Publications

Order by: publication date number of citations

• Symmetry-protected gates of Majorana qubits in a high-$T_c$ higher-order topological superconductor platform

  Matthew F. Lapa, Meng Cheng, Yuxuan Wang

  SciPost Phys. 11, 086 (2021) · published 2 November 2021 | Toggle abstract · pdf

  We propose a platform for braiding Majorana non-Abelian anyons based on a heterostructure between a $d$-wave high-$T_c$ superconductor and a quantum spin-Hall insulator. It has been recently shown that such a setup for a quantum spin-Hall insulator leads to a pair of Majorana zero modes at each corner of the sample, and thus can be regarded as a higher-order topological superconductor. We show that upon applying a Zeeman field in the region, these Majorana modes split in space and can be manipulated for braiding processes by tuning the field and pairing phase. We show that such a setup can achieve full braiding, exchanging, and arbitrary phase gates (including the $\pi/8$ magic gates) of the Majorana zero modes, all of which are robust and protected by symmetries. Our analysis naturally includes interaction effects and can be generalized to cases with fractional bulk excitations. As many of the ingredients of our proposed platform have been realized in recent experiments, our results provide a new route toward universal topological quantum computation.

  7 citations

• Topological field theory approach to intermediate statistics

  Ward L. Vleeshouwers, Vladimir Gritsev

  SciPost Phys. 10, 146 (2021) · published 16 June 2021 | Toggle abstract · pdf

  Random matrix models provide a phenomenological description of a vast variety of physical phenomena. Prominent examples include the eigenvalue statistics of quantum (chaotic) systems, which are characterized by the spectral form factor (SFF). Here, we calculate the SFF of unitary matrix ensembles of infinite order with the weight function satisfying the assumptions of Szegö’s limit theorem. We then consider a parameter-dependent critical ensemble which has intermediate statistics characteristic of ergodic-to-nonergodic transitions such as the Anderson localization transition. This same ensemble is the matrix model of $U(N)$ Chern-Simons theory on $S^3$ , and the SFF of this ensemble is proportional to the HOMFLY invariant of (2n,2)-torus links with one component in the fundamental and one in the antifundamental representation. This is one example of a large class of ensembles with intermediate statistics arising from topological field and string theories. Indeed, the absence of a local order parameter suggests that it is natural to characterize ergodic-to-nonergodic transitions using topological tools, such as we have done here.

  7 citations

• Quantum bit threads

  Andrew Rolph

  SciPost Phys. 14, 097 (2023) · published 8 May 2023 | Toggle abstract · pdf

  We give a bit thread prescription that is equivalent to the quantum extremal surface prescription for holographic entanglement entropy. Our proposal is inspired by considerations of bit threads in doubly holographic models, and equivalence is established by proving a generalisation of the Riemannian max-flow min-cut theorem. We explore our proposal's properties and discuss ways in which islands and spacetime are emergent phenomena from the quantum bit thread perspective.

  7 citations

• Elaborating the phase diagram of spin-1 anyonic chains

  Eric Vernier, Jesper Lykke Jacobsen, Hubert Saleur

  SciPost Phys. 2, 004 (2017) · published 21 February 2017 | Toggle abstract · pdf

  We revisit the phase diagram of spin-1 $su(2)_k$ anyonic chains, originally studied by Gils {\it et. al.} [Phys. Rev. B, {\bf 87} (23) (2013)]. These chains possess several integrable points, which were overlooked (or only briefly considered) so far. Exploiting integrability through a combination of algebraic techniques and exact Bethe ansatz results, we establish in particular the presence of new first order phase transitions, a new critical point described by a $Z_k$ parafermionic CFT, and of even more phases than originally conjectured. Our results leave room for yet more progress in the understanding of spin-1 anyonic chains.

  7 citations

• Quantum Gutzwiller approach for the two-component Bose-Hubbard model

  Victor E. Colussi, Fabio Caleffi, Chiara Menotti, Alessio Recati

  SciPost Phys. 12, 111 (2022) · published 29 March 2022 | Toggle abstract · pdf

  We study the effects of quantum fluctuations in the two-component Bose-Hubbard model generalizing to mixtures the quantum Gutzwiller approach introduced recently in [Phys. Rev. Research 2, 033276 (2020)]. As a basis for our study, we analyze the mean-field ground-state phase diagram and spectrum of elementary excitations, with particular emphasis on the quantum phase transitions of the model. Within the quantum critical regimes, we address both the superfluid transport properties and the linear response dynamics to density and spin probes of direct experimental relevance. Crucially, we find that quantum fluctuations have a dramatic effect on the drag between the superfluid species of the system, particularly in the vicinity of the paired and antipaired phases absent in the usual one-component Bose-Hubbard model. Additionally, we analyse the contributions of quantum corrections to the one-body coherence and density/spin fluctuations from the perspective of the collective modes of the system, providing results for the few-body correlations in all the regimes of the phase diagram.

