Publications

Order by: publication date number of citations

• Quantum robustness and phase transitions of the 3D Toric Code in a field

  David A. Reiss, Kai Phillip Schmidt

  SciPost Phys. 6, 078 (2019) · published 27 June 2019 | Toggle abstract · pdf

  We study the robustness of 3D intrinsic topogical order under external perturbations by investigating the paradigmatic microscopic model, the 3D toric code in an external magnetic field. Exact dualities as well as variational calculations reveal a ground-state phase diagram with first and second-order quantum phase transitions. The variational approach can be applied without further approximations only for certain field directions. In the general field case, an approximative scheme based on an expansion of the variational energy in orders of the variational parameters is developed. For the breakdown of the 3D intrinsic topological order, it is found that the (im-)mobility of the quasiparticle excitations is crucial in contrast to their fractional statistics.

  12 citations

• Thermodynamic limit of the two-spinon form factors for the zero field XXX chain

  Nikolai Kitanine, Giridhar Kulkarni

  SciPost Phys. 6, 076 (2019) · published 25 June 2019 | Toggle abstract · pdf

  In this paper we propose a method based on the algebraic Bethe ansatz leading to explicit results for the form factors of quantum spin chains in the thermodynamic limit. Starting from the determinant representations we retrieve in particular the formula for the two-spinon form factors for the isotropic XXX Heisenberg chain obtained initially in the framework of the $q$-vertex operator approach.

  3 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

• Hydrodynamics of the interacting Bose gas in the Quantum Newton Cradle setup

  Jean-Sébastien Caux, Benjamin Doyon, Jérôme Dubail, Robert Konik, Takato Yoshimura

  SciPost Phys. 6, 070 (2019) · published 20 June 2019 | Toggle abstract · pdf

  Describing and understanding the motion of quantum gases out of equilibrium is one of the most important modern challenges for theorists. In the groundbreaking Quantum Newton Cradle experiment [Kinoshita, Wenger and Weiss, Nature 440, 900, 2006], quasi-one-dimensional cold atom gases were observed with unprecedented accuracy, providing impetus for many developments on the effects of low dimensionality in out-of-equilibrium physics. But it is only recently that the theory of generalized hydrodynamics has provided the adequate tools for a numerically efficient description. Using it, we give a complete numerical study of the time evolution of an ultracold atomic gas in this setup, in an interacting parameter regime close to that of the original experiment. We evaluate the full evolving phase-space distribution of particles. We simulate oscillations due to the harmonic trap, the collision of clouds without thermalization, and observe a small elongation of the actual oscillation period and cloud deformations due to many-body dephasing. We also analyze the effects of weak anharmonicity. In the experiment, measurements are made after release from the one-dimensional trap. We evaluate the gas density curves after such a release, characterizing the actual time necessary for reaching the asymptotic state where the integrable quasi-particle momentum distribution function emerges.

  75 citations

• Charge-current correlation equalities for quantum systems far from equilibrium

  Dragi Karevski, Gunter M. Schütz

  SciPost Phys. 6, 068 (2019) · published 17 June 2019 | Toggle abstract · pdf

  We prove that a recently derived correlation equality between conserved charges and their associated conserved currents for quantum systems far from equilibrium [O.A. Castro-Alvaredo et al., Phys. Rev. X \textbf{6}, 041065 (2016)], is valid under more general conditions than assumed so far. Similar correlation identities, which in generalized Gibbs ensembles give rise to a current symmetry somewhat reminiscent of the Onsager relations, turn out to hold also in the absence of translation invariance, for lattice models, and in any space dimension, and to imply a symmetry of the non-equilibrium linear response functions.

  14 citations

• The propagator of the finite XXZ spin-$\tfrac{1}{2}$ chain

  Gyorgy Z. Fehér, Balázs Pozsgay

  SciPost Phys. 6, 063 (2019) · published 28 May 2019 | Toggle abstract · pdf

  We derive contour integral formulas for the real space propagator of the spin-$\tfrac12$ XXZ chain. The exact results are valid in any finite volume with periodic boundary conditions, and for any value of the anisotropy parameter. The integrals are on fixed contours, that are independent of the Bethe Ansatz solution of the model and the string hypothesis. The propagator is obtained by two different methods. First we compute it through the spectral sum of a deformed model, and as a by-product we also compute the propagator of the XXZ chain perturbed by a Dzyaloshinskii-Moriya interaction term. As a second way we also compute the propagator through a lattice path integral, which is evaluated exactly utilizing the so-called $F$-basis in the mirror (or quantum) channel. The final expressions are similar to the Yudson representation of the infinite volume propagator, with the volume entering as a parameter. As an application of the propagator we compute the Loschmidt amplitude for the quantum quench from a domain wall state.

