Publications

Order by: publication date number of citations

• Dual applications of Chebyshev polynomials method: Efficiently finding thousands of central eigenvalues for many-spin systems

  Haoyu Guan, Wenxian Zhang

  SciPost Phys. 11, 103 (2021) · published 8 December 2021 | Toggle abstract · pdf

  Computation of a large group of interior eigenvalues at the middle spectrum is an important problem for quantum many-body systems, where the level statistics provides characteristic signatures of quantum chaos. We propose an exact numerical method, dual applications of Chebyshev polynomials (DACP), to simultaneously find thousands of central eigenvalues, where the level space decreases exponentially with the system size. To disentangle the near-degenerate problem, we employ twice the Chebyshev polynomials, to construct an exponential semicircle filter as a preconditioning step and to generate a large set of proper basis states in the desired subspace. Numerical calculations on Ising spin chain and spin glass shards confirm the correctness and efficiency of DACP. As numerical results demonstrate, DACP is $30$ times faster than the state-of-the-art shift-invert method for the Ising spin chain while $8$ times faster for the spin glass shards. In contrast to the shift-invert method, the computation time of DACP is only weakly influenced by the required number of eigenvalues, which renders it a powerful tool for large scale eigenvalues computations. Moreover, the consumed memory also remains a small constant (5.6 GB) for spin-$1/2$ systems consisting of up to $20$ spins, making it desirable for parallel computing.

  2 citations

• Wegner's Ising gauge spins versus Kitaev's Majorana partons: Mapping and application to anisotropic confinement in spin-orbital liquids

  Urban F. P. Seifert, Sergej Moroz

  SciPost Phys. 16, 147 (2024) · published 5 June 2024 | Toggle abstract · pdf

  Emergent gauge theories take a prominent role in the description of quantum matter, supporting deconfined phases with topological order and fractionalized excitations. A common construction of $\mathbb{Z}_2$ lattice gauge theories, first introduced by Wegner, involves Ising gauge spins placed on links and subject to a discrete $\mathbb{Z}_2$ Gauss law constraint. As shown by Kitaev, $\mathbb{Z}_2$ lattice gauge theories also emerge in the exact solution of certain spin systems with bond-dependent interactions. In this context, the $\mathbb{Z}_2$ gauge field is constructed from Majorana fermions, with gauge constraints given by the parity of Majorana fermions on each site. In this work, we provide an explicit Jordan-Wigner transformation that maps between these two formulations on the square lattice, where the Kitaev-type gauge theory emerges as the exact solution of a spin-orbital (Kugel-Khomskii) Hamiltonian. We then apply our mapping to study local perturbations to the spin-orbital Hamiltonian, which correspond to anisotropic interactions between electric-field variables in the $\mathbb{Z}_2$ gauge theory. These are shown to induce anisotropic confinement that is characterized by emergence of weakly-coupled one-dimensional spin chains. We study the nature of these phases and corresponding confinement transitions in both absence and presence of itinerant fermionic matter degrees of freedom. Finally, we discuss how our mapping can be applied to the Kitaev spin-1/2 model on the honeycomb lattice.

  2 citations

• Codebase release 0.0 for DFT2kp

  João Victor V. Cassiano, Augusto de Lelis Araújo, Paulo E. Faria Junior, Gerson J. Ferreira

  SciPost Phys. Codebases 25-r0.0 (2024) · published 5 February 2024 | Toggle abstract · src

  The $k\cdot p$ method, combined with group theory, is an efficient approach to obtain the low energy effective Hamiltonians of crystalline materials. Although the Hamiltonian coefficients are written as matrix elements of the generalized momentum operator $\pi= p+ p_{SOC}$ (including spin-orbit coupling corrections), their numerical values must be determined from outside sources, such as experiments or ab initio methods. Here, we develop a code to explicitly calculate the Kane (linear in crystal momentum) and Luttinger (quadratic in crystal momentum) parameters of $k\cdot p$ effective Hamiltonians directly from ab initio wavefunctions provided by Quantum ESPRESSO. Additionally, the code analyzes the symmetry transformations of the wavefunctions to optimize the final Hamiltonian. This is an optional step in the code, where it numerically finds the unitary transformation $U$ that rotates the basis towards an optimal symmetry-adapted representation informed by the user. Throughout the paper, we present the methodology in detail and illustrate the capabilities of the code applying it to a selection of relevant materials. Particularly, we show a "hands-on" example of how to run the code for graphene (with and without spin-orbit coupling). The code is open source and available at https://gitlab.com/dft2kp/dft2kp.

