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SciPost Physics

SciPost Physics Vol. 8 issue 2 (February 2020)

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Current operators in integrable spin chains: lessons from long range deformations

Balázs Pozsgay

SciPost Phys. 8, 016 (2020) · published 3 February 2020 | · pdf

We consider the finite volume mean values of current operators in integrable spin chains with local interactions, and provide an alternative derivation of the exact result found recently by the author and two collaborators. We use a certain type of long range deformation of the local spin chains, which was discovered and explored earlier in the context of the AdS/CFT correspondence. This method is immediately applicable also to higher rank models: as a concrete example we derive the current mean values in the SU(3)-symmetric fundamental model, solvable by the nested Bethe Ansatz. The exact results take the same form as in the Heisenberg spin chains: they involve the one-particle eigenvalues of the conserved charges and the inverse of the Gaudin matrix.
Connecting quasinormal modes and heat kernels in 1-loop determinants

Cynthia Keeler, Victoria L. Martin, Andrew Svesko

SciPost Phys. 8, 017 (2020) · published 3 February 2020 | · pdf

We connect two different approaches for calculating functional determinants on quotients of hyperbolic spacetime: the heat kernel method and the quasinormal mode method. For the example of a rotating BTZ background, we show how the image sum in the heat kernel method builds up the logarithms in the quasinormal mode method, while the thermal sum in the quasinormal mode method builds up the integrand of the heat kernel. More formally, we demonstrate how the heat kernel and quasinormal mode methods are linked via the Selberg zeta function. We show that a 1-loop partition function computed using the heat kernel method may be cast as a Selberg zeta function whose zeros encode quasinormal modes. We discuss how our work may be used to predict quasinormal modes on more complicated spacetimes.
Lorentz symmetry fractionalization and dualities in (2+1)d

Po-Shen Hsin, Shu-Heng Shao

SciPost Phys. 8, 018 (2020) · published 4 February 2020 | · pdf

We discuss symmetry fractionalization of the Lorentz group in (2+1)d non-spin quantum field theory (QFT), and its implications for dualities. We prove that two inequivalent non-spin QFTs are dual as spin QFTs if and only if they are related by a Lorentz symmetry fractionalization with respect to an anomalous $\mathbb{Z}_2$ one-form symmetry. Moreover, if the framing anomalies of two non-spin QFTs differ by a multiple of 8, then they are dual as spin QFTs if and only if they are also dual as non-spin QFTs. Applications to summing over the spin structures, time-reversal symmetry, and level/rank dualities are explored. The Lorentz symmetry fractionalization naturally arises in Chern-Simons matter dualities that obey certain spin/charge relations, and is instrumental for the dualities to hold when viewed as non-spin theories.
The representation theory of seam algebras

Alexis Langlois-Rémillard, Yvan Saint-Aubin

SciPost Phys. 8, 019 (2020) · published 5 February 2020 | · pdf

The boundary seam algebras $\mathsf{b}_{n,k}(\beta=q+q^{-1})$ were introduced by Morin-Duchesne, Ridout and Rasmussen to formulate algebraically a large class of boundary conditions for two-dimensional statistical loop models. The representation theory of these algebras $\mathsf{b}_{n,k}(\beta=q+q^{-1})$ is given: their irreducible, standard (cellular) and principal modules are constructed and their structure explicited in terms of their composition factors and of non-split short exact sequences. The dimensions of the irreducible modules and of the radicals of standard ones are also given. The methods proposed here might be applicable to a large family of algebras, for example to those introduced recently by Flores and Peltola, and Cramp\'e and Poulain d'Andecy.
Ground-state correlation energy of beryllium dimer by the Bethe-Salpeter equation

Jing Li, Ivan Duchemin, Xavier Blase, Valerio Olevano

SciPost Phys. 8, 020 (2020) · published 5 February 2020 | · pdf

Since the '30s the interatomic potential of the beryllium dimer Be$_2$ has been both an experimental and a theoretical challenge. Calculating the ground-state correlation energy of Be$_2$ along its dissociation path is a difficult problem for theory. We present ab initio many-body perturbation theory calculations of the Be$_2$ interatomic potential using the GW approximation and the Bethe-Salpeter equation (BSE). The ground-state correlation energy is calculated by the trace formula with checks against the adiabatic-connection fluctuation-dissipation theorem formula. We show that inclusion of GW corrections already improves the energy even at the level of the random-phase approximation. At the level of the BSE on top of the GW approximation, our calculation is in surprising agreement with the most accurate theories and with experiment. It even reproduces an experimentally observed flattening of the interatomic potential due to a delicate correlations balance from a competition between covalent and van der Waals bonding.
Evaluation of time-dependent correlators after a local quench in iPEPS: hole motion in the t-J model

