Publications

Order by: publication date number of citations

• Topological defects in a double-mirror quadrupole insulator displace diverging charge

  Isidora Araya Day, Anton R. Akhmerov, Dániel Varjas

  SciPost Phys. Core 5, 053 (2022) · published 15 December 2022 | Toggle abstract · pdf

  We show that topological defects in quadrupole insulators do not host quantized fractional charges, contrary to what their Wannier representation indicates. In particular, we test the charge quantization hypothesis based on the Wannier representation of a disclination and a parametric defect. Since disclinations necessarily strain the lattice and parametric defects require closed curves in parameter space, both defects break four-fold rotation symmetry, even away from their origin. The Wannier representation of the defects is thus determined by local reflection symmetries. Contrary to the hypothesis, we find that the local charge density decays as $\sim 1/r^2$ with distance, leading to a diverging defect charge. Because topological defects are incompatible with four-fold rotation symmetry, we conclude that defect charge quantization is protected by sublattice symmetry, and not higher order topology.

  1 citation

• Probing fractional statistics in quantum simulators of spin liquid Hamiltonians

  Shiyu Zhou, Maria Zelenayova, Oliver Hart, Claudio Chamon, Claudio Castelnovo

  SciPost Phys. 15, 194 (2023) · published 14 November 2023 | Toggle abstract · pdf

  Recent advances in programmable quantum devices brought to the fore the intriguing possibility of using them to realise and investigate topological quantum spin liquid phases. This new and exciting direction brings about important research questions on how to probe and determine the presence of such exotic, highly entangled phases in a noisy quantum environment. One of the most promising tools is investigating the behaviour of the topological excitations, and in particular their fractional statistics. In this work we put forward a generic route to achieve this, and we illustrate it in the specific case of $\mathbb{Z}_2$ topological spin liquids implemented with the aid of combinatorial gauge symmetry. We design a convenient architecture to study signatures of fractional statistics via quasiparticle interferometry, and we assess its robustness to diagonal and off-diagonal disorder, as well as to dephasing - effects that are generally pervasive in current quantum programmable devices. Interestingly, when turned on its head, our scheme provides a remarkably clear test of the "quantumness" of these devices, with robust signatures that crucially hinge on quantum coherence and quantum interference effects, and cannot be mimicked by classical stochastic processes.

  1 citation

• A proposal to extract and enhance four-Majorana interactions in hybrid nanowires

  Tasnum Reza, Sergey M. Frolov, David Pekker

  SciPost Phys. 13, 120 (2022) · published 7 December 2022 | Toggle abstract · pdf

  We simulate the smallest building block of the Sachdev-Ye-Kitaev (SYK) model, a system of four interacting Majorana modes. We propose a 1D Kitaev chain that has been split into three segments, i.e., two topological segments separated by a non-topological segment in the middle, hosting four Majorana Zero Modes at the ends of the topological segments. We add a non-local interaction term to this Hamiltonian which produces both bilinear (two-body) interactions and a quartic (four-body) interaction between the Majorana modes. We further tune the parameters in the Hamiltonian to reach the regime with a finite quartic interaction strength and close to zero bilinear interaction strength, as required by the SYK model. To achieve this, we map the Hamiltonian from Majorana basis to a complex fermion basis, and extract the interaction strengths using a method of characterization of low-lying energy levels and then finding the differences in energies between odd and even parity levels. We show that the interaction strengths can be tuned using two methods - (i) an approximate method of tuning overlapping Majorana wave functions (without non-local interactions) to a zero energy point followed by addition of a non-local interaction, and (ii) a direct parameter space optimization method using a genetic algorithm. We propose that this model could be further extended to more Majorana modes, and show a 6-Majorana model as an example. Since eigenspectral characterization of one-dimensional nanowire devices can be done via tunneling spectroscopy in quantum transport measurements, this study could be performed in experiment.

  1 citation

• Exploring the vortex phase diagram of Bogoliubov-de Gennes disordered superconductors

  Bo Fan (范波), Antonio Miguel Garcia Garcia

  SciPost Phys. 15, 196 (2023) · published 15 November 2023 | Toggle abstract · pdf

  We study the interplay of vortices and disorder in a two-dimensional disordered superconductor at zero temperature described by the Bogoliubov-de Gennes (BdG) self-consistent formalism for lattices of sizes up to 100×100 where the magnetic flux is introduced by the Peierls substitution. We model substantially larger lattice size than in previous approaches (≤36×36) which has allowed us to identify a rich phase diagram as a function of the magnetic flux and the disorder strength. For sufficiently weak disorder, and not too strong magnetic flux, we observe a slightly distorted Abrikosov triangular vortex lattice. An increase in the magnetic flux leads to an unexpected rectangular vortex lattice. A further increase in disorder, or flux, gradually destroys the lattice symmetry though strong vortex repulsion persists. An even stronger disorder leads to deformed single vortices with an inhomogeneous core. As the number of vortices increases, vortex overlap becomes more frequent. Finally, we show that global phase coherence is a feature of all these phases and that disorder enhances substantially the critical magnetic flux with respect to the clean limit with a maximum on the metallic side of the insulating transition.

