Publications

Order by: publication date number of citations

• Field theories with a vector global symmetry

  Nathan Seiberg

  SciPost Phys. 8, 050 (2020) · published 3 April 2020 | Toggle abstract · pdf

  Motivated by recent discussions of fractons, we explore nonrelativistic field theories with a continuous global symmetry, whose charge is a spatial vector. We present several such symmetries and demonstrate them in concrete examples. They differ by the equations their Noether currents satisfy. Simple cases, other than the translation symmetry, are an ordinary (relativistic) one-form global symmetry and its nonrelativistic generalization. In the latter case the conserved charge is associated with a codimension-one spatial manifold, but it is not topological. More general examples involve charges that are integrated over the entire space. We also discuss the coupling of these systems to gauge fields for these symmetries. We relate our examples to known continuum and lattice constructions.

  93 citations

• Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits

  Bruno Bertini, Pavel Kos, Tomaz Prosen

  SciPost Phys. 8, 067 (2020) · published 28 April 2020 | Toggle abstract · pdf

  The entanglement in operator space is a well established measure for the complexity of the quantum many-body dynamics. In particular, that of local operators has recently been proposed as dynamical chaos indicator, i.e. as a quantity able to discriminate between quantum systems with integrable and chaotic dynamics. For chaotic systems the local-operator entanglement is expected to grow linearly in time, while it is expected to grow at most logarithmically in the integrable case. Here we study local-operator entanglement in dual-unitary quantum circuits, a class of "statistically solvable" quantum circuits that we recently introduced. We identify a class of "completely chaotic" dual-unitary circuits where the local-operator entanglement grows linearly and we provide a conjecture for its asymptotic behaviour which is in excellent agreement with the numerical results. Interestingly, our conjecture also predicts a "phase transition" in the slope of the local-operator entanglement when varying the parameters of the circuits.

  69 citations

• Exploring phase space with Neural Importance Sampling

  Enrico Bothmann, Timo Janßen, Max Knobbe, Tobias Schmale, Steffen Schumann

  SciPost Phys. 8, 069 (2020) · published 29 April 2020 | Toggle abstract · pdf

  We present a novel approach for the integration of scattering cross sections and the generation of partonic event samples in high-energy physics. We propose an importance sampling technique capable of overcoming typical deficiencies of existing approaches by incorporating neural networks. The method guarantees full phase space coverage and the exact reproduction of the desired target distribution, in our case given by the squared transition matrix element. We study the performance of the algorithm for a few representative examples, including top-quark pair production and gluon scattering into three- and four-gluon final states.

  57 citations

• How to GAN away detector effects

  Marco Bellagente, Anja Butter, Gregor Kasieczka, Tilman Plehn, Ramon Winterhalder

  SciPost Phys. 8, 070 (2020) · published 29 April 2020 | Toggle abstract · pdf

  LHC analyses directly comparing data and simulated events bear the danger of using first-principle predictions only as a black-box part of event simulation. We show how simulations, for instance, of detector effects can instead be inverted using generative networks. This allows us to reconstruct parton level information from measured events. Our results illustrate how, in general, fully conditional generative networks can statistically invert Monte Carlo simulations. As a technical by-product we show how a maximum mean discrepancy loss can be staggered or cooled.

  48 citations

• Operator Entanglement in Local Quantum Circuits II: Solitons in Chains of Qubits

  Bruno Bertini, Pavel Kos, Tomaz Prosen

  SciPost Phys. 8, 068 (2020) · published 28 April 2020 | Toggle abstract · pdf

  We provide exact results for the dynamics of local-operator entanglement in quantum circuits with two-dimensional wires featuring ultralocal solitons, i.e. single-site operators which, up to a phase, are simply shifted by the time evolution. We classify all circuits allowing for ultralocal solitons and show that only dual-unitary circuits can feature moving ultralocal solitons. Then, we rigorously prove that if a circuit has an ultralocal soliton moving to the left (right), the entanglement of local operators initially supported on even (odd) sites saturates to a constant value and its dynamics can be computed exactly. Importantly, this does not bound the growth of complexity in chiral circuits, where solitons move only in one direction, say to the left. Indeed, in this case we observe numerically that operators on the odd sublattice have unbounded entanglement. Finally, we present a closed-form expression for the local-operator entanglement entropies in circuits with ultralocal solitons moving in both directions. Our results hold irrespectively of integrability.

