Publications

Order by: publication date number of citations

• Engineering spectral properties of non-interacting lattice Hamiltonians

  Ali G. Moghaddam, Dmitry Chernyavsky, Corentin Morice, Jasper van Wezel, Jeroen van den Brink

  SciPost Phys. 11, 109 (2021) · published 22 December 2021 | Toggle abstract · pdf

  We investigate the spectral properties of one-dimensional lattices with position-dependent hopping amplitudes and on-site potentials that are smooth bounded functions of the position. We find an exact integral form for the density of states (DOS) in the limit of an infinite number of sites, which we derive using a mixed Bloch-Wannier basis consisting of piecewise Wannier functions. Next, we provide an exact solution for the inverse problem of constructing the position-dependence of hopping in a lattice model yielding a given DOS. We confirm analytic results by comparing them to numerics obtained by exact diagonalization for various incarnations of position-dependent hoppings and on-site potentials. Finally, we generalize the DOS integral form to multi-orbital tight-binding models with longer-range hoppings and in higher dimensions.

  4 citations

• Fragmentation-induced localization and boundary charges in dimensions two and above

  Julius Lehmann, Pablo Sala de Torres-Solanot, Frank Pollmann, Tibor Rakovszky

  SciPost Phys. 14, 140 (2023) · published 1 June 2023 | Toggle abstract · pdf

  We study higher dimensional models with symmetric correlated hoppings, which generalize a one-dimensional model introduced in the context of dipole-conserving dynamics. We prove rigorously that whenever the local configuration space takes its smallest non-trivial value, these models exhibit localized behavior due to fragmentation, in any dimension. For the same class of models, we then construct a hierarchy of conserved quantities that are power-law localized at the boundary of the system with increasing powers. Combining these with Mazur's bound, we prove that boundary correlations are infinitely long lived, even when the bulk is not localized. We use our results to construct quantum Hamiltonians that exhibit the analogues of strong zero modes in two and higher dimensions.

  4 citations

• Why space could be quantised on a different scale to matter

  Matthew J. Lake

  SciPost Phys. Proc. 4, 014 (2021) · published 13 August 2021 | Toggle abstract · pdf

  The scale of quantum mechanical effects in matter is set by Planck's constant, $\hbar$. This represents the quantisation scale for material objects. In this article, we present a simple argument why the quantisation scale for space, and hence for gravity, may not be equal to $\hbar$. Indeed, assuming a single quantisation scale for both matter and geometry leads to the `worst prediction in physics', namely, the huge difference between the observed and predicted vacuum energies. Conversely, assuming a different quantum of action for geometry, $\beta \ll \hbar$, allows us to recover the observed density of the Universe. Thus, by measuring its present-day expansion, we may in principle determine, empirically, the scale at which the geometric degrees of freedom should be quantised.

  4 citations

• Correlations of quantum curvature and variance of Chern numbers

  Omri Gat, Michael Wilkinson

  SciPost Phys. 10, 149 (2021) · published 21 June 2021 | Toggle abstract · pdf

  We analyse the correlation function of the quantum curvature in complex quantum systems, using a random matrix model to provide an exemplar of a universal correlation function. We show that the correlation function diverges as the inverse of the distance at small separations. We also define and analyse a correlation function of mixed states, showing that it is finite but singular at small separations. A scaling hypothesis on a universal form for both types of correlations is supported by Monte-Carlo simulations. We relate the correlation function of the curvature to the variance of Chern integers which can describe quantised Hall conductance.

  4 citations

• Ferromagnetism of LaCoO$_3$ films

  Andrii Sotnikov, Kyo-Hoon Ahn, Jan Kuneš

  SciPost Phys. 8, 082 (2020) · published 2 June 2020 | Toggle abstract · pdf

  We study ferromagnetic ordering and microscopic inhomogeneity in tensile strained LaCoO$_3$ using numerical simulations. We argue that both phenomena originate from effective superexchange interactions between atoms in the high-spin (HS) state mediated by the intermediate-spin excitations. We derive a model of the HS excitation as a bare atomic state dressed by electron and electron-hole fluctuations on the neighbor atoms. We construct a series of approximations to account for electron correlation effects responsible for HS fluctuations and magnetic exchange. The obtained amplitudes and directional dependence of magnetic couplings between the "dressed" HS states show a qualitative agreement with experimental observations and provide a new physical picture of LaCoO$_3$ films.

