Publications

Order by: publication date number of citations

• Edge mode locality in perturbed symmetry protected topological order

  Marcel Goihl, Christian Krumnow, Marek Gluza, Jens Eisert, Nicolas Tarantino

  SciPost Phys. 6, 072 (2019) · published 21 June 2019 | Toggle abstract · pdf

  Spin chains with symmetry-protected edge zero modes can be seen as prototypical systems for exploring topological signatures in quantum systems. These are useful for robustly encoding quantum information. However in an experimental realization of such a system, spurious interactions may cause the edge zero modes to delocalize. To stabilize against this influence beyond simply increasing the bulk gap, it has been proposed to harness suitable notions of disorder. Equipped with numerical tools for constructing locally conserved operators that we introduce, we comprehensively explore the interplay of local interactions and disorder on localized edge modes in the XZX cluster Hamiltonian. This puts us in a position to challenge the narrative that disorder necessarily stabilizes topological order. Contrary to heuristic reasoning, we find that disorder has no effect on the edge modes in the Anderson localized regime. Moreover, disorder helps localize only a subset of edge modes in the many-body interacting regime. We identify one edge mode operator that behaves as if subjected to a non-interacting perturbation, i.e., shows no disorder dependence. This implies that in finite systems, edge mode operators effectively delocalize at distinct interaction strengths. In essence, our findings suggest that the ability to identify and control the best localized edge mode trumps any gains from introducing disorder.

  5 citations

• Large second-order Josephson effect in planar superconductor-semiconductor junctions

  P. Zhang, A. Zarassi, L. Jarjat, V. Van de Sande, M. Pendharkar, J. S. Lee, C. P. Dempsey, A. P. McFadden, S. D. Harrington, J. T. Dong, H. Wu, A. -H. Chen, M. Hocevar, C. J. Palmstrøm, S. M. Frolov

  SciPost Phys. 16, 030 (2024) · published 25 January 2024 | Toggle abstract · pdf

  We investigate the current-phase relations of Al/InAs-quantum well planar Josephson junctions fabricated using nanowire shadowing technique. Based on several experiments, we conclude that the junctions exhibit an unusually large second-order Josephson harmonic, the $\sin(2\varphi)$ term. First, superconducting quantum interference devices (dc-SQUIDs) show half-periodic oscillations, tunable by gate voltages as well as magnetic flux. Second, Josephson junction devices exhibit kinks near half-flux quantum in supercurrent diffraction patterns. Third, half-integer Shapiro steps are present in the junctions. Similar phenomena are observed in Sn/InAs quantum well devices. We perform data fitting to a numerical model with a two-component current phase relation. Analysis including a loop inductance suggests that the sign of the second harmonic term is negative. The microscopic origins of the observed effect remain to be understood. We consider alternative explanations which can account for some but not all of the evidence.

  5 citations

• 3D Ising CFT and exact diagonalization on icosahedron: The power of conformal perturbation theory

  Bing-Xin Lao, Slava Rychkov

  SciPost Phys. 15, 243 (2023) · published 18 December 2023 | Toggle abstract · pdf

  We consider the transverse field Ising model in (2+1)D, putting 12 spins at the vertices of the regular icosahedron. The model is tiny by the exact diagonalization standards, and breaks rotation invariance. Yet we show that it allows a meaningful comparison to the 3D Ising CFT on $\mathbb{R}× S^2$, by including effective perturbations of the CFT Hamiltonian with a handful of local operators. This extreme example shows the power of conformal perturbation theory in understanding finite N effects in models on regularized $S^2$. Its ideal arena of application should be the recently proposed models of fuzzy sphere regularization.

  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

• Self-dual $S_3$-invariant quantum chains

  Edward O'Brien, Paul Fendley

  SciPost Phys. 9, 088 (2020) · published 16 December 2020 | Toggle abstract · pdf

  We investigate the self-dual three-state quantum chain with nearest-neighbor interactions and $S_3$, time-reversal, and parity symmetries. We find a rich phase diagram including gapped phases with order-disorder coexistence, integrable critical points with U(1) symmetry, and ferromagnetic and antiferromagnetic critical regions described by three-state Potts and free-boson conformal field theories respectively. We also find an unusual critical phase which appears to be described by combining two conformal field theories with distinct "Fermi velocities". The order-disorder coexistence phase has an emergent fractional supersymmetry, and we find lattice analogs of its generators.