Claudius Hubig, Annabelle Bohrdt, Michael Knap, Fabian Grusdt, J. Ignacio Cirac

SciPost Phys. 8, 021 (2020) · published 6 February 2020 | · pdf

Infinite projected entangled pair states (iPEPS) provide a convenient variational description of infinite, translationally-invariant two-dimensional quantum states. However, the simulation of local excitations is not directly possible due to the translationally-invariant ansatz. Furthermore, as iPEPS are either identical or orthogonal, expectation values between different states as required during the evaluation of non-equal-time correlators are ill-defined. Here, we show that by introducing auxiliary states on each site, it becomes possible to simulate both local excitations and evaluate non-equal-time correlators in an iPEPS setting under real-time evolution. We showcase the method by simulating the t-J model after a single hole has been placed in the half-filled antiferromagnetic background and evaluating both return probabilities and spin correlation functions, as accessible in quantum gas microscopes.
Quantum spin systems versus Schroedinger operators: A case study in spontaneous symmetry breaking

Christiaan J. F. van de Ven, Gerrit C. Groenenboom, Robin Reuvers, Nicolaas P. Landsman

SciPost Phys. 8, 022 (2020) · published 6 February 2020 | · pdf

Spontaneous symmetry breaking (SSB) is mathematically tied to some limit, but must physically occur, approximately, before the limit. Approximate SSB has been independently understood for Schroedinger operators with double well potential in the classical limit (Jona-Lasinio et al, 1981; Simon, 1985) and for quantum spin systems in the thermodynamic limit (Anderson, 1952; Tasaki, 2019). We relate these to each other in the context of the Curie-Weiss model, establishing a remarkable relationship between this model (for finite N) and a discretized Schroedinger operator with double well potential.
CapsNets continuing the convolutional quest

Sascha Diefenbacher, Hermann Frost, Gregor Kasieczka, Tilman Plehn, Jennifer M. Thompson

SciPost Phys. 8, 023 (2020) · published 7 February 2020 | · pdf

Capsule networks are ideal tools to combine event-level and subjet information at the LHC. After benchmarking our capsule network against standard convolutional networks, we show how multi-class capsules extract a resonance decaying to top quarks from both, QCD di-jet and the top continuum backgrounds. We then show how its results can be easily interpreted. Finally, we use associated top-Higgs production to demonstrate that capsule networks can work on overlaying images to go beyond calorimeter information.
Time dependent variational principle for tree Tensor Networks

Daniel Bauernfeind, Markus Aichhorn

SciPost Phys. 8, 024 (2020) · published 7 February 2020 | · pdf

We present a generalization of the Time Dependent Variational Principle (TDVP) to any finite sized loop-free tensor network. The major advantage of TDVP is that it can be employed as long as a representation of the Hamiltonian in the same tensor network structure that encodes the state is available. Often, such a representation can be found also for long-range terms in the Hamiltonian. As an application we use TDVP for the Fork Tensor Product States tensor network for multi-orbital Anderson impurity models. We demonstrate that TDVP allows to account for off-diagonal hybridizations in the bath which are relevant when spin-orbit coupling effects are important, or when distortions of the crystal lattice are present.
Fast simulation of detector effects in Rivet

Andy Buckley, Deepak Kar, Karl Nordström

SciPost Phys. 8, 025 (2020) · published 10 February 2020 | · pdf

We describe the design and implementation of detector-bias emulation in the Rivet MC event analysis system. Implemented using C++ efficiency and kinematic smearing functors, it allows detector effects to be specified within an analysis routine, customised to the exact phase-space and reconstruction working points of the analysis. A set of standard detector functions for the physics objects of Runs 1 and 2 of the ATLAS and CMS experiments is also provided. Finally, as jet substructure is an important class of physics observable usually considered to require an explicit detector simulation, we demonstrate that a smearing approach, tuned to available substructure data and implemented in Rivet, can accurately reproduce jet-structure biases observed by ATLAS.
Robust Independent Validation of Experiment and Theory: Rivet version 3

Christian Bierlich, Andy Buckley, Jonathan Butterworth, Christian Holm Christensen, Louie Corpe, David Grellscheid, Jan Fiete Grosse-Oetringhaus, Christian Gutschow, Przemyslaw Karczmarczyk, Jochen Klein, Leif Lonnblad, Christopher Samuel Pollard, Peter Richardson, Holger Schulz, Frank Siegert

SciPost Phys. 8, 026 (2020) · published 11 February 2020 | · pdf

First released in 2010, the Rivet library forms an important repository for analysis code, facilitating comparisons between measurements of the final state in particle collisions and theoretical calculations of those final states. We give an overview of Rivet's current design and implementation, its uptake for analysis preservation and physics results, and summarise recent developments including propagation of MC systematic-uncertainty weights, heavy-ion and $ep$ physics, and systems for detector emulation. In addition, we provide a short user guide that supplements and updates the Rivet user manual.
A global view of the off-shell Higgs portal

