Condensed Matter

The Aubry-André-Harper model provides a paradigmatic example of aperiodic order in a one-dimensional lattice displaying a delocalization-localization phase transition at a finite critical value V c of the quasiperiodic potential amplitude V . In terms of dynamical behavior of the system, the phase transition is discontinuous when one measures the quantum diffusion exponent δ of wave packet spreading, with δ=1 in the delocalized phase V< V c (ballistic transport), δ??/2 at the critical point V= V c (diffusive transport), and δ=0 in the localized phase V> V c (dynamical localization). However, the phase transition turns out to be smooth when one measures, as a dynamical variable, the speed v(V) of excitation transport in the lattice, which is a continuous function of potential amplitude V and vanishes as the localized phase is approached. Here we consider a non-Hermitian extension of the Aubry-André-Harper model, in which hopping along the lattice is asymmetric, and show that the dynamical localization-delocalization transition is discontinuous not only in the diffusion exponent δ , but also in the speed v of ballistic transport. This means that, even very close to the spectral phase transition point, rather counter-intuitively ballistic transport with a finite speed is allowed in the lattice. Also, we show that the ballistic velocity can increase as V is increased above zero, i.e. surprisingly disorder in the lattice can result in an enhancement of transport.

With an ongoing trend in computing hardware towards increased heterogeneity, domain-specific co-processors are emerging as alternatives to centralized paradigms. The tensor core unit (TPU) has shown to outperform graphic process units by almost 3-orders of magnitude enabled by higher signal throughout and energy efficiency. In this context, photons bear a number of synergistic physical properties while phase-change materials allow for local nonvolatile mnemonic functionality in these emerging distributed non van-Neumann architectures. While several photonic neural network designs have been explored, a photonic TPU to perform matrix vector multiplication and summation is yet outstanding. Here we introduced an integrated photonics-based TPU by strategically utilizing a) photonic parallelism via wavelength division multiplexing, b) high 2 Peta-operations-per second throughputs enabled by 10s of picosecond-short delays from optoelectronics and compact photonic integrated circuitry, and c) zero power-consuming novel photonic multi-state memories based on phase-change materials featuring vanishing losses in the amorphous state. Combining these physical synergies of material, function, and system, we show that the performance of this 8-bit photonic TPU can be 2-3 orders higher compared to an electrical TPU whilst featuring similar chip areas. This work shows that photonic specialized processors have the potential to augment electronic systems and may perform exceptionally well in network-edge devices in the looming 5G networks and beyond.

The nature of bosonic excitations in disordered materials has remained elusive due to the difficulties in defining key concepts such as quasi-particles in the presence of disorder. We report on the experimental observation of phonon-polaritons in glasses, including a boson peak (BP), i.e. excess of THz modes over the Debye law. A theoretical framework based on the concept of diffusons is developed to model the broadening linewidth of the polariton due to disorder-induced scattering. It is shown that the scaling of the BP frequency with the diffusion constant of the linewidth strongly correlates with that of the Ioffe-Regel (IR) crossover frequency of the polariton. This result demonstrates the universality of the BP in the low-energy spectra of collective bosonic-like excitations in glasses, well beyond the traditional case of acoustic phonons, and establishes the IR crossover as the fundamental physical mechanism behind the BP.

Periodically driven quantum many-body systems play a central role for our understanding of nonequilibrium phenomena. For studies of quantum chaos, thermalization, many-body localization and time crystals, the properties of eigenvectors and eigenvalues of the unitary evolution operator, and their scaling with physical system size L are of interest. While for static systems, powerful methods for the partial diagonalization of the Hamiltonian were developed, the unitary eigenproblem remains daunting. In this paper, we introduce a Krylov space diagonalization method to obtain exact eigenpairs of the unitary Floquet operator with eigenvalue closest to a target on the unit circle. Our method is based on a complex polynomial spectral transformation given by the geometric sum, leading to rapid convergence of the Arnoldi algorithm. We demonstrate that our method is much more efficient than the shift invert method in terms of both runtime and memory requirements, pushing the accessible system sizes to the realm of 20 qubits, with Hilbert space dimensions ??10 6 .

