Publications

Order by: publication date number of citations

• Hamiltonian Truncation Effective Theory

  Timothy Cohen, Kara Farnsworth, Rachel Houtz, Markus A. Luty

  SciPost Phys. 13, 011 (2022) · published 4 August 2022 | Toggle abstract · pdf

  Hamiltonian truncation is a non-perturbative numerical method for calculating observables of a quantum field theory. The starting point for this method is to truncate the interacting Hamiltonian to a finite-dimensional space of states spanned by the eigenvectors of the free Hamiltonian $H_0$ with eigenvalues below some energy cutoff $E_\text{max}$. In this work, we show how to treat Hamiltonian truncation systematically using effective field theory methodology. We define the finite-dimensional effective Hamiltonian by integrating out the states above $E_\text{max}$. The effective Hamiltonian can be computed by matching a transition amplitude to the full theory, and gives corrections order by order as an expansion in powers of $1/E_\text{max}$. The effective Hamiltonian is non-local, with the non-locality controlled in an expansion in powers of $H_0/E_\text{max}$. The effective Hamiltonian is also non-Hermitian, and we discuss whether this is a necessary feature or an artifact of our definition. We apply our formalism to 2D $\lambda \phi^4$ theory, and compute the the leading $1/E_\text{max}^2$ corrections to the effective Hamiltonian. We show that these corrections non-trivially satisfy the crucial property of separation of scales. Numerical diagonalization of the effective Hamiltonian gives residual errors of order $1/E_\text{max}^3$, as expected by our power counting. We also present the power counting for 3D $\lambda \phi^4$ theory and perform calculations that demonstrate the separation of scales in this theory.

  4 citations

• Computing associators of endomorphism fusion categories

  Daniel Barter, Jacob C. Bridgeman, Ramona Wolf

  SciPost Phys. 13, 029 (2022) · published 19 August 2022 | Toggle abstract · pdf

  Many applications of fusion categories, particularly in physics, require the associators or $F$-symbols to be known explicitly. Finding these matrices typically involves solving vast systems of coupled polynomial equations in large numbers of variables. In this work, we present an algorithm that allows associator data for some category with unknown associator to be computed from a Morita equivalent category with known data. Given a module category over the latter, we utilize the representation theory of a module tube category, built from the known data, to compute this unknown associator data. When the input category is unitary, we discuss how to ensure the obtained data is also unitary. We provide several worked examples to illustrate this algorithm. In addition, we include several Mathematica files showing how the algorithm can be used to compute the data for the Haagerup category $\mathcal{H}_1$, whose data was previously unknown.

  4 citations

• Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d

  Tomohiro Hashizume, Jad C. Halimeh, Philipp Hauke, Debasish Banerjee

  SciPost Phys. 13, 017 (2022) · published 12 August 2022 | Toggle abstract · pdf

  The exploration of phase diagrams of strongly interacting gauge theories coupled to matter in lower dimensions promises the identification of exotic phases and possible new universality classes, and it facilitates a better understanding of salient phenomena in Nature, such as confinement or high-temperature superconductivity. The emerging new techniques of quantum synthetic matter experiments as well as efficient classical computational methods with matrix product states have been extremely successful in one spatial dimension, and are now motivating such studies in two spatial dimensions. In this work, we consider a $\mathrm{U}(1)$ quantum link lattice gauge theory where the gauge fields, represented by spin-$\frac{1}{2}$ operators are coupled to a single flavor of staggered fermions. Using matrix product states on infinite cylinders with increasing diameter, we conjecture its phase diagram in $(2+1)$-d. This model allows us to smoothly tune between the $\mathrm{U}(1)$ quantum link and the quantum dimer models by adjusting the strength of the fermion mass term, enabling us to connect to the well-studied phases of those models. Our study reveals a rich phase diagram with exotic phases and interesting phase transitions to a potential liquid-like phase. It thus furthers the collection of gauge theory models that may guide future quantum-simulation experiments.

  4 citations

• Hitting two BSM particles with one lepton-jet: search for a top partner decaying to a dark photon, resulting in a lepton-jet

  K. du Plessis, M. M. Flores, D. Kar, S. Sinha, H. van der Schyf

  SciPost Phys. 13, 018 (2022) · published 15 August 2022 | Toggle abstract · pdf

  A maverick top partner model, decaying to a dark photon was suggested. The dark photon decays to two overlapping electrons for dark photon masses of $\approx 100$ GeV, and results in a so-called lepton-jet. The event includes a top quark as well, which results in events with two boosted objects, one heavy and the other light. We propose a search strategy exploiting the unique signal topology. We show that for a set of kinematic selections, both in hadronic and leptonic decay channel of the SM top quark, almost all background can be eliminated, leaving enough signal events up to top partner mass of about 3 TeV for the search to be viable at the LHC.

  3 citations

• Reduced Dynamics of Full Counting Statistics

  Felix A. Pollock, Emanuel Gull, K. Modi, Guy Cohen

  SciPost Phys. 13, 027 (2022) · published 18 August 2022 | Toggle abstract · pdf

  We present a theory of modified reduced dynamics in the presence of counting fields. Reduced dynamics techniques are useful for describing open quantum systems at long emergent timescales when the memory timescales are short. However, they can be difficult to formulate for observables spanning the system and its environment, such as those characterizing transport properties. A large variety of mixed system--environment observables, as well as their statistical properties, can be evaluated by considering counting fields. Given a numerical method able to simulate the field-modified dynamics over the memory timescale, we show that the long-lived full counting statistics can be efficiently obtained from the reduced dynamics. We demonstrate the utility of the technique by computing the long-time current in the nonequilibrium Anderson impurity model from short-time Monte Carlo simulations.

