Publications

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Identifying Chern numbers of superconductors from local measurements

Paul Baireuther, Marcin Płodzień, Teemu Ojanen, Jakub Tworzydło, Timo Hyart

SciPost Phys. Core 6, 087 (2023) · published 15 December 2023 | · pdf

Fascination in topological materials originates from their remarkable response properties and exotic quasiparticles which can be utilized in quantum technologies. In particular, large-scale efforts are currently focused on realizing topological superconductors and their Majorana excitations. However, determining the topological nature of superconductors with current experimental probes is an outstanding challenge. This shortcoming has become increasingly pressing due to rapidly developing designer platforms which are theorized to display very rich topology and are better accessed by local probes rather than transport experiments. We introduce a robust machine learning protocol for classifying the topological states of two-dimensional (2D) chiral superconductors and insulators from local density of states (LDOS) data. Since the LDOS can be measured with standard experimental techniques, our protocol contributes to overcoming the almost three decades standing problem of identifying the topological phase of 2D superconductors with broken time-reversal symmetry.
Entanglement-enabled symmetry-breaking orders

Cheng-Ju Lin, Liujun Zou

SciPost Phys. Core 7, 010 (2024) · published 11 March 2024 | · pdf

A spontaneous symmetry-breaking order is conventionally described by a tensor-product wavefunction of some few-body clusters; some standard examples include the simplest ferromagnets and valence bond solids. We discuss a type of symmetry-breaking orders, dubbed entanglement-enabled symmetry-breaking orders, which cannot be realized by any such tensor-product state. Given a symmetry breaking pattern, we propose a criterion to diagnose if the symmetry-breaking order is entanglement-enabled, by examining the compatibility between the symmetries and the tensor-product description. For concreteness, we present an infinite family of exactly solvable gapped models on one-dimensional lattices with nearest-neighbor interactions, whose ground states exhibit entanglement-enabled symmetry-breaking orders from a discrete symmetry breaking. In addition, these ground states have gapless edge modes protected by the unbroken symmetries. We also propose a construction to realize entanglement-enabled symmetry-breaking orders with spontaneously broken continuous symmetries. Under the unbroken symmetries, some of our examples can be viewed as symmetry-protected topological states that are beyond the conventional classifications.
Quantum revivals in HgTe/CdTe quantum wells and topological phase transitions

Alberto Mayorgas, Manuel Calixto, Nicolás A. Cordero, Elvira Romera, Octavio Héctor Castaños Garza

SciPost Phys. Core 7, 029 (2024) · published 13 May 2024 | · pdf

The time evolution of a wave packet is a tool to detect topological phase transitions in two-dimensional Dirac materials, such as graphene and silicene. Here we extend the analysis to HgTe/CdTe quantum wells and study the evolution of their electron current wave packet, using 2D effective Dirac Hamiltonians and different layer thicknesses. We show that the two different periodicities that appear in this temporal evolution reach a minimum near the critical thickness, where the system goes from normal to inverted regime. Moreover, the maximum of the electron current amplitude changes with the layer thickness, identifying that current maxima reach their higher value at the critical thickness. Thus, we can characterize the topological phase transitions in terms of the periodicity and amplitude of the electron currents.
A linear algebra-based approach to understanding the relation between the winding number and zero-energy edge states

Chen-Shen Lee

SciPost Phys. Core 7, 003 (2024) · published 30 January 2024 | · pdf

The one-to-one relation between the winding number and the number of robust zero-energy edge states, known as bulk-boundary correspondence, is a celebrated feature of 1$d$ systems with chiral symmetry. Although this property can be explained by the K-theory, the underlying mechanism remains elusive. Here, we demonstrate that, even without resorting to advanced mathematical techniques, one can prove this correspondence and clearly illustrate the mechanism using only Cauchy's integral and elementary algebra. Furthermore, our approach to proving bulk-boundary correspondence also provides clear insights into a kind of system that doesn't respect chiral symmetry but can have robust left or right zero-energy edge states. In such systems, one can still assign the winding number to characterize these zero-energy edge states.
Ground state of the staggered Heisenberg-Γ honeycomb model in a magnetic field

Mojtaba Ahmadi-Yazdi, Mohammad-Hossein Zare, Hamid Mosadeq, Farhad Fazileh

SciPost Phys. Core 7, 030 (2024) · published 15 May 2024 | · pdf

We study the ground state properties of the S=1/2 staggered Heisenberg-$\Gamma$ honeycomb model under a magnetic field based on analytical and numerical methods. Our calculations show that the conventional zigzag and stripy phases are favored because of the staggered Heisenberg interaction away from the pure $\Gamma$ limit. In our classical analysis, we find that the field induces a series of competing magnetic phases with relatively large unit cells in the region sandwiched between the two magnetic phases with long-range ordering. In the quantum treatment, these large magnetic unit cells are destabilized by strong quantum fluctuations that result in the stabilization of a gapless quantum spin liquid behavior. In a honeycomb $\Gamma$ magnet, we disclose an intermediate-field gapless quantum spin liquid phase driven by a tilted field away from the out-of-plane direction only for a narrow region between the low-field zigzag and high-field fully polarized phases.
Nonlinear sigma model description of deconfined quantum criticality in arbitrary dimensions

