Publications

Order by: publication date number of citations

• The Conformal Spectrum of Non-Abelian Anyons

  Nima Doroud, David Tong, Carl Turner

  SciPost Phys. 4, 022 (2018) · published 30 April 2018 | Toggle abstract · pdf

  We study the spectrum of multiple non-Abelian anyons in a harmonic trap. The system is described by Chern-Simons theory, coupled to either bosonic or fermionic non-relativistic matter, and has an SO(2,1) conformal invariance. We describe a number of special properties of the spectrum, focussing on a class of protected states whose energies are dictated by their angular momentum. We show that the angular momentum of a bound state of non-Abelian anyons is determined by the quadratic Casimirs of their constituents.

  6 citations

• A comment on instantons and their fermion zero modes in adjoint QCD_2

  Andrei Smilga

  SciPost Phys. 10, 152 (2021) · published 22 June 2021 | Toggle abstract · pdf

  The adjoint 2-dimensional $QCD$ with the gauge group $SU(N)/Z_N$ admits topologically nontrivial gauge field configurations associated with nontrivial $\pi_1[SU(N)/Z_N] = Z_N$. The topological sectors are labelled by an integer $k=0,\ldots, N-1$. However, in contrast to $QED_2$ and $QCD_4$, this topology is not associated with an integral invariant like the magnetic flux or Pontryagin index. These instantons may admit fermion zero modes, but there is always an equal number of left-handed and right-handed modes, so that the Atiyah-Singer theorem, which determines in other cases the number of the modes, does not apply. The mod. 2 argument suggests that, for a generic gauge field configuration, there is either a single doublet of such zero modes or no modes whatsoever. However, the known solution of the Dirac problem for a wide class of gauge field configurations indicates the presence of $k(N-k)$ zero mode doublets in the topological sector $k$. In this note, we demonstrate in an explicit way that these modes are not robust under a generic enough deformation of the gauge background and confirm thereby the mod. 2 conjecture. The implications for the physics of this theory (screening vs. confinement issue) are briefly discussed.

  6 citations

• Current status and prospects of muonium spectroscopy at PSI

  B. Ohayon, Z. Burkley, P. Crivelli

  SciPost Phys. Proc. 5, 029 (2021) · published 6 September 2021 | Toggle abstract · pdf

  Recent and ongoing developments of low energy muon beamlines are heralding a new era of precision Muonium spectroscopy. While past spectroscopic measurements of Muonium were performed at pulsed muon facilities and were statistically limited, the advent of continuous low energy muon beams, such as at the LEM beamline at PSI, paired with the development of efficient muon-muonium converters and laser advancements, will overcome these limitations. Current experiments presently underway at the LEM facility and in the near future at the muCool beamline, which is under development at PSI, aim to improve the precision of both the 1S-2S transition determination and Lamb shift by several orders of magnitude. In this Chapter we give an overview of the current status and future prospects of these activities at PSI, highlighting how their projected significance fits into a broader context of other ongoing efforts worldwide.

  6 citations

• Minimal Zeeman field requirement for a topological transition in superconductors

  Kim Pöyhönen, Daniel Varjas, Michael Wimmer, Anton R. Akhmerov

  SciPost Phys. 10, 108 (2021) · published 18 May 2021 | Toggle abstract · pdf

  Platforms for creating Majorana quasiparticles rely on superconductivity and breaking of time-reversal symmetry. By studying continuous deformations to known trivial states, we find that the relationship between superconducting pairing and time reversal breaking imposes rigorous bounds on the topology of the system. Applying these bounds to $s$-wave systems with a Zeeman field, we conclude that a topological phase transition requires that the Zeeman energy at least locally exceed the superconducting pairing by the energy gap of the full Hamiltonian. Our results are independent of the geometry and dimensionality of the system.

  6 citations

• Nonlocal correlations in noisy multiqubit systems simulated using matrix product operators

  Haggai Landa, Grégoire Misguich

  SciPost Phys. Core 6, 037 (2023) · published 1 May 2023 | Toggle abstract · pdf

  We introduce an open-source solver for the Lindblad master equation, based on matrix product states and matrix product operators. Using this solver we study the dynamics of tens of interacting qubits with different connectivities, focusing on a problem where an edge qubit is being continuously driven on resonance, which is a fundamental operation in quantum devices. Because of the driving, induced excitations propagate through the qubits until the system reaches a steady state due to the incoherent terms. We find that with alternating-frequency qubits whose interactions with their off-resonant neighbors appear weak, the tunneling excitations lead to large correlations between distant qubits in the system. Some two-qubit correlation functions are found to increase as a function of distance in the system (in contrast to the typical decay with distance), peaking on the two edge qubits farthest apart from each other.

