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.

  10 citations

• Systematic analysis of crystalline phases in bosonic lattice models with algebraically decaying density-density interactions

  Jan A. Koziol, Antonia Duft, Giovanna Morigi, Kai P. Schmidt

  SciPost Phys. 14, 136 (2023) · published 30 May 2023 | Toggle abstract · pdf

  We propose a general approach to analyse diagonal ordering patterns in bosonic lattice models with algebraically decaying density-density interactions on arbitrary lattices. The key idea is a systematic search for the energetically best order on all unit cells of the lattice up to a given extent. Using resummed couplings we evaluate the energy of the ordering patterns in the thermodynamic limit using finite unit cells. We apply the proposed approach to the atomic limit of the extended Bose-Hubbard model on the triangular lattice at fillings $f=1/2$ and $f=1$. We investigate the ground-state properties of the antiferromagnetic long-range Ising model on the triangular lattice and determine a six-fold degenerate plain-stripe phase to be the ground state for finite decay exponents. We also probe the classical limit of the Fendley-Sengupta-Sachdev model describing Rydberg atom arrays. We focus on arrangements where the atoms are placed on the sites or links of the Kagome lattice. Our method provides a general framework to treat cristalline structures resulting from long-range interactions.

  10 citations

• The simple-cubic structure of elemental Polonium and its relation to combined charge and orbital order in other elemental chalcogens

  Ana Silva, Jasper van Wezel

  SciPost Phys. 4, 028 (2018) · published 13 June 2018 | Toggle abstract · pdf

  Polonium is the only element to crystallise into a simple cubic structure at ambient conditions. Moreover, at high temperatures it undergoes a structural phase transition into a less symmetric trigonal configuration. It has long been suspected that the strong spin-orbit coupling in Polonium is involved in both peculiarities, but the precise mechanism by which it operates remains controversial. Here, we introduce a single microscopic model capable of capturing the atomic structure of all chalcogen crystals: Selenium, Tellurium, and Polonium. We show that the strong spin-orbit coupling in Polonium suppresses the trigonal charge and orbital ordered state known to be the ground state configuration of Selenium and Tellurium, and allows the simple cubic state to prevail instead. We also confirm a recent suggestion based on ab initio calculations that a small increase in the lattice constant may effectively decrease the role of spin-orbit coupling, leading to a re-emergence of the trigonal orbital ordered state at high temperatures. We conclude that Polonium is a unique element, in which spins, orbitals, electronic charges, and lattice deformations all cooperate and collectively cause the emergence of the only elemental crystal structure with the simplest possible, cubic, lattice.

  10 citations

• Statistical Floquet prethermalization of the Bose-Hubbard model

  Emanuele G. Dalla Torre, David Dentelski

  SciPost Phys. 11, 040 (2021) · published 24 August 2021 | Toggle abstract · pdf

  The manipulation of many-body systems often involves time-dependent forces that cause unwanted heating. One strategy to suppress heating is to use time-periodic (Floquet) forces at large driving frequencies. For quantum spin systems with bounded spectra, it was shown rigorously that the heating rate is exponentially small in the driving frequency. Recently, the exponential suppression of heating has also been observed in an experiment with ultracold atoms, realizing a periodically driven Bose-Hubbard model. This model has an unbounded spectrum and, hence, is beyond the reach of previous theoretical approaches. Here, we study this model with two semiclassical approaches valid, respectively, at large and weak interaction strengths. In both limits, we compute the heating rates by studying the statistical probability to encounter a many-body resonance, and obtain a quantitative agreement with the exact diagonalization of the quantum model. Our approach demonstrates the relevance of statistical arguments to Floquet perthermalization of interacting many-body quantum systems.

  10 citations

• Resolving the nonequilibrium Kondo singlet in energy- and position-space using quantum measurements

  Andre Erpenbeck, Guy Cohen

  SciPost Phys. 10, 142 (2021) · published 11 June 2021 | Toggle abstract · pdf

  The Kondo effect, a hallmark of strong correlation physics, is characterized by the formation of an extended cloud of singlet states around magnetic impurities at low temperatures. While many implications of the Kondo cloud's existence have been verified, the existence of the singlet cloud itself has not been directly demonstrated. We suggest a route for such a demonstration by considering an observable that has no classical analog, but is still experimentally measurable: ``singlet weights'', or projections onto particular entangled two-particle states. Using approximate theoretical arguments, we show that it is possible to construct highly specific energy- and position-resolved probes of Kondo correlations. Furthermore, we consider a quantum transport setup that can be driven away from equilibrium by a bias voltage. There, we show that singlet weights are enhanced by voltage even as the Kondo effect is weakened by it. This exposes a patently nonequilibrium mechanism for the generation of Kondo-like entanglement that is inherently different from its equilibrium counterpart.