Da-Chuan Lu

SciPost Phys. Core 6, 047 (2023) · published 6 July 2023 | · pdf

In this paper, we propose using the nonlinear sigma model (NLSM) with the Wess-Zumino-Witten (WZW) term as a general description of deconfined quantum critical points that separate two spontaneously symmetry-breaking (SSB) phases in arbitrary dimensions. In particular, we discuss the suitable choice of the target space of the NLSM, which is in general the homogeneous space G/K, where $G$ is the UV symmetry and $K$ is generated by ${\mathfrak k}={\mathfrak h}_1\cap {\mathfrak h}_2$, and ${\mathfrak h}_i$ is the Lie algebra of the unbroken symmetry in each SSB phase. With this specific target space, the symmetry defects in both SSB phases are on equal footing, and their intertwinement is captured by the WZW term. The DQCP transition is then tuned by proliferating the symmetry defects. By coupling the $G/K$ NLSM with the WZW term to the background gauge field, the 't Hooft anomaly of this theory can be determined. The bulk symmetry-protected topological (SPT) phase that cancels the anomaly is described by the relative Chern-Simons term in odd spacetime dimensions or mixed $\theta$ term in even dimensions. We construct and discuss a series of models with Grassmannian symmetry defects in 3+1d. We also provide the fermionic model that reproduces the $G/K$ NLSM with the WZW term.
Efficient qudit based scheme for photonic quantum computing

Márton Karácsony, László Oroszlány, Zoltan Zimboras

SciPost Phys. Core 7, 032 (2024) · published 3 June 2024 | · pdf

Linear optics is a promising alternative for the realization of quantum computation protocols due to the recent advancements in integrated photonic technology. In this context, usually qubit based quantum circuits are considered, however, photonic systems naturally allow also for d-ary, i.e., qudit based, algorithms. This work investigates qudits defined by the possible photon number states of a single photon in d > 2 optical modes. We demonstrate how to construct locally optimal non-deterministic many-qudit gates using linear optics and photon number resolving detectors, and explore the use of qudit cluster states in the context of a d-ary optimization problem. We find that the qudit cluster states require less optical modes and are encoded by a fewer number of entangled photons than the qubit cluster states with similar computational capabilities. We illustrate the benefit of our qudit scheme by applying it to the k-coloring problem.
Krylov complexity in a natural basis for the Schrödinger algebra

Dimitrios Patramanis, Watse Sybesma

SciPost Phys. Core 7, 037 (2024) · published 20 June 2024 | · pdf

We investigate operator growth in quantum systems with two-dimensional Schrödinger group symmetry by studying the Krylov complexity. While feasible for semisimple Lie algebras, cases such as the Schrödinger algebra which is characterized by a semi-direct sum structure are complicated. We propose to compute Krylov complexity for this algebra in a natural orthonormal basis, which produces a pentadiagonal structure of the time evolution operator, contrasting the usual tridiagonal Lanczos algorithm outcome. The resulting complexity behaves as expected. We advocate that this approach can provide insights to other non-semisimple algebras.
Precise predictions for boosted Higgs production

Kathrin Becker, Fabrizio Caola, Andrea Massironi, Bernhard Mistlberger, Pier F. Monni, Xuan Chen, Stefano Frixione, Thomas Gehrmann, Nigel Glover, Keith Hamilton, Alexander Huss, Stephen P. Jones, Alexander Karlberg, Matthias Kerner, Kirill Kudashkin, Jonas M. Lindert, Gionata Luisoni, Michelangelo L. Mangano, Stefano Pozzorini, Emanuele Re, Gavin P. Salam, Eleni Vryonidou, Christopher Wever

SciPost Phys. Core 7, 001 (2024) · published 4 January 2024 | · pdf

Inclusive Higgs boson production at large transverse momentum is induced by different production channels. We focus on the leading production mechanism through gluon fusion, and perform a consistent combination of the state of the art calculations obtained in the infinite-top-mass effective theory at next-to-next-to-leading order (NNLO) and in the full Standard Model (SM) at next-to-leading order (NLO). We thus present approximate QCD predictions for this process at NNLO, and a study of the corresponding perturbative uncertainties. This calculation is then compared with those obtained with commonly used event generators, and we observe that the description of the considered kinematic regime provided by these tools is in good agreement with state of the art calculations. Finally, we present accurate predictions for other production channels such as vector boson fusion, and associated production with a gauge boson, and with a $t\bar{t}$ pair. We find that, at large transverse momentum, the contribution of other production modes is substantial, and therefore must be included for a precise theory prediction of this observable.
Probing a leptophobic top-colour model with cross section measurements and precise signal and background predictions: A case study

Mohammad Mahdi Altakach, Jonathan Mark Butterworth, Tomáš Ježo, Michael Klasen, Ingo Schienbein

SciPost Phys. Core 6, 014 (2023) · published 17 March 2023 | · pdf

The sensitivity of particle-level fiducial cross section measurements from ATLAS, CMS and LHCb to a leptophobic top-colour model is studied. The model has previously been the subject of resonance searches. Here we compare it directly to state-of-the-art predictions for Standard Model top quark production and also take into account next-to-leading order predictions for the new physics signal. We make use of the Contur framework to evaluate the sensitivity of the current measurements, first under the default Contur assumption that the measurement and the SM exactly coincide, and then using the full SM theory calculation for $t\bar{t}$ at next-to-leading and next-to-next-to-leading order as the background model. We derive exclusion limits, discuss the differences between these approaches, and compare to the limits from resonance searches by ATLAS and CMS.

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