  3 citations

• Jet modifications from colour rope formation in dense systems of non-parallel strings

  Christian Bierlich, Smita Chakraborty, Gösta Gustafson, Leif Lönnblad

  SciPost Phys. 13, 023 (2022) · published 17 August 2022 | Toggle abstract · pdf

  We revisit our rope model for string fragmentation that has been shown to give a reasonable description of strangeness and baryon enhancement in high-multiplicity pp events at the LHC. A key feature of the model is that the enhancement is driven by the increased string tension due to strings overlapping in dense systems. By introducing an improved space-time picture for the overlap between fragmenting strings, where also non-parallel strings are properly taken into account, we are now able to investigate the enhancement both in jets and in the underlying event in a consistent way.

  3 citations

• YFS Resummation for Future Lepton-Lepton Colliders in SHERPA

  Frank Krauss, Alan Price, Marek Schönherr

  SciPost Phys. 13, 026 (2022) · published 18 August 2022 | Toggle abstract · pdf

  We present an implementation of the Yennie-Frautschi-Suura (YFS) scheme for the all-orders resummation of logarithms from the emission of soft real and virtual photons in processes that are critical for future lepton colliders. They include, in particular, $e^-e^+\to f\bar{f}$ and $e^-e^+\to W^-W^+$, where we validate the results of our implementation, improved with fixed-order corrections, with those obtained from the most precise calculations. We also show, for the first time, results for the Higgs-Strahlungs process, $e^-e^+\to ZH$, in YFS resummation including fixed-order improvements up to order $\alpha^3L^3$.

  2 citations

• Quantifying Non-Markovianity in Open Quantum Dynamics

  Chu Guo

  SciPost Phys. 13, 028 (2022) · published 19 August 2022 | Toggle abstract · pdf

  Characterization of non-Markovian open quantum dynamics is both of theoretical and practical relevance. In a seminal work [Phys. Rev. Lett. 120, 040405 (2018)], a necessary and sufficient quantum Markov condition is proposed, with a clear operational interpretation and correspondence with the classical limit. Here we propose two non-Markovianity measures for general open quantum dynamics, which are fully reconciled with the Markovian limit and can be efficiently calculated based on the multi-time quantum measurements of the system. A heuristic algorithm for reconstructing the underlying open quantum dynamics is proposed, whose complexity is directly related to the proposed non-Markovianity measures. The non-Markovianity measures and the reconstruction algorithm are demonstrated with numerical examples, together with a careful reexamination of the non-Markovianity in quantum dephasing dynamics.

  2 citations

• Charge order and antiferromagnetism in twisted bilayer graphene from the variational cluster approximation

  B. Pahlevanzadeh, P. Sahebsara, D. Sénéchal

  SciPost Phys. 13, 040 (2022) · published 30 August 2022 | Toggle abstract · pdf

  We study the possibility of charge order at quarter filling and antiferromagnetism at half-filling in a tight-binding model of magic angle twisted bilayer graphene. We build on the model proposed by Kang and Vafek, relevant to a twist angle of $1.30^\circ$, and add on-site and extended density-density interactions. Applying the variational cluster approximation with an exact-diagonalization impurity solver, we find that the system is indeed a correlated (Mott) insulator at fillings $\frac14$, $\frac12$ and $\frac34$. At quarter filling, we check that the most probable charge orders do not arise, for all values of the interaction tested. At half-filling, antiferromagnetism only arises if the local repulsion $U$ is sufficiently large compared to the extended interactions, beyond what is expected from the simplest model of extended interactions.

  1 citation

• Time-dependent variational Monte Carlo study of the dynamic response of bosons in an optical lattice

  Mathias Gartner, Ferran Mazzanti, Robert E. Zillich

  SciPost Phys. 13, 025 (2022) · published 18 August 2022 | Toggle abstract · pdf

  We study the dynamics of a one-dimensional Bose gas at unit filling in both shallow and deep optical lattices and obtain the dynamic structure factor ${S(k,\omega)}$ by monitoring the linear response to a weak probe pulse. We introduce a new procedure, based on the time-dependent variational Monte Carlo method (tVMC), which allows to evolve the system in real time, using as a variational model a Jastrow-Feenberg wave function that includes pair correlations. Comparison with exact diagonalization results of ${S(k,\omega)}$ obtained on a lattice in the Bose-Hubbard limit shows good agreement of the dispersion relation for sufficiently deep optical lattices, while for shallow lattices we observe the influence of higher Bloch bands. We also investigate non-linear response to strong pulses. From the power spectrum of the density fluctuations we obtain the excitation spectrum, albeit broadened, by higher harmonic generation after a strong pulse with a single low wave number. As a remarkable feature of our simulations we furthermore demonstrate that the full excitation spectrum can be retrieved from the power spectrum of the density fluctuations due to the stochastic noise inherent in any Monte Carlo method, without applying an actual perturbation.

  1 citation