Publications

Order by: publication date number of citations

• Topological Orders in (4+1)-Dimensions

  Theo Johnson-Freyd, Matthew Yu

  SciPost Phys. 13, 068 (2022) · published 27 September 2022 | Toggle abstract · pdf

  We investigate the Morita equivalences of (4+1)-dimensional topological orders. We show that any (4+1)-dimensional super (fermionic) topological order admits a gapped boundary condition -- in other words, all (4+1)-dimensional super topological orders are Morita trivial. As a result, there are no inherently gapless super (3+1)-dimensional theories. On the other hand, we show that there are infinitely many algebraically Morita-inequivalent bosonic (4+1)-dimensional topological orders.

  4 citations

• Mechanisms of Andreev reflection in quantum Hall graphene

  Antonio L. R. Manesco, Ian Matthias Flór, Chun-Xiao Liu, Anton R. Akhmerov

  SciPost Phys. Core 5, 045 (2022) · published 27 September 2022 | Toggle abstract · pdf

  We simulate a hybrid superconductor-graphene device in the quantum Hall regime to identify the origin of downstream resistance oscillations in a recent experiment [Zhao et. al. Nature Physics 16, (2020)]. In addition to the previously studied Mach-Zehnder interference between the valley-polarized edge states, we consider disorder-induced scattering, and the previously overlooked appearance of the counter-propagating states generated by the interface density mismatch. Comparing our results with the experiment, we conclude that the observed oscillations are induced by the interfacial disorder, and that lattice-matched superconductors are necessary to observe the alternative ballistic effects.

  12 citations

• Higher central charges and topological boundaries in 2+1-dimensional TQFTs

  Justin Kaidi, Zohar Komargodski, Kantaro Ohmori, Sahand Seifnashri, Shu-Heng Shao

  SciPost Phys. 13, 067 (2022) · published 26 September 2022 | Toggle abstract · pdf

  A 2+1-dimensional topological quantum field theory (TQFT) may or may not admit topological (gapped) boundary conditions. A famous necessary, but not sufficient, condition for the existence of a topological boundary condition is that the chiral central charge $c_-$ has to vanish. In this paper, we consider conditions associated with "higher" central charges, which have been introduced recently in the math literature. In terms of these new obstructions, we identify necessary and sufficient conditions for the existence of a topological boundary in the case of bosonic, Abelian TQFTs, providing an alternative to the identification of a Lagrangian subgroup. Our proof relies on general aspects of gauging generalized global symmetries. For non-Abelian TQFTs, we give a geometric way of studying topological boundary conditions, and explain certain necessary conditions given again in terms of the higher central charges. Along the way, we find a curious duality in the partition functions of Abelian TQFTs, which begs for an explanation via the 3d-3d correspondence.

  25 citations

• Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality

  Weicheng Ye, Meng Guo, Yin-Chen He, Chong Wang, Liujun Zou

  SciPost Phys. 13, 066 (2022) · published 26 September 2022 | Toggle abstract · pdf

  Lieb-Schultz-Mattis (LSM) theorems provide powerful constraints on the emergibility problem, i.e. whether a quantum phase or phase transition can emerge in a many-body system. We derive the topological partition functions that characterize the LSM constraints in spin systems with $G_s\times G_{int}$ symmetry, where $G_s$ is an arbitrary space group in one or two spatial dimensions, and $G_{int}$ is any internal symmetry whose projective representations are classified by $\mathbb{Z}_2^k$ with $k$ an integer. We then apply these results to study the emergibility of a class of exotic quantum critical states, including the well-known deconfined quantum critical point (DQCP), $U(1)$ Dirac spin liquid (DSL), and the recently proposed non-Lagrangian Stiefel liquid. These states can emerge as a consequence of the competition between a magnetic state and a non-magnetic state. We identify all possible realizations of these states on systems with $SO(3)\times \mathbb{Z}_2^T$ internal symmetry and either $p6m$ or $p4m$ lattice symmetry. Many interesting examples are discovered, including a DQCP adjacent to a ferromagnet, stable DSLs on square and honeycomb lattices, and a class of quantum critical spin-quadrupolar liquids of which the most relevant spinful fluctuations carry spin-$2$. In particular, there is a realization of spin-quadrupolar DSL that is beyond the usual parton construction. We further use our formalism to analyze the stability of these states under symmetry-breaking perturbations, such as spin-orbit coupling. As a concrete example, we find that a DSL can be stable in a recently proposed candidate material, NaYbO$_2$.

  12 citations

• Renormalization group and effective potential: a simple non-perturbative approach

  Jose Gaite

  SciPost Phys. Core 5, 044 (2022) · published 26 September 2022 | Toggle abstract · pdf

  We develop a simple non-perturbative approach to the calculation of a field theory effective potential that is based on the Wilson or exact renormalization group. Our approach follows Shepard et al's idea [Phys. Rev. D51, 7017 (1995)] of converting the exact renormalization group into a self-consistent renormalization method. It yields a simple second order differential equation for the effective potential. The equation can be solved and its solution is compared with other non-perturbative results and with results of perturbation theory. In three dimensions, we are led to study the sextic field theory ($\lambda\phi^4+g\phi^6$). We work out this theory at two-loop perturbative order and find the non-perturbative approach to be superior.

