy of dimensions, which is the key feature of higher-order topological phenomena. Moreover, the edge bands undergo topological transitions without closing the bulk band gap, revealing rich topological physics in both the bulk and edges. We characterize the higher-order topological bands using symmetry indicators in the Brillouin zone and link the symmetry indicators with the corner charge—a corner topological index. This approach allows us to identify higher-order topological boundary states through symmetry properties of the Bloch bands. We then generalize the higher-order topological phenomena protected by the inversion symmetry to arch-shaped sonic crystals with nonsymmorphic symmetries where similar but slightly different topological phenomena are revealed. In these systems, the rich, multidimensional topological transitions can be exploited for topological transfer among 0D (corner), 1D (edge), and 2D (bulk) acoustic modes by tuning the geometry of acoustic metamaterials.

We investigate electron spin currents induced optically via plasmonic modes in the Kretschmann configuration. By utilizing the scattering matrix formalism, we take the plasmonic mode coupled to an external laser drive into consideration and calculate induced magnetization in the metal. The spatial distribution of the plasmonic mode is inherited by the induced magnetization, which acts as an inhomogeneous effective magnetic field and causes the Stern-Gerlach effect to drive electron spin currents in the metal. We solve the spin diffusion equation with a source term to analyze the spin current as a function of the spin diffusion length of the metal, the frequency, and the incident angle of the external drive.

The self-averaging behavior of interacting many-body quantum systems has been mostly studied at equilibrium. The present paper addresses what happens out of equilibrium, as the increase of the strength of on-site disorder takes the system to the localized phase. We consider two local and two nonlocal quantities of great experimental and theoretical interest. In the delocalized phase, self-averaging depends on the observable and on the timescale, but the picture simplifies substantially when localization is reached. In the localized phase, the local observables become self-averaging at all times while the nonlocal quantities are throughout non-self-averaging. These behaviors are explained and scaling analysis is provided using the $\ell$-bit model and a toy model.

We study the dynamics of a Lipkin-Meshkov-Glick model in the presence of Markovian dissipation, with a focus on late-time dynamics and the approach to thermal equilibrium. Making use of a vectorized bosonic representation of the corresponding Lindblad master equation, we use degenerate perturbation theory in the weak-dissipation limit to analytically obtain the eigenvalues and eigenvectors of the Liouvillian superoperator, which in turn give access to closed-form analytical expressions for the time evolution of the density operator and observables. Our approach is valid for large systems but takes into account leading-order finite-size corrections to the infinite-system result. As an application, we show that the dissipative Lipkin-Meshkov-Glick model equilibrates by passing through a continuum of thermal states with damped oscillations superimposed, until finally reaching an equilibrium state with a temperature that in general differs from the bath temperature. We discuss limitations of our analytic techniques by comparing to exact numerical results.

In this paper we continue our analysis of the interplay between the pairing and the non-Fermi liquid behavior in a metal for a set of quantum-critical models with an effective dynamical electron-electron interaction $V\left({\mathrm{\Omega }}_m\right)\propto 1/{\left|{\mathrm{\Omega }}_m\right|}^{\gamma }$ (the $\gamma$ model). We analyze both the original model and its extension, in which we introduce an extra parameter $N$ to account for nonequal interactions in the particle-hole and particle-particle channel. In two previous papers [A. Abanov and A. V. Chubukov, Phys. Rev. B 102, 024524 (2020) and Y. Wu et al. Phys. Rev. B 102, 024525 (2020)] we considered the case $0<\gamma <1$ and argued that (i) at $T=0$, there exists an infinite discrete set of topologically different gap functions ${\mathrm{\Delta }}_n\left({\omega }_m\right)$, all with the same spatial symmetry, and (ii) each ${\mathrm{\Delta }}_n$ evolves with temperature and terminates at a particular $T_{p,n}$. In this paper we analyze how the system behavior changes between $\gamma <1$ and $\gamma >1$, both at $T=0$ and a finite $T$. The limit $\gamma \to 1$ is singular due to infrared divergence of $\int d{\omega }_{m}V\left({\mathrm{\Omega }}_m\right)$, and the system behavior is highly sensitive to how this limit is taken. We show that for $N=1$, the divergencies in the gap equation cancel out, and ${\mathrm{\Delta }}_n\left({\omega }_m\right)$ gradually evolve through $\gamma =1$ both at $T=0$ and a finite $T$. For $N\ne 1$, divergent terms do not cancel, and a qualitatively new behavior emerges for $\gamma >1$. Namely, the form of ${\mathrm{\Delta }}_n\left({\omega }_m\right)$ changes qualitatively, and the spectrum of condensation energies $E_{c,n}$ becomes continuous at $T=0$. We introduce different extension of the model, which is free from singularities for $\gamma >1$.

