Abelian and non-abelian symmetries in infinite projected entangled pair states

We explore in detail the implementation of arbitrary abelian and non-abelian symmetries in the setting of infinite projected entangled pair states on the two-dimensional square lattice. We observe a large computational speed-up; easily allowing bond dimensions $D = 10$ in the square lattice Heisenberg model at computational effort comparable to calculations at $D = 6$ without symmetries. We also find that implementing an unbroken symmetry does not negatively affect the representative power of the state and leads to identical or improved ground-state energies. Finally, we point out how to use symmetry implementations to detect spontaneous symmetry breaking.Comment: 18 pages, submitted to SciPost Physic

Time-dependent study of disordered models with infinite projected entangled pair states

Infinite projected entangled pair states (iPEPS), the tensor network ansatz for two-dimensional systems in the thermodynamic limit, already provide excellent results on ground-state quantities using either imaginary-time evolution or variational optimisation. Here, we show (i) the feasibility of real-time evolution in iPEPS to simulate the dynamics of an infinite system after a global quench and (ii) the application of disorder-averaging to obtain translationally invariant systems in the presence of disorder. To illustrate the approach, we study the short-time dynamics of the square lattice Heisenberg model in the presence of a bi-valued disorder field

Error estimates for extrapolations with matrix-product states

We introduce a new error measure for matrix-product states without requiring the relatively costly two-site density matrix renormalization group (2DMRG). This error measure is based on an approximation of the full variance $\langle \psi | ( \hat H - E )^2 |\psi \rangle$. When applied to a series of matrix-product states at different bond dimensions obtained from a single-site density matrix renormalization group (1DMRG) calculation, it allows for the extrapolation of observables towards the zero-error case representing the exact ground state of the system. The calculation of the error measure is split into a sequential part of cost equivalent to two calculations of $\langle \psi | \hat H | \psi \rangle$ and a trivially parallelized part scaling like a single operator application in 2DMRG. The reliability of the new error measure is demonstrated at four examples: the $L=30, S=\frac{1}{2}$ Heisenberg chain, the $L=50$ Hubbard chain, an electronic model with long-range Coulomb-like interactions and the Hubbard model on a cylinder of size $10 \times 4$. Extrapolation in the new error measure is shown to be on-par with extrapolation in the 2DMRG truncation error or the full variance $\langle \psi | ( \hat H - E )^2 |\psi \rangle$ at a fraction of the computational effort.Comment: 10 pages, 11 figure

Generic Construction of Efficient Matrix Product Operators

Matrix Product Operators (MPOs) are at the heart of the second-generation Density Matrix Renormalisation Group (DMRG) algorithm formulated in Matrix Product State language. We first summarise the widely known facts on MPO arithmetic and representations of single-site operators. Second, we introduce three compression methods (Rescaled SVD, Deparallelisation and Delinearisation) for MPOs and show that it is possible to construct efficient representations of arbitrary operators using MPO arithmetic and compression. As examples, we construct powers of a short-ranged spin-chain Hamiltonian, a complicated Hamiltonian of a two-dimensional system and, as proof of principle, the long-range four-body Hamiltonian from quantum chemistry.Comment: 13 pages, 10 figure

Vorlesung: Hegel "Phänomenologie" im WS 1998/99

1) Traditioneller Begriff der Phänomenologie: Lehre vom Schein (vs Gewißheit) (2) Hegel (3) Struktur dieses Weges (Vorrede) (4) Wahrheit (5) Bewußtsein (6) Sinnliche Gewißheit / unmittelbares Wissen / "Wahrhaftigkeit" (7) Wahrnehmung (8) Verstand (9) Vom Bewußtsein zum Selbstbewußtsein ­ Herrschaft und Knechtschaft (10) Vernunft als tätiges Bewußtsein (11) Verwirklichung des Selbstbewußtseins durch sich selbst (12) Die reelle Individualität / Geistiges Tierreich / "Betrug" (13) Der (objektive) Geist: Sittlichkeit (14) Der sich entfremdete Geist (15) Moralitat (16) Religio