  4 citations

• Classification of chiral fermionic CFTs of central charge $\le$ 16

  Philip Boyle Smith, Ying-Hsuan Lin, Yuji Tachikawa, Yunqin Zheng

  SciPost Phys. 16, 058 (2024) · published 27 February 2024 | Toggle abstract · pdf

  We classify two-dimensional purely chiral unitary conformal field theories which are defined on two-dimensional surfaces equipped with spin structure and have central charge less than or equal to $16$, and discuss their duality webs. This result can be used to confirm that the list of non-supersymmetric ten-dimensional heterotic string theories found in the late 1980s is complete and does not miss any exotic example.

  4 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.

  4 citations

• Chiral anomaly trapped in Weyl metals: Nonequilibrium valley polarization at zero magnetic field

  Pablo M. Perez-Piskunow, Nicandro Bovenzi, Anton R. Akhmerov, Maxim Breitkreiz

  SciPost Phys. 11, 046 (2021) · published 31 August 2021 | Toggle abstract · pdf

  In Weyl semimetals the application of parallel electric and magnetic fields leads to valley polarization -- an occupation disbalance of valleys of opposite chirality -- a direct consequence of the chiral anomaly. In this work, we present numerical tools to explore such nonequilibrium effects in spatially confined three-dimensional systems with a variable disorder potential, giving exact solutions to leading order in the disorder potential and the applied electric field. Application to a Weyl-metal slab shows that valley polarization also occurs without an external magnetic field as an effect of chiral anomaly "trapping": Spatial confinement produces chiral bulk states, which enable the valley polarization in a similar way as the chiral states induced by a magnetic field. Despite its finite-size origin, the valley polarization can persist up to macroscopic length scales if the disorder potential is sufficiently long ranged, so that direct inter-valley scattering is suppressed and the relaxation then goes via the Fermi-arc surface states.

  4 citations

• Quantum computation with cat qubits

  Jérémie Guillaud, Joachim Cohen, Mazyar Mirrahimi

  SciPost Phys. Lect. Notes 72 (2023) · published 16 June 2023 | Toggle abstract · pdf

  These are the lecture notes from the 2019 Les Houches Summer School on "Quantum Information Machines". After a brief introduction to quantum error correction and bosonic codes, we focus on the case of cat qubits stabilized by a nonlinear multi-photon driven dissipation process. We argue that such a system can be seen as a self-correcting qubit where bit-flip errors are robustly and exponentially suppressed. Next, we provide some experimental directions to engineer such a multi-photon driven dissipation process with superconducting circuits. Finally, we analyze various logical gates that can be implemented without re-introducing bit-flip errors. This set of bias-preserving gates pave the way towards a hardware-efficient and fault-tolerant quantum processor.

  4 citations

• Testing the mechanism of lepton compositeness

  Vincenzo Afferrante, Axel Maas, René Sondenheimer, Pascal Törek

  SciPost Phys. 10, 062 (2021) · published 10 March 2021 | Toggle abstract · pdf

  Strict gauge invariance requires that physical left-handed leptons are actually bound states of the elementary left-handed lepton doublet and the Higgs field within the standard model. That they nonetheless behave almost like pure elementary particles is explained by the Fr\"ohlich-Morchio-Strocchi mechanism. Using lattice gauge theory, we test and confirm this mechanism for fermions. Though, due to the current inaccessibility of non-Abelian gauged Weyl fermions on the lattice, a model which contains vectorial leptons but which obeys all other relevant symmetries has been simulated.

  4 citations