  1 citation

• Active particles driven by competing spatially dependent self-propulsion and external force

  Lorenzo Caprini, Umberto Marini Bettolo Marconi, René Wittmann , Hartmut Löwen

  SciPost Phys. 13, 065 (2022) · published 23 September 2022 | Toggle abstract · pdf

  We investigate how the competing presence of a nonuniform motility landscape and an external confining field affects the properties of active particles. We employ the active Ornstein-Uhlenbeck particle (AOUP) model with a periodic swim-velocity profile to derive analytical approximations for the steady-state probability distribution of position and velocity, encompassing both the Unified Colored Noise Approximation and the theory of potential-free active particles with spatially dependent swim velocity recently developed. We test the theory by confining an active particle in a harmonic trap, which gives rise to interesting properties, such as a transition from a unimodal to a bimodal (and, eventually multimodal) spatial density, induced by decreasing the spatial period of the self propulsion. Correspondingly, the velocity distribution shows pronounced deviations from the Gaussian shape, even displaying a bimodal profile in the high-motility regions. We thus show that the interplay of two relatively simple physical fields can be employed to generate complex emerging behavior.

  8 citations

• How to GAN Higher Jet Resolution

  Pierre Baldi, Lukas Blecher, Anja Butter, Julian Collado, Jessica N. Howard, Fabian Keilbach, Tilman Plehn, Gregor Kasieczka, Daniel Whiteson

  SciPost Phys. 13, 064 (2022) · published 23 September 2022 | Toggle abstract · pdf

  QCD-jets at the LHC are described by simple physics principles. We show how super-resolution generative networks can learn the underlying structures and use them to improve the resolution of jet images. We test this approach on massless QCD-jets and on fat top-jets and find that the network reproduces their main features even without training on pure samples. In addition, we show how a slim network architecture can be constructed once we have control of the full network performance.

  6 citations

• Hamiltonian reconstruction as metric for variational studies

  Kevin Zhang, Samuel Lederer, Kenny Choo, Titus Neupert, Giuseppe Carleo, Eun-Ah Kim

  SciPost Phys. 13, 063 (2022) · published 23 September 2022 | Toggle abstract · pdf

  Variational approaches are among the most powerful techniques to approximately solve quantum many-body problems. These encompass both variational states based on tensor or neural networks, and parameterized quantum circuits in variational quantum eigensolvers. However, self-consistent evaluation of the quality of variational wavefunctions is a notoriously hard task. Using a recently developed Hamiltonian reconstruction method, we propose a multi-faceted approach to evaluating the quality of neural-network based wavefunctions. Specifically, we consider convolutional neural network (CNN) and restricted Boltzmann machine (RBM) states trained on a square lattice spin-1/2 J1-J2 Heisenberg model. We find that the reconstructed Hamiltonians are typically less frustrated, and have easy-axis anisotropy near the high frustration point. In addition, the reconstructed Hamiltonians suppress quantum fluctuations in the large J2 limit. Our results highlight the critical importance of the wavefunction's symmetry. Moreover, the multi-faceted insight from the Hamiltonian reconstruction reveals that a variational wave function can fail to capture the true ground state through suppression of quantum fluctuations.

  2 citations

• Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function

  Hiroshi Shinaoka, Naoya Chikano, Emanuel Gull, Jia Li, Takuya Nomoto, Junya Otsuki, Markus Wallerberger, Tianchun Wang, Kazuyoshi Yoshimi

  SciPost Phys. Lect. Notes 63 (2022) · published 22 September 2022 | Toggle abstract · pdf

  This lecture note reviews recently proposed sparse-modeling approaches for efficient ab initio many-body calculations based on the data compression of Green's functions. The sparse-modeling techniques are based on a compact orthogonal basis, an intermediate representation (IR) basis, for imaginary-time and Matsubara Green's functions. A sparse sampling method based on the IR basis enables solving diagrammatic equations efficiently. We describe the basic properties of the IR basis, the sparse sampling method and its applications to ab initio calculations based on the GW approximation and the Migdal-Eliashberg theory. We also describe a numerical library for the IR basis and the sparse sampling method, sparse-ir, and provide its sample codes. This lecture note follows the Japanese review article with major revisions [H. Shinaoka et al., Solid State Physics 56(6), 301 (2021)].

  5 citations

• Probing multi-particle unitarity with the Landau equations

  Miguel Correia, Amit Sever, Alexander Zhiboedov

  SciPost Phys. 13, 062 (2022) · published 22 September 2022 | Toggle abstract · pdf

  We consider the $2\to 2$ scattering amplitude of identical massive particles. We identify the Landau curves in the multi-particle region $16m^2 \leq s, t < 36m^2$. We systematically generate and select the relevant graphs and numerically solve the associated Landau equations for the leading singularity. We find an infinite sequence of Landau curves that accumulates at finite $s$ and $t$ on the physical sheet. We expect that such accumulations are generic for $s,t > 16m^2$. Our analysis sheds new light on the complicated analytic structure of nonperturbative relativistic scattering amplitudes.

  11 citations