Polynomially filtered exact diagonalization method (POLFED) for large sparse matrices is introduced. The algorithm finds an optimal basis of a subspace spanned by eigenvectors with eigenvalues close to a specified energy target by a spectral transformation using a high order polynomial of the matrix. The memory requirements scale better with system size than in the state-of-the-art shift-invert approach. The potential of POLFED is demonstrated examining many-body localization transition in 1D interacting quantum spin-1/2 chains. We investigate the disorder strength and system size scaling of Thouless time. System size dependence of bipartite entanglement entropy and of the gap ratio highlights the importance of finite-size effects in the system. We discuss possible scenarios regarding the many-body localization transition obtaining estimates for the critical disorder strength.

The dynamics of entanglement in `hybrid' non-unitary circuits (for example, involving both unitary gates and quantum measurements) has recently become an object of intense study. A major hurdle toward experimentally realizing this physics is the need to apply \emph{postselection} on random measurement outcomes in order to repeatedly prepare a given output state, resulting in an exponential overhead. We propose a method to sidestep this issue in a wide class of non-unitary circuits by taking advantage of \emph{spacetime duality}. This method maps the purification dynamics of a mixed state under non-unitary evolution onto a particular correlation function in an associated unitary circuit. This translates to an operational protocol which could be straightforwardly implemented on a digital quantum simulator. We discuss the signatures of different entanglement phases, and demonstrate examples via numerical simulations. With minor modifications, the proposed protocol allows measurement of the purity of arbitrary subsystems, which could shed light on the properties of the quantum error correcting code formed by the mixed phase in this class of hybrid dynamics.

A new type of delocalization induced by coherent harmonic perturbations in one-dimensional Anderson-localized disordered systems is investigated. With only a few M frequencies a normal diffusion is realized, but the transition to localized state always occurs as the perturbation strength is weakened below a critical value. The nature of the transition qualitatively follows the Anderson transition (AT) if the number of degrees of freedom M+1 is regarded as the spatial dimension d , but the critical dimension is not d=M+1−2 of the ordinary AT but d=3 .

We present a theoretical study of the potential of Principal Component Analysis to analyse magnetic diffuse neutron scattering data on quantum materials. To address this question, we simulate the scattering function S(q) for a model describing a cluster magnet with anisotropic spin-spin interactions under different conditions of applied field and temperature. We find high dimensionality reduction and that the algorithm can be trained with surprisingly small numbers of simulated observations. Subsequently, observations can be projected onto the reduced-dimensionality space defined by the learnt principal components. Constant-field temperature scans corresponds to trajectories in this space which show characteristic bifurcations at the critical fields corresponding to ground-state phase boundaries. Such "bifurcation plots" allow the ground-state phase diagram to be accurately determined from finite-temperature measurements.

The numerical emulation of quantum systems often requires an exponential number of degrees of freedom which translates to a computational bottleneck. Methods of machine learning have been used in adjacent fields for effective feature extraction and dimensionality reduction of high-dimensional datasets. Recent studies have revealed that neural networks are further suitable for the determination of macroscopic phases of matter and associated phase transitions as well as efficient quantum state representation. In this work, we address quantum phase transitions in quantum spin chains, namely the transverse field Ising chain and the anisotropic XY chain, and show that even neural networks with no hidden layers can be effectively trained to distinguish between magnetically ordered and disordered phases. Our neural network acts to predict the corresponding crossovers finite-size systems undergo. Our results extend to a wide class of interacting quantum many-body systems and illustrate the wide applicability of neural networks to many-body quantum physics.

We numerically study the possibility of many-body localization transition in a disordered quantum dimer model on the honeycomb lattice. By using the peculiar constraints of this model and state-of-the-art exact diagonalization and time evolution methods, we probe both eigenstates and dynamical properties and conclude on the existence of a localization transition, on the available time and length scales (system sizes of up to N=108 sites). We critically discuss these results and their implications.