  1 citation

• Seven Études on dynamical Keldysh model

  Dmitri V. Efremov, Mikhail N. Kiselev

  SciPost Phys. Lect. Notes 65 (2022) · published 6 December 2022 | Toggle abstract · pdf

  We present a comprehensive pedagogical discussion of a family of models describing the propagation of a single particle in a multicomponent non-Markovian Gaussian random field. We report some exact results for single-particle Green's functions, self-energy, vertex part and T-matrix. These results are based on a closed form solution of the Dyson equation combined with the Ward identity. Analytical properties of the solution are discussed. Further we describe the combinatorics of the Feynman diagrams for the Green's function and the skeleton diagrams for the self-energy and vertex, using recurrence relations between the Taylor expansion coefficients of the self-energy. Asymptotically exact equations for the number of skeleton diagrams in the limit of large $N$ are derived. Finally, we consider possible realizations of a multicomponent Gaussian random potential in quantum transport via complex quantum dot experiments.

  1 citation

• Codebase release 1.3 for GrassmannTN

  Atis Yosprakob

  SciPost Phys. Codebases 20-r1.3 (2023) · published 16 November 2023 | Toggle abstract · src

  We present GrassmannTN, a Python package for the computation of the Grassmann tensor network. The package is built to assist in the numerical computation without the need to input the fermionic sign factor manually. It prioritizes coding readability by designing every tensor manipulating function around the tensor subscripts. The computation of the Grassmann tensor renormalization group and Grassmann isometries using GrassmannTN are given as the use case examples.

  1 citation

• Brane detectors of a dynamical phase transition in a driven CFT

  Suchetan Das, Bobby Ezhuthachan, Arnab Kundu, Somnath Porey, Baishali Roy, Krishnendu Sengupta

  SciPost Phys. 15, 202 (2023) · published 23 November 2023 | Toggle abstract · pdf

  We show that a dynamical transition from a non-heating to a heating phase of a periodic $SL(2,\mathbb{R})$ driven two dimensional conformal field theory (CFT) with a large central charge is perceived as a first order transition by a bulk brane embedded in the dual AdS. We construct the dual bulk metric corresponding to a driven CFT for both the heating and the non-heating phases. These metrics are different AdS$_2$ slices of the pure AdS$_3$ metric. We embed a brane in the obtained dual AdS space and provide an explicit computation of its free energy both in the probe limit and for an end-of-world (EOW) brane taking into account its backreaction. Our analysis indicates a finite discontinuity in the first derivative of the brane free energy as one moves from the non-heating to the heating phase (by tuning the drive amplitude and/or frequency of the driven CFT) thus demonstrating the presence of the bulk first order transition. Interestingly, no such transition is perceived by the bulk in the absence of the brane. We also provide explicit computations of two-point, four-point out-of-time correlators (OTOC) using the bulk picture. Our analysis shows that the structure of these correlators in different phases match their counterparts computed in the driven CFT. We analyze the effect of multiple EOW branes in the bulk and discuss possible extensions of our work for richer geometries and branes.

  1 citation

• Dipole symmetry breaking and fractonic Nambu-Goldstone mode

  Evangelos Afxonidis, Alessio Caddeo, Carlos Hoyos, Daniele Musso

  SciPost Phys. Core 6, 082 (2023) · published 28 November 2023 | Toggle abstract · pdf

  We introduce a family of quantum field theories for fields carrying monopole and dipole charges. In contrast to previous realizations, fields have quadratic two-derivative kinetic terms. The dipole symmetry algebra is realized in a discretized internal space and connected to the physical space through a background gauge field. We study spontaneous symmetry breaking of dipole symmetry in 1+1 dimensions in a large-$N$ limit. The trivial classical vacuum is lifted by quantum corrections into a vacuum which breaks dipole symmetry while preserving monopole charge. By means of a Hubbard-Stratonovich transformation, heat-kernel and large-$N$ techniques, we compute the effective action for the low-energy modes. We encounter a fractonic immobile Nambu-Goldstone mode whose dispersion characteristics avoid Coleman-Hohenberg-Mermin-Wagner theorem independently of the large-$N$ limit.

  1 citation

• Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations

  Oleksandr Gamayun, Oleg Lychkovskiy

  SciPost Phys. 12, 175 (2022) · published 25 May 2022 | Toggle abstract · pdf

  The Kitaev model on the honeycomb lattice, while being integrable via the spin-fermion mapping, has generally resisted an analytical treatment of the far-from-equilibrium dynamics due to the extensive number of relevant configurations of conserved charges. Here we study a close proxy of this model, the isotropic Kitaev spin-$1/2$ model on the Bethe lattice. Instead of relying on the spin-fermion mapping, we take a straightforward approach of solving Heisenberg equations for a tailored subset of spin operators. The simplest operator in this subset corresponds to the energy contribution of a single bond direction. As an example, we calculate the time-dependent expectation value of this observable for a factorized translation-invariant (or staggered-translation-invariant) initial state with arbitrary initial (staggered) polarization.

  1 citation

• Ground state topology of a four-terminal superconducting double quantum dot

  Lev Teshler, Hannes Weisbrich, Jonathan Sturm, Raffael L. Klees, Gianluca Rastelli, Wolfgang Belzig

  SciPost Phys. 15, 214 (2023) · published 29 November 2023 | Toggle abstract · pdf

  In recent years, various classes of systems were proposed to realize topological states of matter. One of them are multiterminal Josephson junctions where topological Andreev bound states are constructed in the synthetic space of superconducting phases. Crucially, the topology in these systems results in a quantized transconductance between two of its terminals comparable to the quantum Hall effect. In this work, we study a double quantum dot with four superconducting terminals and show that it has an experimentally accessible topological regime in which the non-trivial topology can be measured. We also include Coulomb repulsion between electrons which is usually present in experiments and show how the topological region can be maximized in parameter space.

  1 citation