"Dispositiv" als Kategorie

In der vorliegenden Untersuchung verfolge ich drei Ziele: - Ich will klären, was Foucault unter Dispositiv" versteht. - Ich will klären, welchen Status der Aufweis von Dispositiven für Foucaults Vorstellung von Geschichte hat, ohne mich von der expliziten Theorie- und Methodologieabstinenz Foucaults abschrecken zu lassen (JSH 243). Wenn es vielmehr" (!) dessen Absicht war, eine Geschichte der verschiedenen Verfahren zu entwerfen, durch die in unserer Kultur Menschen zu Subjekten gemacht werden" (JSH 243), dann bedarf ein solcher Entwurf sehr wohl höherstufig einer Methodologie, zu der sich Foucault ja auch geäußert hat. Er selbst spricht von Ideen", die freilich nicht den Status einer Theorie oder einer substantiierten Methode haben (ebd.). - Ich will klären, welcher Status den Dispositiven für oder im Rahmen der von Foucault vorgenommenen Modellierung oder Konstruktion von Moderne zukommt. Zwar spricht Foucault nicht von Moderne im terminologischen Sinne, sehr wohl jedoch von der modernen Epoche" (z.B. OD 25) oder dem modernen Denken" (z.B. OD 387). Es ist zu fragen, ob jenseits der Kennzeichnung einer bestimmten diskursiven Formation als modern" Foucaults Ansatz noch einen Spielraum eröffnet für ein weiteres Konzept von Modernisierung im Sinne der Realisierung eines Neuen gegenüber dem Alten: Hierauf wird uns sein Konzept der strategischen Wiederauffüllung von Dispositiven" bringen

Diels−Alder Topochemistry via Charge-Transfer Crystals: Novel (Thermal) Single-Crystal-to-Single-Crystal Transformations

The solid-state [4+2] cycloaddition of anthracene to bis(N-ethylimino)-1,4-dithiin occurs via a unique single-phase topochemical reaction in the intermolecular (1:1) charge-transfer crystal. The thermal heteromolecular solid-state condensation involves the entire crystal, and this rare crystalline event follows topochemical control during the entire cycloaddition. As a result, a new crystalline modification of the Diels−Alder product is formed with a crystal-packing similar to that of the starting charge-transfer crystal but very different from that of the (thermodynamically favored) product modification obtained from solution-phase crystallization. Such a single-phase transformation is readily monitored by X-ray crystallography at various conversion stages, and the temporal changes in crystallographic parameters are correlated with temperature-dependent (solid-state) kinetic data that are obtained by 1H NMR spectroscopy at various reaction times. Thus, an acceleration of the solid-state reaction over time is found which results from a progressive lowering of the activation barrier for cycloaddition in a single crystal as it slowly and homogeneously converts from the reactant to the product lattice

Interaction quench and thermalization in a one-dimensional topological Kondo insulator

We study the nonequilibrium dynamics of a one-dimensional topological Kondo insulator, modelled by a $p$-wave Anderson lattice model, following a quantum quench of the on-site interaction strength. Our goal is to examine how the quench influences the topological properties of the system, therefore our main focus is the time evolution of the string order parameter, entanglement spectrum and the topologically-protected edge states. We point out that postquench local observables can be well captured by a thermal ensemble up to a certain interaction strength. Our results demonstrate that the topological properties after the interaction quench are preserved. Though the absolute value of the string order parameter decays in time, the analysis of the entanglement spectrum, Loschmidt echo and the edge states indicates the robustness of the topological properties in the time-evolved state. These predictions could be directly tested in state-of-the-art cold-atom experiments.Comment: 8.5 pages, 11 figure

Photoinduced Coupling of Acetylenes and Quinone in the Solid State as Preorganized Donor−Acceptor Pairs

Crystalline electron donor−acceptor (EDA) complexes of various diarylacetylenes (DA) and dichlorobenzoquinone (DB) are isolated and structurally characterized by X-ray crystallography. Deliberate excitation of either the DB acceptor at λDB = 355 nm or the 1:2 [DA, 2DB] complex at λCT = 532 nm in the solid state leads to [2 + 2] cycloaddition and identical (isomeric) mixtures of the quinone methide products. Time-resolved (ps) diffuse reflectance spectroscopy identifies the ion-radical pair [DA•+, DB•-] as the reactive intermediate derived by photoinduced electron transfer in both photochemical procedures. The effects of crystal-lattice control on the subsequent ion-radical pair dynamics are discussed in comparison with the same photocouplings of acetylenes and quinone previously carried out in solution