  34 citations

• Anomaly matching in the symmetry broken phase: Domain walls, CPT, and the Smith isomorphism

  Itamar Hason, Zohar Komargodski, Ryan Thorngren

  SciPost Phys. 8, 062 (2020) · published 17 April 2020 | Toggle abstract · pdf

  Symmetries in Quantum Field Theory may have 't Hooft anomalies. If the symmetry is unbroken in the vacuum, the anomaly implies a nontrivial low-energy limit, such as gapless modes or a topological field theory. If the symmetry is spontaneously broken, for the continuous case, the anomaly implies low-energy theorems about certain couplings of the Goldstone modes. Here we study the case of spontaneously broken discrete symmetries, such as Z/2 and T. Symmetry breaking leads to domain walls, and the physics of the domain walls is constrained by the anomaly. We investigate how the physics of the domain walls leads to a matching of the original discrete anomaly. We analyze the symmetry structure on the domain wall, which requires a careful analysis of some properties of the unbreakable CPT symmetry. We demonstrate the general results on some examples and we explain in detail the mod 4 periodic structure that arises in the Z/2 and T case. This gives a physical interpretation for the Smith isomorphism, which we also extend to more general abelian groups. We show that via symmetry breaking and the analysis of the physics on the wall, the computations of certain discrete anomalies are greatly simplified. Using these results we perform new consistency checks on the infrared phases of 2+1 dimensional QCD.

  31 citations

• The negativity contour: a quasi-local measure of entanglement for mixed states

  Jonah Kudler-Flam, Hassan Shapourian, Shinsei Ryu

  SciPost Phys. 8, 063 (2020) · published 20 April 2020 | Toggle abstract · pdf

  In this paper, we study the entanglement structure of mixed states in quantum many-body systems using the $\textit{negativity contour}$, a local measure of entanglement that determines which real-space degrees of freedom in a subregion are contributing to the logarithmic negativity and with what magnitude. We construct an explicit contour function for Gaussian states using the fermionic partial-transpose. We generalize this contour function to generic many-body systems using a natural combination of derivatives of the logarithmic negativity. Though the latter negativity contour function is not strictly positive for all quantum systems, it is simple to compute and produces reasonable and interesting results. In particular, it rigorously satisfies the positivity condition for all holographic states and those obeying the quasi-particle picture. We apply this formalism to quantum field theories with a Fermi surface, contrasting the entanglement structure of Fermi liquids and holographic (hyperscale violating) non-Fermi liquids. The analysis of non-Fermi liquids show anomalous temperature dependence of the negativity depending on the dynamical critical exponent. We further compute the negativity contour following a quantum quench and discuss how this may clarify certain aspects of thermalization.

  27 citations

• On duality between Cosserat elasticity and fractons

  Andrey Gromov, Piotr Surówka

  SciPost Phys. 8, 065 (2020) · published 21 April 2020 | Toggle abstract · pdf

  We present a dual formulation of the Cosserat theory of elasticity. In this theory a local element of an elastic body is described in terms of local displacement and local orientation. Upon the duality transformation these degrees of freedom map onto a coupled theory of a vector-valued one-form gauge field and an ordinary $U(1)$ gauge field. We discuss the degrees of freedom in the corresponding gauge theories, the defect matter and coupling to the curved space.

  27 citations

• A non-abelian analogue of DBI from $T \overline{T}$

  T. Daniel Brennan, Christian Ferko, Savdeep Sethi

  SciPost Phys. 8, 052 (2020) · published 7 April 2020 | Toggle abstract · pdf

  The Dirac action describes the physics of the Nambu-Goldstone scalars found on branes. The Born-Infeld action defines a non-linear theory of electrodynamics. The combined Dirac-Born-Infeld (DBI) action describes the leading interactions supported on a single D-brane in string theory. We define a non-abelian analogue of DBI using the $T \overline{T}$ deformation in two dimensions. The resulting quantum theory is compatible with maximal supersymmetry and such theories are quite rare.

  22 citations

• Zero temperature momentum distribution of an impurity in a polaron state of one-dimensional Fermi and Tonks-Girardeau gases

  Oleksandr Gamayun, Oleg Lychkovskiy, Mikhail B. Zvonarev

  SciPost Phys. 8, 053 (2020) · published 7 April 2020 | Toggle abstract · pdf

  We investigate the momentum distribution function of a single distinguishable impurity particle which formed a polaron state in a gas of either free fermions or Tonks-Girardeau bosons in one spatial dimension. We obtain a Fredholm determinant representation of the distribution function for the Bethe ansatz solvable model of an impurity-gas δ-function interaction potential at zero temperature, in both repulsive and attractive regimes. We deduce from this representation the fourth power decay at a large momentum, and a weakly divergent (quasi-condensate) peak at a finite momentum. We also demonstrate that the momentum distribution function in the limiting case of infinitely strong interaction can be expressed through a correlation function of the one-dimensional impenetrable anyons.

  16 citations