  2 citations

• Constructing non-Abelian quantum spin liquids using combinatorial gauge symmetry

  Dmitry Green, Claudio Chamon

  SciPost Phys. 15, 067 (2023) · published 22 August 2023 | Toggle abstract · pdf

  We construct Hamiltonians with only 1- and 2-body interactions that exhibit an exact non-Abelian gauge symmetry (specifically, combinatiorial gauge symmetry). Our spin Hamiltonian realizes the quantum double associated to the group of quaternions. It contains only ferromagnetic and anti-ferromagnetic $ZZ$ interactions, plus longitudinal and transverse fields, and therefore is an explicit example of a spin Hamiltonian with no sign problem that realizes a non-Abelian topological phase. In addition to the spin model, we propose a superconducting quantum circuit version with the same symmetry.

  2 citations

• 5d SCFTs and their non-supersymmetric cousins

  Mohammad Akhond, Masazumi Honda, Francesco Mignosa

  SciPost Phys. 16, 036 (2024) · published 29 January 2024 | Toggle abstract · pdf

  We consider generalisations of the recently proposed supersymmetry breaking deformation of the 5d rank-1 $E_1$ superconformal field theory to higher rank. We generalise the arguments to theories which admit a mass deformation leading to gauge theories coupled to matter hypermultiplets at low energies. These theories have a richer space of non-supersymmetric deformations, due to the existence of a larger global symmetry. We show that there is a one-to-one correspondence between the non-SUSY deformations of the gauge theory and their $(p,q)$ 5-brane web. We comment on the (in)stability of these deformations both from the gauge theory and the 5-brane web point of view. UV duality plays a key role in our analysis, fixing the effective Chern-Simons level for the background vector multiplets, together with their complete prepotential. We partially classify super-Yang-Mills theories known to enjoy UV dualities which show a phase transition where different phases are separated by a jump of Chern-Simons levels of both a perturbative and an instantonic global symmetry. When this transition can be reached by turning on a non-supersymmetric deformation of the UV superconformal field theory, it can be a good candidate to host a 5d non-supersymmetric CFT. We also discuss consistency of the proposed phase diagram with the 't Hooft anomalies of the models that we analyse.

  2 citations

• Codebase release 2.2 for HEJ

  Jeppe R. Andersen, Bertrand Ducloué, Conor Elrick, Hitham Hassan, Andreas Maier, Graeme Nail, Jérémy Paltrinieri, Andreas Papaefstathiou, Jennifer M. Smillie

  SciPost Phys. Codebases 21-r2.2 (2023) · published 6 December 2023 | Toggle abstract · src

  We present version 2.2 of the High Energy Jets (HEJ) Monte Carlo event generator for hadronic scattering processes at high energies. The new version adds support for two further processes of central phenomenological interest, namely the production of a W boson pair with equal charge together with two or more jets and the production of a Higgs boson with at least one jet. Furthermore, a new prediction for charged lepton pair production with high jet multiplicities is provided in the high-energy limit. The accuracy of HEJ 2.2 can be increased further through an enhanced interface to standard predictions based on conventional perturbation theory. We describe all improvements and provide extensive usage examples. HEJ 2.2 can be obtained from https://hej.hepforge.org.

  2 citations

• Understanding the proton mass in QCD

  Andreas Metz, Barbara Pasquini, Simone Rodini

  SciPost Phys. Proc. 8, 105 (2022) · published 13 July 2022 | Toggle abstract · pdf

  Understanding the proton mass in quantum chromodynamics (QCD) is a very important and current topic in hadronic physics. The decomposition (sum rule) of the proton mass is not unique, and different sum rules, which are related to the QCD energy-momentum tensor, can be found in the literature. We review and compare these sum rules and identify open questions in this field.