  5 citations

• Spin-$\frac{1}{2}$ kagome Heisenberg antiferromagnet with strong breathing anisotropy

  Saeed S. Jahromi, Román Orús, Didier Poilblanc, Frédéric Mila

  SciPost Phys. 9, 092 (2020) · published 29 December 2020 | Toggle abstract · pdf

  We study the zero-temperature phase diagram of the spin-$\frac{1}{2}$ Heisenberg model with breathing anisotropy (i.e., with different coupling strength on the upward and downward triangles) on the kagome lattice. Our study relies on large scale tensor network simulations based on infinite projected entangled-pair state and infinite projected entangled-simplex state methods adapted to the kagome lattice. Our energy analysis suggests that the U(1) algebraic quantum spin-liquid (QSL) ground-state of the isotropic Heisenberg model is stable up to very large breathing anisotropy until it breaks down to a critical lattice-nematic phase that breaks rotational symmetry in real space through a first-order quantum phase transition. Our results also provide further insight into the recent experiment on vanadium oxyfluoride compounds which has been shown to be relevant platforms for realizing QSL in the presence of breathing anisotropy.

  5 citations

• From complex to simple : hierarchical free-energy landscape renormalized in deep neural networks

  Hajime Yoshino

  SciPost Phys. Core 2, 005 (2020) · published 15 April 2020 | Toggle abstract · pdf

  We develop a statistical mechanical approach based on the replica method to study the design space of deep and wide neural networks constrained to meet a large number of training data. Specifically, we analyze the configuration space of the synaptic weights and neurons in the hidden layers in a simple feed-forward perceptron network for two scenarios: a setting with random inputs/outputs and a teacher-student setting. By increasing the strength of constraints,~i.e. increasing the number of training data, successive 2nd order glass transition (random inputs/outputs) or 2nd order crystalline transition (teacher-student setting) take place layer-by-layer starting next to the inputs/outputs boundaries going deeper into the bulk with the thickness of the solid phase growing logarithmically with the data size. This implies the typical storage capacity of the network grows exponentially fast with the depth. In a deep enough network, the central part remains in the liquid phase. We argue that in systems of finite width N, the weak bias field can remain in the center and plays the role of a symmetry-breaking field that connects the opposite sides of the system. The successive glass transitions bring about a hierarchical free-energy landscape with ultrametricity, which evolves in space: it is most complex close to the boundaries but becomes renormalized into progressively simpler ones in deeper layers. These observations provide clues to understand why deep neural networks operate efficiently. Finally, we present some numerical simulations of learning which reveal spatially heterogeneous glassy dynamics truncated by a finite width $N$ effect.

  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

• Polariton condensation into vortex states in the synthetic magnetic field of a strained honeycomb lattice

  Cristóbal Lledó, Iacopo Carusotto, Marzena H. Szymańska

  SciPost Phys. 12, 068 (2022) · published 18 February 2022 | Toggle abstract · pdf

  Photonic materials are a rapidly growing platform for studying condensed matter physics with light, where the exquisite control capability is allowing us to learn about the relation between microscopic dynamics and macroscopic properties. One of the most interesting aspects of condensed matter is the interplay between interactions and the effect of an external magnetic field or rotation, responsible for a plethora of rich phenomena---Hall physics and quantized vortex arrays. At first sight, however, these effects for photons seem vetoed: they do not interact with each other and they are immune to magnetic fields and rotations. Yet in specially devised structures these effects can be engineered. Here, we propose the use of a synthetic magnetic field induced by strain in a honeycomb lattice of resonators to create a non-equilibrium Bose-Einstein condensate of light-matter particles (polaritons) in a rotating state, without the actual need for external rotation nor reciprocity-breaking elements. We show that thanks to the competition between interactions, dissipation and a suitably designed incoherent pump, the condensate spontaneously becomes chiral by selecting a single Dirac valley of the honeycomb lattice, occupying the lowest Landau level and forming a vortex array. Our results offer a new platform where to study the exciting physics of arrays of quantized vortices with light and pave the way to explore the transition from a vortex-dominated phase to the photonic analogue of the fractional quantum Hall regime.

  5 citations

• 't Hooft lines of ADE-type and topological quivers

  Youssra Boujakhrout, El Hassan Saidi, Rachid Ahl Laamara, Lalla Btissam Drissi

  SciPost Phys. 15, 078 (2023) · published 5 September 2023 | Toggle abstract · pdf

  We investigate 4D Chern-Simons theory with ADE gauge symmetries in the presence of interacting Wilson and 't Hooft line defects. We analyse the intrinsic properties of these lines' coupling and explicate the building of oscillator-type Lax matrices verifying the RLL integrability equation. We propose gauge quiver diagrams Q$_{G}^{\mu}$ encoding the topological data carried by the Lax operators and give several examples where Darboux coordinates are interpreted in terms of topological bi-fundamental matter. We exploit this graphical description (i) to give new results regarding solutions in representations beyond the fundamentals of $sl_{N}$, $ so_{2N}$ and $e_{6,7}$, and (ii) to classify the Lax operators for simply laced symmetries in a unified E$_{7}$ CS theory. For quick access, a summary list of the leading topological quivers Q$ _{ADE}^{\mu}$ is given in the conclusion section [Figures 29.(a-e), 30.(a-d) and 31.(a-d)].

  5 citations