We analyze the Josephson $I_J$ and dissipative $I_{\text{dis}}$ currents in a magnetic Andreev interferometer in the presence of the long-range spin triplet component (LRSTC). The Andreev interferometer has a crosslike geometry and consists of a ${\mathrm{SF}}_l\text{−}\mathrm{F}\text{−}{\mathrm{F}}_r\mathrm{S}$ circuit and perpendicular to it a N-F-N circuit, where S, ${\mathrm{F}}_{l,r}$ are superconductors and weak ferromagnets with noncollinear magnetizations ${\mathbf{M}}_{l,r}$, and F is a ferromagnet with a high exchange energy. The ferromagnetic wire F can be replaced with a nonmagnetic wire n. In the limit of a weak proximity effect (PE), we obtain simple analytical expressions for the currents $I_J=I_c(\alpha ,\beta )sin\phi$ and $I_{\text{dis}}=I_V(\alpha ,\beta )cos\phi$. In particular, the critical Josephson current in a long Josephson junction (JJ) is $I_c(\alpha ,\beta )=I_{c0}\chi (\alpha ,\beta )$, where the function $\chi (\alpha ,\beta )$ is a function of angles ${(\alpha ,\beta )}_{l,r}$ that characterize the orientations of ${\mathbf{M}}_{l,r}$. The oscillating part of the dissipative current $I_{\text{osc}}\left(V\right)=\chi (\alpha ,\beta )cos\phi I_{V0}\left(V\right)$ in the N-F/n-N circuit depends on the angles ${(\alpha ,\beta )}_{l,r}$ in the same way as the critical Josephson current $I_c(\alpha ,\beta )$ but can be much greater than the $I_c(\alpha ,\beta )$. At some angles the current $I_c(\alpha ,\beta )$ changes sign. We briefly discuss a relation between the negative current $I_c(\alpha ,\beta )$ and paramagnetic response. We argue that the measurements of the conductance in the N-F/n-N circuit can be used as another complementary method to identify the LRSTC in S/F heterostructures.

Effective Hamiltonian simulations are conducted to unveil the nature of the low-frequency polar modes in the prototype relaxor ferroelectric, $\mathrm{Pb}\left({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}\right){\mathrm{O}}_3$. Above the so-called $T^{*}$ temperature, only a single soft-mode exists, with its frequency increasing under heating. On the other hand, for temperatures lower than the freezing temperature, this single soft-mode splits into two modes, with one mode slightly changing its low resonant frequency while the other exhibiting a resonant frequency sharply increasing under cooling, in agreement with previous measurements. More importantly, we present evidences that these two modes can be regarded as Goldstone-like and Higgs-like modes, inherent to the Mexican-hat-form of the atomic displacement potential we also reveal here, therefore extending the types of systems exhibiting Higgs-boson characteristics to relaxor ferroelectrics.

The chirality of chiral multifold fermions in reciprocal space is related to the chirality of crystal lattice structures in real space. In this study, we propose a strategy to detect and identify multifold fermions of opposite chirality in nonmagnetic systems using second-order optical transports. Chiral crystals related with inversion operations cannot be made to overlap with each other via any experimental operation. Further, chiral multifold fermions within such crystals host opposite chiralities corresponding to a given $k$ point. A change in chirality is indicated by a corresponding change in the sign of the second-order charge current dominated by chiral fermions. This property can be exploited to study the relationship between chiralities in reciprocal and real spaces by utilizing bulk transport.