  2 citations

• Thermal pure matrix product state in two dimensions: Tracking thermal equilibrium from paramagnet down to the Kitaev honeycomb spin liquid state

  Matthias Gohlke, Atsushi Iwaki, Chisa Hotta

  SciPost Phys. 15, 206 (2023) · published 24 November 2023 | Toggle abstract · pdf

  We present the first successful application of the matrix product state (MPS) representing a thermal quantum pure state (TPQ) in equilibrium in two spatial dimensions over almost the entire temperature range. We use the Kitaev honeycomb model as a prominent example hosting a quantum spin liquid (QSL) ground state to target the two specific-heat peaks previously solved nearly exactly using the free Majorana fermionic description. Starting from the high-temperature random state, our TPQ-MPS framework on a cylinder precisely reproduces these peaks, showing that the quantum many-body description based on spins can still capture the emergent itinerant Majorana fermions in a ${\mathbb Z}_2$ gauge field. The truncation process efficiently discards the high-energy states, eventually reaching the long-range entangled topological state approaching the exact ground state for a given finite size cluster. An advantage of TPQ-MPS over exact diagonalization or purification-based methods is its lowered numerical cost coming from a reduced effective Hilbert space even at finite temperature.

  2 citations

• On the unexpected fate of scientific ideas: An archeology of the Carroll group

  Jean-Marc Lévy-Leblond

  SciPost Phys. Proc. 14, 006 (2023) · published 23 November 2023 | Toggle abstract · pdf

  In 1965, I published a paper, exhibiting a hitherto unknown limit of the Lorentz group, which I christened "Carroll group" due to its seemingly paradoxical physical contents. Since I saw it as more curious than relevant, I published it in French in a journal somewhat afar from the mainstream of theoretical physics at that time. It was most gratifying to witness the quite unexpected favour this paper started to enjoy half a century later, so much that a so-called "Carrollian physics" is now developing, with applications in various domains of forefront theoretical physics, such as quantum gravitation, supersymmetry, string theory, etc. I offer this narrative as an example of the very diverse time scales with which scientific ideas may develop — or not.

  2 citations

• Parametrization and thermodynamic scaling of pair correlation functions for the fractional quantum Hall effect

  Jørgen Fulsebakke, Mikael Fremling, Niall Moran, Joost K. Slingerland

  SciPost Phys. 14, 149 (2023) · published 9 June 2023 | Toggle abstract · pdf

  The calculation of pair correlations and density profiles of quasiholes are routine steps in the study of proposed fractional quantum Hall states. Nevertheless, the field has not adopted a standard way to present the results of such calculations in an easily reproducible form. We develop a polynomial expansion that allows for easy quantitative comparison between different candidate wavefunctions, as well as reliable scaling of correlation and quasihole profiles to the thermodynamic limit. We start from the well-known expansion introduced by Girvin [PRB, 30 (1984)] (see also [Girvin, MacDonald and Platzman, PRB, 33 (1986)]), which is physically appealing but, as we demonstrate, numerically unstable. We orthogonalize their basis set to obtain a new basis of modified Jacobi polynomials, whose coefficients can be stably calculated. We then apply our expansion to extract pair correlation expansion coefficients and quasihole profiles in the thermodynamic limit for a wide range of fractional quantum Hall wavefunctions. These include the Laughlin series, composite fermion states with both reverse and direct flux attachment, the Moore-Read Pfaffian state, and BS hierarchy states. The expansion procedure works for both abelian and non-abelian quasiholes, even when the density at the core is not zero. We find that the expansion coefficients for all quantum Hall states considered can be fit remarkably well using a cosine oscillation with exponentially decaying amplitude. The frequency and the decay length are related in an intuitive, but not elementary way to the filling fraction. Different states at the same filling fraction can have distinct values for these parameters. Finally, we also use our scaled correlation functions to calculate estimates for the magneto-roton gaps of the various states.

  2 citations