  10 citations

• Exceptional points in the Baxter-Fendley free parafermion model

  Robert A. Henry, Murray T. Batchelor

  SciPost Phys. 15, 016 (2023) · published 19 July 2023 | Toggle abstract · pdf

  Certain spin chains, such as the quantum Ising chain, have free fermion spectra which can be expressed as the sum of decoupled two-level fermionic systems. Free parafermions are a generalisation of this idea to $\mathbb{Z}_N$-symmetric clock models. In 1989 Baxter discovered a non-Hermitian but $\mathcal{PT}$-symmetric model directly generalising the Ising chain, which was later described by Fendley as a free parafermion spectrum. By extending the model's magnetic field parameter to the complex plane, it is shown that a series of exceptional points emerges, where the quasienergies defining the free spectrum become degenerate. An analytic expression for the locations of these points is derived, and various numerical investigations are performed. These exceptional points also exist in the Ising chain with a complex transverse field. Although the model is not in general $\mathcal{PT}$-symmetric at these exceptional points, their proximity can have a profound impact on the model on the $\mathcal{PT}$-symmetric real line. Furthermore, in certain cases an exceptional point may appear on the real line (with negative field).

  10 citations

• The equilibrium landscape of the Heisenberg spin chain

  Enej Ilievski, Eoin Quinn

  SciPost Phys. 7, 033 (2019) · published 13 September 2019 | Toggle abstract · pdf

  We characterise the equilibrium landscape, the entire manifold of local equilibrium states, of an interacting integrable quantum model. Focusing on the isotropic Heisenberg spin chain, we describe in full generality two complementary frameworks for addressing equilibrium ensembles: the functional integral Thermodynamic Bethe Ansatz approach, and the lattice regularisation transfer matrix approach. We demonstrate the equivalence between the two, and in doing so clarify several subtle features of generic equilibrium states. In particular we explain the breakdown of the canonical Y-system, which reflects a hidden structure in the parametrisation of equilibrium ensembles.

  10 citations

• Hydrodynamics of higher-rank gauge theories

  Marvin Qi, Oliver Hart, Aaron J. Friedman, Rahul Nandkishore, Andrew Lucas

  SciPost Phys. 14, 029 (2023) · published 8 March 2023 | Toggle abstract · pdf

  We extend recent work on hydrodynamics with global multipolar symmetries — known as "fracton hydrodynamics" — to systems in which the multipolar symmetries are gauged. We refer to the latter as "fracton magnetohydrodynamics", in analogy to conventional magnetohydrodynamics (MHD), which governs systems with gauged charge conservation. We show that fracton MHD arises naturally from higher-rank Maxwell's equations and in systems with one-form symmetries obeying certain constraints; while we focus on "minimal" higher-rank generalizations of MHD that realize diffusion, our methods may also be used to identify other, more exotic hydrodynamic theories (e.g., with magnetic subdiffusion). In contrast to semi-microscopic derivations of MHD, our approach elucidates the origin of the hydrodynamic modes by identifying the corresponding higher-form symmetries. Being rooted in symmetries, the hydrodynamic modes may persist even when the semi-microscopic equations no longer provide an accurate description of the system.

  10 citations

• Generalised Onsager Algebra in Quantum Lattice Models

  Yuan Miao

  SciPost Phys. 13, 070 (2022) · published 28 September 2022 | Toggle abstract · pdf

  The Onsager algebra is one of the cornerstones of exactly solvable models in statistical mechanics. Starting from the generalised Clifford algebra, we demonstrate its relations to the graph Temperley-Lieb algebra, and a generalisation of the Onsager algebra. We present a series of quantum lattice models as representations of the generalised Clifford algebra, possessing the structure of a special type of the generalised Onsager algebra. The integrability of those models is presented, analogous to the free fermionic eight-vertex model. We also mention further extensions of the models and physical properties related to the generalised Onsager algebras, hinting at a general framework that includes families of quantum lattice models possessing the structure of the generalised Onsager algebras.

  10 citations

• Isolated flat bands in 2D lattices based on a novel path-exchange symmetry

  Jun-Hyung Bae, Tigran Sedrakyan, Saurabh Maiti

  SciPost Phys. 15, 139 (2023) · published 5 October 2023 | Toggle abstract · pdf

  The increased ability to engineer two-dimensional (2D) systems, either using materials, photonic lattices, or cold atoms, has led to the search for 2D structures with interesting properties. One such property is the presence of flat bands. Typically, the presence of these requires long-ranged hoppings, fine-tuning of nearest neighbor hoppings, or breaking time-reversal symmetry by using a staggered flux distribution in the unit cell. We provide a prescription based on carrying out projections from a parent system to generate different flat band systems. We identify the conditions for maintaining the flatness and identify a path-exchange symmetry in such systems that cause the flat band to be degenerate with the other dispersive ones. Breaking this symmetry leads to lifting the degeneracy while still preserving the flatness of the band. This technique does not require changing the topology nor breaking time-reversal symmetry as was suggested earlier in the literature. The prescription also eliminates the need for any fine-tuning. Moreover, it is shown that the subsequent projected systems inherit the precise fine-tuning conditions that were discussed in the literature for similar systems, in order to have and isolate a flat band. As examples, we demonstrate the use of our prescription to arrive at the flat band conditions for popular systems like the Kagomé, the Lieb, and the Dice lattices. Finally, we are also able to show that a flat band exists in a recently proposed chiral spin-liquid state of the Kagomé lattice only if it is associated with a gauge field that produces a flux modulation of the Chern-Simons type.

  10 citations