The phenomenon of many-body Stark localization of bosons in tilted optical lattice is studied. Despite the fact that no disorder is necessary for Stark localization to occur, it is very similar to well-known many-body localization (MBL) in sufficiently strong disorder. Not only the mean gap ratio reaches Poissonian value as characteristic for localized situations, but also the eigenstates reveal multifractal character as in standard MBL. Stark localization enables a coexistence of spacially separated thermal and localized phases in the harmonic trap similarly to fermions. Stark localization may also lead to spectacular trapping of particles in a reversed harmonic field which naively might be considered as an unstable configuration.

The Loschmidt amplitude of the purified states of mixed-state density matrices is shown to have zeros when the system undergoes a quasistatic, quench, or Uhlmann process. While the Loschmidt-amplitude zero of a quench process corresponds to a dynamical quantum phase transition (DQPT) accompanied by the diverging dynamical free energy, the Loschmidt-amplitude zero of the Uhlmann process corresponds to a topological phase transition (TQPT) accompanied by a jump of the Uhlmann phase. Although the density matrix remains intact in a quasistatic process, the Loschmidt amplitude can have zeros not associated with a phase transition. We present examples of two-level and three-level systems exhibiting finite- or infinite-temperature DQPTs and finite-temperature TQPTs associated with the Loschmidt-amplitude zeros. Moreover, the dynamical phase or geometrical phase of mixed states can be extracted from the Loschmidt amplitude. Those phases may become quantized or exhibit discontinuity at the Loschmidt-amplitude zeros. A spinor representation of the purified states of a general two-level system is presented to offer more insights into the change of purification in different processes. The quasistatic process, for example, is shown to cause a rotation of the spinor.

The Kibble-Zurek mechanism describes the saturation of critical scaling upon dynamically approaching a phase transition. This is a consequence of the breaking of adiabaticity due to the scale set by the slow drive. By driving the gap parameter, this can be used to determine the leading critical exponents. But this is just the ‘tip of the iceberg:’ Driving more general couplings allows one to activate the entire universal spectrum of critical exponents. Here we establish this phenomenon and its observable phenomenology for the quantum phase transitions in an analytically solvable minimal model and the experimentally relevant transverse XY model. The excitation density is shown to host the sequence of exponents including the subleading ones in the asymptotic scaling behavior by a proper design of the geometry of the driving protocol in the phase diagram. The case of a parallel drive relative to the phase boundary can still lead to the breaking of adiabaticity, and exposes the subleading exponents in the clearest way. Complementarily to disclosing universal information, we extract the restrictions due to the nonuniversal content of the models onto the extent of the subleading scalings regimes.

It is generally accepted that quantized vortices formed in coherent bosonic fluids are “excitations” and as such do not arise in a one-mode condensate at zero temperature. To excite them, one needs either inhomogeneities (impurities, rotation, etc.) or essentially finite fluctuations. Here, we predict a perfectly spontaneous formation of vortices even at zero temperature, which takes place in a homogeneous cavity-polariton system under one-mode optical excitation at normal incidence. In spite of the absence of equilibrium and U(1) invariance, this system shows a counterpart of the Berezinskii-Kosterlitz-Thouless crossover between single vortices and coupled vortex-antivortex states ranging from small dipoles to rectilinear filaments with long-range ordering.

We consider a magnetic skyrmion driven by a spin-polarized electrical current that is periodic in time, and is periodic and asymmetric in a direction different from that of the current itself. We study its classical stochastic transport in a finite temperature, by using the Fokker-Planck equation of the probability distribution, derived from the stochastic equation of motion, the Langevin equation. We also perform numerical simulation of the original Landau-Lifshitz-Gilbert equation describing the spins constituting the skrymion. The probabilistic average velocity of the skyrmion is along the direction of the periodicity. When the thermal energy is much lower than the potential energy, and their ratio is also much smaller than that between the time periodicity and the diffusion time, the time and probabilistic average velocity is the ratio between the spatial and temporal periodicities multiplied by topological integer called the Chern number. This result provides a practical way of realizing topological numbers in classical stochastic systems and suggests a convenient way of manipulating skyrmions at finite temperatures.