Publications

Order by: publication date number of citations

• Gauging tensor networks with belief propagation

  Joseph Tindall, Matt Fishman

  SciPost Phys. 15, 222 (2023) · published 1 December 2023 | Toggle abstract · pdf

  Effectively compressing and optimizing tensor networks requires reliable methods for fixing the latent degrees of freedom of the tensors, known as the gauge. Here we introduce a new algorithm for gauging tensor networks using belief propagation, a method that was originally formulated for performing statistical inference on graphical models and has recently found applications in tensor network algorithms. We show that this method is closely related to known tensor network gauging methods. It has the practical advantage, however, that existing belief propagation implementations can be repurposed for tensor network gauging, and that belief propagation is a very simple algorithm based on just tensor contractions so it can be easier to implement, optimize, and generalize. We present numerical evidence and scaling arguments that this algorithm is faster than existing gauging algorithms, demonstrating its usage on structured, unstructured, and infinite tensor networks. Additionally, we apply this method to improve the accuracy of the widely used simple update gate evolution algorithm.

  5 citations

• Integrability and complexity in quantum spin chains

  Ben Craps, Marine De Clerck, Oleg Evnin, Philip Hacker

  SciPost Phys. 16, 041 (2024) · published 7 February 2024 | Toggle abstract · pdf

  There is a widespread perception that dynamical evolution of integrable systems should be simpler in a quantifiable sense than the evolution of generic systems, though demonstrating this relation between integrability and reduced complexity in practice has remained elusive. We provide a connection of this sort by constructing a specific matrix in terms of the eigenvectors of a given quantum Hamiltonian. The null eigenvalues of this matrix are in one-to-one correspondence with conserved quantities that have simple locality properties (a hallmark of integrability). The typical magnitude of the eigenvalues, on the other hand, controls an explicit bound on Nielsen's complexity of the quantum evolution operator, defined in terms of the same locality specifications. We demonstrate how this connection works in a few concrete examples of quantum spin chains that possess diverse arrays of highly structured conservation laws mandated by integrability.

  5 citations

• Introduction to the theory of open quantum systems

  Piotr Szańkowski

  SciPost Phys. Lect. Notes 68 (2023) · published 18 April 2023 | Toggle abstract · pdf

  This manuscript is an edited and refined version of the lecture script for a one-semester graduate course given originally at the PhD school in the Institute of Physics of Polish Academy of Sciences in the Spring/Summer semester of 2022. The course expects from the student only a basic knowledge on graduate-level quantum mechanics. The script itself is largely self-contained and could be used as a textbook on the topic of open quantum systems. The program of this course is based on a novel approach to the description of the open system dynamics: It is showed how the environmental degrees of freedom coupled to the system can be represented by a multi-component quasi-stochastic process. Using this representation one constructs the super-quasi-cumulant (or super-qumulant) expansion for the system's dynamical map-a parametrization that naturally lends itself for the development of a robust and practical perturbation theory. Thus, even an experienced researcher might find this manuscript of some interest.

  5 citations

• M$_k$ models: the field theory connection

  T. Fokkema, K. Schoutens

  SciPost Phys. 3, 004 (2017) · published 13 July 2017 | Toggle abstract · pdf

  The M$_k$ models for 1D lattice fermions are characterised by ${\cal N}=2$ supersymmetry and by an order-$k$ clustering property. This paper highlights connections with quantum field theories (QFTs) in various regimes. At criticality the QFTs are minimal models of ${\cal N}=2$ supersymmetric conformal field theory (CFT) - we analyse finite size spectra on open chains with a variety of supersymmetry preserving boundary conditions. Specific staggering perturbations lead to a gapped regime corresponding to massive ${\cal N}=2$ supersymmetric QFT with Chebyshev superpotentials. At `extreme staggering' we uncover a simple physical picture with degenerate supersymmetric vacua and mobile kinks. We connect this kink-picture to the Chebyshev QFTs and use it to derive novel CFT character formulas. For clarity the focus in this paper is on the simplest models, M$_1$, M$_2$ and M$_3$.

  5 citations

• Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d

  Tomohiro Hashizume, Jad C. Halimeh, Philipp Hauke, Debasish Banerjee

  SciPost Phys. 13, 017 (2022) · published 12 August 2022 | Toggle abstract · pdf

  The exploration of phase diagrams of strongly interacting gauge theories coupled to matter in lower dimensions promises the identification of exotic phases and possible new universality classes, and it facilitates a better understanding of salient phenomena in Nature, such as confinement or high-temperature superconductivity. The emerging new techniques of quantum synthetic matter experiments as well as efficient classical computational methods with matrix product states have been extremely successful in one spatial dimension, and are now motivating such studies in two spatial dimensions. In this work, we consider a $\mathrm{U}(1)$ quantum link lattice gauge theory where the gauge fields, represented by spin-$\frac{1}{2}$ operators are coupled to a single flavor of staggered fermions. Using matrix product states on infinite cylinders with increasing diameter, we conjecture its phase diagram in $(2+1)$-d. This model allows us to smoothly tune between the $\mathrm{U}(1)$ quantum link and the quantum dimer models by adjusting the strength of the fermion mass term, enabling us to connect to the well-studied phases of those models. Our study reveals a rich phase diagram with exotic phases and interesting phase transitions to a potential liquid-like phase. It thus furthers the collection of gauge theory models that may guide future quantum-simulation experiments.