Maximilian Ruhdorfer, Ennio Salvioni, Andreas Weiler

SciPost Phys. 8, 027 (2020) · published 12 February 2020 | · pdf

We study for the first time the collider reach on the derivative Higgs portal, the leading effective interaction that couples a pseudo Nambu-Goldstone boson (pNGB) scalar Dark Matter to the Standard Model. We focus on Dark Matter pair production through an off-shell Higgs boson, which is analyzed in the vector boson fusion channel. A variety of future high-energy lepton colliders as well as hadron colliders are considered, including CLIC, a muon collider, the High-Luminosity and High-Energy versions of the LHC, and FCC-hh. Implications on the parameter space of pNGB Dark Matter are discussed. In addition, we give improved and extended results for the collider reach on the marginal Higgs portal, under the assumption that the new scalars escape the detector, as motivated by a variety of beyond the Standard Model scenarios.
Relative anomalies in (2+1)D symmetry enriched topological states

Maissam Barkeshli, Meng Cheng

SciPost Phys. 8, 028 (2020) · published 18 February 2020 | · pdf

Certain patterns of symmetry fractionalization in topologically ordered phases of matter are anomalous, in the sense that they can only occur at the surface of a higher dimensional symmetry-protected topological (SPT) state. An important question is to determine how to compute this anomaly, which means determining which SPT hosts a given symmetry-enriched topological order at its surface. While special cases are known, a general method to compute the anomaly has so far been lacking. In this paper we propose a general method to compute relative anomalies between different symmetry fractionalization classes of a given (2+1)D topological order. This method applies to all types of symmetry actions, including anyon-permuting symmetries and general space-time reflection symmetries. We demonstrate compatibility of the relative anomaly formula with previous results for diagnosing anomalies for $\mathbb{Z}_2^{\bf T}$ space-time reflection symmetry (e.g. where time-reversal squares to the identity) and mixed anomalies for $U(1) \times \mathbb{Z}_2^{\bf T}$ and $U(1) \rtimes \mathbb{Z}_2^{\bf T}$ symmetries. We also study a number of additional examples, including cases where space-time reflection symmetries are intertwined in non-trivial ways with unitary symmetries, such as $\mathbb{Z}_4^{\bf T}$ and mixed anomalies for $\mathbb{Z}_2 \times \mathbb{Z}_2^{\bf T}$ symmetry, and unitary $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry with non-trivial anyon permutations.
Dynamics of hot Bose-Einstein condensates: stochastic Ehrenfest relations for number and energy damping

Rob G. McDonald, Peter S. Barnett, Fradom Atayee, Ashton S. Bradley

SciPost Phys. 8, 029 (2020) · published 18 February 2020 | · pdf

Describing partially-condensed Bose gases poses a long-standing theoretical challenge. We present exact stochastic Ehrenfest relations for the stochastic projected Gross-Pitaevskii equation, including both number and energy damping mechanisms, and all projector terms that arise from the energy cutoff separating system from reservoir. We test the theory by applying it to the centre of mass fluctuations of a harmonically trapped prolate system, finding close agreement between c-field simulations and analytical results. The formalism lays the foundation to analytically explore experimentally accessible hot Bose-Einstein condensates.
First-order transition in a model of prestige bias

Brian Skinner

SciPost Phys. 8, 030 (2020) · published 19 February 2020 | · pdf

One of the major benefits of belonging to a prestigious group is that it affects the way you are viewed by others. Here I use a simple mathematical model to explore the implications of this "prestige bias" when candidates undergo repeated rounds of evaluation. In the model, candidates who are evaluated most highly are admitted to a "prestige class", and their membership biases future rounds of evaluation in their favor. I use the language of Bayesian inference to describe this bias, and show that it can lead to a runaway effect in which the weight given to the prior expectation associated with a candidate's class becomes stronger with each round. Most dramatically, the strength of the prestige bias after many rounds undergoes a first-order transition as a function of the precision of the examination on which the evaluation is based.
Microscopic theory of fractional excitations in gapless quantum Hall states: semi-quantized quantum Hall states

Oğuz Türker, Tobias Meng

SciPost Phys. 8, 031 (2020) · published 28 February 2020 | · pdf

We derive the low-energy theory of semi-quantized quantum Hall states, a recently observed class of gapless bilayer fractional quantum Hall states. Our theory shows these states to feature gapless quasiparticles of fractional charge coupled to an emergent Chern-Simons gauge field. These gapless quasiparticles can be understood as composites of electrons and Laughlin-like quasiparticles. We show that semi-quantized quantum Hall states exhibit perfect interlayer drag, host non-Fermi liquid physics, and serve as versatile parent states for fully gapped topological phases hosting anyonic excitations.