  6 citations

• A dark state of Chern bands: Designing flat bands with higher Chern number

  Mateusz Łącki, Jakub Zakrzewski, Nathan Goldman

  SciPost Phys. 10, 112 (2021) · published 20 May 2021 | Toggle abstract · pdf

  We introduce a scheme by which flat bands with higher Chern number $\vert C\vert>1$ can be designed in ultracold gases through a coherent manipulation of Bloch bands. Inspired by quantum-optics methods, our approach consists in creating a "dark Bloch band" by coupling a set of source bands through resonant processes. Considering a $\Lambda$ system of three bands, the Chern number of the dark band is found to follow a simple sum rule in terms of the Chern numbers of the source bands: $C_D\!=\!C_1+C_2-C_3$. Altogether, our dark-state scheme realizes a nearly flat Bloch band with predictable and tunable Chern number $C_D$. We illustrate our method based on a $\Lambda$ system, formed of the bands of the Harper-Hofstadter model, which leads to a nearly flat Chern band with $C_D\!=\!2$. We explore a realistic sequence to load atoms into the dark Chern band, as well as a probing scheme based on Hall drift measurements. Dark Chern bands offer a practical platform where exotic fractional quantum Hall states could be realized in ultracold gases.

  6 citations

• Investigating the roots of the nonlinear Luttinger liquid phenomenology

  Lisa Markhof, Mikhail Pletyukhov, Volker Meden

  SciPost Phys. 7, 047 (2019) · published 9 October 2019 | Toggle abstract · pdf

  The nonlinear Luttinger liquid phenomenology of one-dimensional correlated Fermi systems is an attempt to describe the effect of the band curvature beyond the Tomonaga-Luttinger liquid paradigm. It relies on the observation that the dynamical structure factor of the interacting electron gas shows a logarithmic threshold singularity when evaluated to first order perturbation theory in the two-particle interaction. This term was interpreted as the linear one in an expansion which was conjectured to resum to a power law. A field theory, the mobile impurity model, which is constructed such that it provides the power law in the structure factor, was suggested to be the proper effective model and used to compute the single-particle spectral function. This forms the basis of the nonlinear Luttinger liquid phenomenology. Surprisingly, the second order perturbative contribution to the structure factor was so far not studied. We first close this gap and show that it is consistent with the conjectured power law. Secondly, we critically assess the steps leading to the mobile impurity Hamiltonian. We show that the model does not allow to include the effect of the momentum dependence of the (bulk) two-particle potential. This dependence was recently shown to spoil power laws in the single-particle spectral function which previously were believed to be part of the Tomonaga-Luttinger liquid universality. Although our second order results for the structure factor are consistent with power-law scaling, this raises doubts that the conjectured nonlinear Luttinger liquid phenomenology can be considered as universal. We conclude that more work is required to clarify this.

  6 citations

• On spectrally flowed local vertex operators in AdS$_3$

  Sergio Iguri, Nicolas Kovensky

  SciPost Phys. 13, 115 (2022) · published 23 November 2022 | Toggle abstract · pdf

  We provide a novel local definition for spectrally flowed vertex operators in the $SL(2,\mathbb{R})$-WZW model, generalising the proposal of Maldacena and Ooguri in [arXiv:hep-th/0111180] for the singly-flowed case to all $\omega>1$. This allows us to establish the precise connection between the computation of correlators using the so-called spectral flow operator, and the methods introduced recently by Dei and Eberhardt in [arXiv:2105.12130] based on local Ward identities. We show that the auxiliary variable $y$ used in the latter paper arises naturally from a point-splitting procedure in the space-time coordinate. The recursion relations satisfied by spectrally flowed correlators, which take the form of partial differential equations in $y$-space, then correspond to null-state conditions for generalised spectral flowed operators. We highlight the role of certain $SL(2,\mathbb{R})$ discrete module isomorphisms in this context, and prove the validity of the conjecture put forward in [arXiv:2105.12130] for $y$-space structure constants of three-point functions with arbitrary spectral flow charges.

  6 citations

• Holonomic implementation of CNOT gate on topological Majorana qubits

  Alessio Calzona, Nicolas P. Bauer, Björn Trauzettel

  SciPost Phys. Core 3, 014 (2020) · published 3 December 2020 | Toggle abstract · pdf

  The CNOT gate is a two-qubit gate which is essential for universal quantum computation. A well-established approach to implement it within Majorana-based qubits relies on subsequent measurement of (joint) Majorana parities. We propose an alternative scheme which operates a protected CNOT gate via the holonomic control of a handful of system parameters, without requiring any measurement. We show how the adiabatic tuning of pair-wise couplings between Majoranas can robustly lead to the full entanglement of two qubits, insensitive with respect to small variations in the control of the parameters.

  6 citations

• On the descriptive power of Neural-Networks as constrained Tensor Networks with exponentially large bond dimension

  Mario Collura, Luca Dell'Anna, Timo Felser, Simone Montangero

  SciPost Phys. Core 4, 001 (2021) · published 2 February 2021 | Toggle abstract · pdf

  In many cases, Neural networks can be mapped into tensor networks with an exponentially large bond dimension. Here, we compare different sub-classes of neural network states, with their mapped tensor network counterpart for studying the ground state of short-range Hamiltonians. We show that when mapping a neural network, the resulting tensor network is highly constrained and thus the neural network states do in general not deliver the naive expected drastic improvement against the state-of-the-art tensor network methods. We explicitly show this result in two paradigmatic examples, the 1D ferromagnetic Ising model and the 2D antiferromagnetic Heisenberg model, addressing the lack of a detailed comparison of the expressiveness of these increasingly popular, variational ans\"atze.

  6 citations