  5 citations

• The Return of the Singularities: Applications of the Smeared Null Energy Condition

  Ben Freivogel, Eleni-Alexandra Kontou, Dimitrios Krommydas

  SciPost Phys. 13, 001 (2022) · published 15 July 2022 | Toggle abstract · pdf

  The classic singularity theorems of General Relativity rely on energy conditions that can be violated in semiclassical gravity. Here, we provide motivation for an energy condition obeyed by semiclassical gravity: the smeared null energy condition (SNEC), a proposed bound on the weighted average of the null energy along a finite portion of a null geodesic. We then prove a semiclassical singularity theorem using SNEC as an assumption. This theorem extends the Penrose theorem to semiclassical gravity. We also apply our bound to evaporating black holes and the traversable wormhole of Maldacena-Milekhin-Popov, and comment on the relationship of our results to other proposed semiclassical singularity theorems.

  5 citations

• Strictly local one-dimensional topological quantum error correction with symmetry-constrained cellular automata

  Nicolai Lang, Hans Peter Büchler

  SciPost Phys. 4, 007 (2018) · published 31 January 2018 | Toggle abstract · pdf

  Active quantum error correction on topological codes is one of the most promising routes to long-term qubit storage. In view of future applications, the scalability of the used decoding algorithms in physical implementations is crucial. In this work, we focus on the one-dimensional Majorana chain and construct a strictly local decoder based on a self-dual cellular automaton. We study numerically and analytically its performance and exploit these results to contrive a scalable decoder with exponentially growing decoherence times in the presence of noise. Our results pave the way for scalable and modular designs of actively corrected one-dimensional topological quantum memories.

  5 citations

• Codebase release 2.0 for ALF (Algorithms for Lattice Fermions)

  F. F. Assaad, M. Bercx, F. Goth, A. Götz, J. S. Hofmann, E. Huffman, Z. Liu, F. Parisen Toldin, J. S. E. Portela, J. Schwab

  SciPost Phys. Codebases 1-r2.0 (2022) · published 22 August 2022 | Toggle abstract · src

  The Algorithms for Lattice Fermions package provides a general code for the finite-temperature and projective auxiliary-field quantum Monte Carlo algorithm. The code is engineered to be able to simulate any model that can be written in terms of sums of single-body operators, of squares of single-body operators and single-body operators coupled to a bosonic field with given dynamics. The package includes five pre-defined model classes: SU(N) Kondo, SU(N) Hubbard, SU(N) t-V and SU(N) models with long range Coulomb repulsion on honeycomb, square and N-leg lattices, as well as $Z_2$ unconstrained lattice gauge theories coupled to fermionic and $Z_2$ matter. An implementation of the stochastic Maximum Entropy method is also provided. One can download the code from our Git instance at https://git.physik.uni-wuerzburg.de/ALF/ALF/-/tree/ALF-2.0 and sign in to file issues.

  5 citations

• Parity effects and universal terms of $\mathcal{O}(1)$ in the entanglement near a boundary

  Henning Schlömer, Chunyu Tan, Stephan Haas, Hubert Saleur

  SciPost Phys. 13, 110 (2022) · published 17 November 2022 | Toggle abstract · pdf

  In the presence of boundaries, the entanglement entropy in lattice models is known to exhibit oscillations with the (parity of the) length of the subsystem, which however decay to zero with increasing distance from the edge. We point out in this article that, when the subsystem starts at the boundary and ends at an impurity, oscillations of the entanglement (as well as of charge fluctuations) appear which do not decay with distance, and which exhibit universal features. We study these oscillations in detail for the case of the XX chain with one modified link (a conformal defect) or two successive modified links (a relevant defect), both numerically and analytically. We then generalize our analysis to the case of extended (conformal) impurities, which we interpret as SSH models coupled to metallic leads. In this context, the parity effects can be interpreted in terms of the existence of non-trivial topological phases.

  5 citations

• Toward density functional theory on quantum computers?

  Bruno Senjean, Saad Yalouz, Matthieu Saubanère

  SciPost Phys. 14, 055 (2023) · published 30 March 2023 | Toggle abstract · pdf

  Quantum Chemistry and Physics have been pinpointed as killer applications for quantum computers, and quantum algorithms have been designed to solve the Schrödinger equation with the wavefunction formalism. It is yet limited to small systems, as their size is dictated by the number of qubits available. Computations on large systems rely mainly on mean-field-type approaches such as density functional theory, for which no quantum advantage has been envisioned so far. In this work, we question this a priori by proposing a counter-intuitive mapping from the non-interacting to an auxiliary interacting Hamiltonian that may provide the desired advantage.

  5 citations