  7 citations

• Holographic S-fold theories at one loop

  Connor Behan

  SciPost Phys. 12, 149 (2022) · published 6 May 2022 | Toggle abstract · pdf

  A common feature of tree-level holography is that a correlator in one theory can serve as a generating function for correlators in another theory with less continuous symmetry. This is the case for a family of 4d CFTs with eight supercharges which have protected operators dual to gluons in the bulk. The most recent additions to this family were defined using S-folds which combine a spatial identification with an action of the S-duality group in type IIB string theory. Differences between these CFTs which have a dynamical origin first become manifest at one loop. To explore this phenomenon at the level of anomalous dimensions, we use the AdS unitarity method to bootstrap a one-loop double discontinuity. Compared to previous studies, the subsequent analysis is performed without any assumption about which special functions are allowed. Instead, the Casimir singular and Casimir regular terms are extracted iteratively in order to move from one Regge trajectory to the next. Our results show that anomalous dimensions in the presence of an S-fold are no longer rational functions of the spin.

  7 citations

• A gauge theory for shallow water

  David Tong

  SciPost Phys. 14, 102 (2023) · published 9 May 2023 | Toggle abstract · pdf

  The shallow water equations describe the horizontal flow of a thin layer of fluid with varying height. We show that the equations can be rewritten as a $d=2+1$ dimensional Abelian gauge theory. The magnetic field corresponds to the conserved height of the fluid, while the electric charge corresponds to the conserved vorticity. In a certain linearised approximation, the shallow water equations reduce to relativistic Maxwell-Chern-Simons theory. This describes Poincaré waves. The chiral edge modes of the theory are identified as coastal Kelvin waves.

  7 citations

• Periodically and quasi-periodically driven dynamics of Bose-Einstein condensates

  Pengfei Zhang, Yingfei Gu

  SciPost Phys. 9, 079 (2020) · published 23 November 2020 | Toggle abstract · pdf

  We study the quantum dynamics of Bose-Einstein condensates when the scattering length is modulated periodically or quasi-periodically in time within the Bogoliubov framework. For the periodically driven case, we consider two protocols where the modulation is a square-wave or a sine-wave. In both protocols for each fixed momentum, there are heating and non-heating phases, and a phase boundary between them. The two phases are distinguished by whether the number of excited particles grows exponentially or not. For the quasi-periodically driven case, we again consider two protocols: the square-wave quasi-periodicity, where the excitations are generated for almost all parameters as an analog of the Fibonacci-type quasi-crystal; and the sine-wave quasi-periodicity, where there is a finite measure parameter regime for the non-heating phase. We also plot the analogs of the Hofstadter butterfly for both protocols.

  7 citations

• The Asymptotically Safe Standard Model: From quantum gravity to dynamical chiral symmetry breaking

  Álvaro Pastor-Gutiérrez, Jan M. Pawlowski, Manuel Reichert

  SciPost Phys. 15, 105 (2023) · published 20 September 2023 | Toggle abstract · pdf

  We present a comprehensive non-perturbative study of the phase structure of the asymptotically safe Standard Model. The physics scales included range from the asymptotically safe trans-Planckian regime in the ultraviolet, the intermediate high-energy regime with electroweak symmetry breaking to strongly correlated QCD in the infrared. All flows are computed with a self-consistent functional renormalisation group approach, using a vertex expansion in the fluctuation fields. In particular, this approach takes care of all physical threshold effects and the respective decoupling of ultraviolet degrees of freedom. Standard Model and gravity couplings and masses are fixed by their experimental low energy values. Importantly, we accommodate for the difference between the top pole mass and its Euclidean analogue. Both, the correct mass determination and the threshold effects have a significant impact on the qualitative properties, and in particular on the stability properties of the specific ultraviolet-infrared trajectory with experimental Standard Model physics in the infrared. We show that in the present rather advanced approximation the matter part of the asymptotically safe Standard Model has the same number of relevant parameters as the Standard Model, and is asymptotically free. This result is based on the novel UV fixed point found in the present work: the fixed point Higgs potential is flat but has two relevant directions. These results and their analysis are accompanied by a thorough discussion of the systematic error of the present truncation, also important for systematic improvements.

  7 citations

• Phonon redshift and Hubble friction in an expanding BEC

  Stephen Eckel, Ted Jacobson

  SciPost Phys. 10, 064 (2021) · published 11 March 2021 | Toggle abstract · pdf

  We revisit the theoretical analysis of an expanding ring-shaped Bose-Einstein condensate. Starting from the action and integrating over dimensions orthogonal to the phonon's direction of travel, we derive an effective one-dimensional wave equation for azimuthally-travelling phonons. This wave equation shows that expansion redshifts the phonon frequency at a rate determined by the effective azimuthal sound speed, and damps the amplitude of the phonons at a rate given by $\dot{\cal V}/{\cal V}$, where $\cal{V}$ is the volume of the background condensate. This behavior is analogous to the redshifting and "Hubble friction" for quantum fields in the expanding universe and, given the scalings with radius determined by the shape of the ring potential, is consistent with recent experimental and theoretical results. The action-based dimensional reduction methods used here should be applicable in a variety of settings, and are well suited for systematic perturbation expansions.

  7 citations