  3 citations

• On the size of the space spanned by a nonequilibrium state in a quantum spin lattice system

  Maurizio Fagotti

  SciPost Phys. 6, 059 (2019) · published 15 May 2019 | Toggle abstract · pdf

  We consider the time evolution of a state in an isolated quantum spin lattice system with energy cumulants proportional to the number of the sites $L^d$. We compute the distribution of the eigenvalues of the time averaged state over a time window $[t_0,t_0+t]$ in the limit of large $L$. This allows us to infer the size of a subspace that captures time evolution in $[t_0,t_0+t]$ with an accuracy $1-\epsilon$. We estimate the size to be $ \frac{\sqrt{2\mathfrak{e}_2}}{\pi}\mathrm{erf}^{-1}(1-\epsilon) L^{\frac{d}{2}}t$, where $\mathfrak{e}_2$ is the energy variance per site, and $\mathrm{erf}^{-1}$ is the inverse error function.

  3 citations

• Free fermions at the edge of interacting systems

  Jean-Marie Stéphan

  SciPost Phys. 6, 057 (2019) · published 10 May 2019 | Toggle abstract · pdf

  We study the edge behavior of inhomogeneous one-dimensional quantum systems, such as Lieb-Liniger models in traps or spin chains in spatially varying magnetic fields. For free systems these fall into several universality classes, the most generic one being governed by the Tracy-Widom distribution. We investigate in this paper the effect of interactions. Using semiclassical arguments, we show that since the density vanishes to leading order, the strong interactions in the bulk are renormalized to zero at the edge, which simply explains the survival of Tracy-Widom scaling in general. For integrable systems, it is possible to push this argument further, and determine exactly the remaining length scale which controls the variance of the edge distribution. This analytical prediction is checked numerically, with excellent agreement. We also study numerically the edge scaling at fronts generated by quantum quenches, which provide new universality classes awaiting theoretical explanation.

  28 citations

• Experimental input from $e^+e^-$ for $a_{\mu}$ light-by-light

  Yuping Guo on behalf of BESIII Collaboration

  SciPost Phys. Proc. 1, 054 (2019) · published 9 May 2019 | Toggle abstract · pdf

  The anomalous magnetic momentum of the muon, $a_{\mu}$, has been measured and calculated with a precision up to $~0.5$ ppm, but there is a 3 to 4 standard deviations between these two values. The uncertainty in the calculation is dominated by the hadronic part, including the hadronic vacuum polarization and the hadronic light-by-light. The meson transition form factors and the helicity amplitudes can be used as input or constraint to the calculation of the hadronic light-by-light contribution. Latest experimental studies of the transition form factors of $\pi^0$, $\eta$, and $\eta^{*}$ and the cross-section of $\gamma\gamma^*\to\pi^+\pi-$from $e^+e^-$ collider are presented.

• Finite temperature effects on Majorana bound states in chiral $p$-wave superconductors

  Henrik Schou Røising, Roni Ilan, Tobias Meng, Steven H. Simon, Felix Flicker

  SciPost Phys. 6, 055 (2019) · published 8 May 2019 | Toggle abstract · pdf

  We study Majorana fermions bound to vortex cores in a chiral $p$-wave superconductor at temperatures non-negligible compared to the superconducting gap. Thermal occupation of Caroli de Gennes-Matricon states, below the full gap, causes the free energy difference between the two fermionic parity sectors to decay algebraically with increasing temperature. The power law acquires an additional factor of $T^{-1}$ for each bound state thermally excited. The zero-temperature result is exponentially recovered well below the minigap (lowest-lying CdGM level). Our results suggest that temperatures larger than the minigap may not be disastrous for topological quantum computation. We discuss the prospect of precision measurements of pinning forces on vortices as a readout scheme for Majorana qubits.

  6 citations