Variational Schrieffer-Wolff transformations for quantum many-body dynamics

Building on recent results for adiabatic gauge potentials, we propose a variational approach for computing the generator of Schrieffer-Wolff transformations. These transformations consist of block diagonalizing a Hamiltonian through a unitary rotation, which leads to effective dynamics in a computationally tractable reduced Hilbert space. The generators of these rotations are computed variationally and thus go beyond standard perturbative methods, with error controlled by the locality of the variational ansatz. The method is demonstrated on two models. First, in the attractive Fermi-Hubbard model with onsite disorder, we find indications of a lack of observable many-body localization in the thermodynamic limit due to the inevitable mixture of different spinon sectors. Second, in the low-energy sector of the XY spin model with a broken U(1) symmetry, we analyze ground-state response functions by combining the variational Schrieffer-Wolf transformation with the truncated spectrum approach.Published versio

On information in static and dynamic factor models

This paper employs concepts from information theory in factor models. We show that in the exact factor model the whole distribution of eigenvalues of the covariance matrix contributes to the information and not only the largest ones. In addition, we derive the condition that the first q say eigenvalues diverge whereas the rest remain bounded in the static model rather than having to assume it. Finally, we calculate information in static and dynamic factor models, which can be used to find the dimensions of the factor space. We illustrate the concepts with simulation experiments.

Effects of self-phase modulation on weak nonlinear optical quantum gates

A possible two-qubit gate for optical quantum computing is the parity gate based on the weak Kerr effect. Two photonic qubits modulate the phase of a coherent state, and a quadrature measurement of the coherent state reveals the parity of the two qubits without destroying the photons. This can be used to create so-called cluster states, a universal resource for quantum computing. Here, the effect of self-phase modulation on the parity gate is studied, introducing generating functions for the Wigner function of a modulated coherent state. For materials with non-EIT-based Kerr nonlinearities, there is typically a self-phase modulation that is half the magnitude of the cross-phase modulation. Therefore, this effect cannot be ignored. It is shown that for a large class of physical implementations of the phase modulation, the quadrature measurement cannot distinguish between odd and even parity. Consequently, weak nonlinear parity gates must be implemented with physical systems where the self-phase modulation is negligable.Comment: 7 pages, 4 figure

Read-Green resonances in a topological superconductor coupled to a bath

We study a topological superconductor capable of exchanging particles with an environment. This additional interaction breaks particle-number symmetry and can be modelled by means of an integrable Hamiltonian, building on the class of Richardson-Gaudin pairing models. The isolated system supports zero-energy modes at a topological phase transition, which disappear when allowing for particle exchange with an environment. However, it is shown from the exact solution that these still play an important role in system-environment particle exchange, which can be observed through resonances in low-energy and -momentum level occupations. These fluctuations signal topologically protected Read-Green points and cannot be observed within traditional mean-field theory.Comment: 7 pages, 4 figure

Floquet-engineering counterdiabatic protocols in quantum many-body systems

Counterdiabatic (CD) driving presents a way of generating adiabatic dynamics at arbitrary pace, where excitations due to non-adiabaticity are exactly compensated by adding an auxiliary driving term to the Hamiltonian. While this CD term is theoretically known and given by the adiabatic gauge potential, obtaining and implementing this potential in many-body systems is a formidable task, requiring knowledge of the spectral properties of the instantaneous Hamiltonians and control of highly nonlocal multibody interactions. We show how an approximate gauge potential can be systematically built up as a series of nested commutators, remaining well-defined in the thermodynamic limit. Furthermore, the resulting CD driving protocols can be realized up to arbitrary order without leaving the available control space using tools from periodically-driven (Floquet) systems. This is illustrated on few- and many-body quantum systems, where the resulting Floquet protocols significantly suppress dissipation and provide a drastic increase in fidelity.Comment: 6+3 page

Inner products in integrable Richardson-Gaudin models

We present the inner products of eigenstates in integrable Richardson-Gaudin models from two different perspectives and derive two classes of Gaudin-like determinant expressions for such inner products. The requirement that one of the states is on-shell arises naturally by demanding that a state has a dual representation. By implicitly combining these different representations, inner products can be recast as domain wall boundary partition functions. The structure of all involved matrices in terms of Cauchy matrices is made explicit and used to show how one of the classes returns the Slavnov determinant formula. This framework provides a further connection between two different approaches for integrable models, one in which everything is expressed in terms of rapidities satisfying Bethe equations, and one in which everything is expressed in terms of the eigenvalues of conserved charges, satisfying quadratic equations.Comment: 21+16 pages, minor revisions compared to the previous versio

Energy-Efficient Streaming Using Non-volatile Memory

The disk and the DRAM in a typical mobile system consume a significant fraction (up to 30%) of the total system energy. To save on storage energy, the DRAM should be small and the disk should be spun down for long periods of time. We show that this can be achieved for predominantly streaming workloads by connecting the disk to the DRAM via a large non-volatile memory (NVM). We refer to this as the NVM-based architecture (NVMBA); the conventional architecture with only a DRAM and a disk is referred to as DRAMBA. The NVM in the NVMBA acts as a traffic reshaper from the disk to the DRAM. The total system costs are balanced, since the cost increase due to adding the NVM is compensated by the decrease in DRAM cost. We analyze the energy saving of NVMBA, with NAND flash memory serving as NVM, relative to DRAMBA with respect to (1) the streaming demand, (2) the disk form factor, (3) the best-effort provision, and (4) the stream location on the disk. We present a worst-case analysis of the reliability of the disk drive and the flash memory, and show that a small flash capacity is sufficient to operate the system over a year at negligible cost. Disk lifetime is superior to flash, so that is of no concern

Influence of the bulk and surface morphology on adhesion of polystyrene-inter-poly-cross-2-ethylhexyl-methacrylate films and particles

The adhesion behavior of semi-interpenetrating polymer networks (semi-IPNs) of linear polystyrene (PS) in crosslinked poly-2-ethylhexylmethacrylate (EHMA) was studied by variation of the bulk and surface morphology, i.e., domain size, continuity, and concentration in the domains. Semi-IPNs were prepared by liquid-liquid demixing upon cooling of a homogeneous solution of PS in methacrylate monomer, followed by gelation of the PS-rich phase and UV polymerization of the methacrylate resin. Welding of films allowed the preparation of larger objects provided that (1) the samples were phase separated to a high degree and contained domains with a high PS concentration (>90%) and (2) polystyrene was present at the interface. For semi-IPN films, a linear dependence of the adhesion strength on the (crack healing time)1/4 was obtained. Based on these considerations, a process was developed to obtain melt-processable semi-IPN particles, by quenching droplets of the polymer solution into a cold liquid. These particles obtained a PS-rich skin layer and showed good adhesion after blending with a thermoplast