Publications

Order by: publication date number of citations

• Neural network quantum states analysis of the Shastry-Sutherland model

  Matěj Mezera, Jana Menšíková, Pavel Baláž, Martin Žonda

  SciPost Phys. Core 6, 088 (2023) · published 22 December 2023 | Toggle abstract · pdf

  We utilize neural network quantum states (NQS) to investigate the ground state properties of the Heisenberg model on a Shastry-Sutherland lattice using the variational Monte Carlo method. We show that already relatively simple NQSs can be used to approximate the ground state of this model in its different phases and regimes. We first compare several types of NQSs with each other on small lattices and benchmark their variational energies against the exact diagonalization results. We argue that when precision, generality, and computational costs are taken into account, a good choice for addressing larger systems is a shallow restricted Boltzmann machine NQS. We then show that such NQS can describe the main phases of the model in zero magnetic field. Moreover, NQS based on a restricted Boltzmann machine correctly describes the intriguing plateaus forming in magnetization of the model as a function of increasing magnetic field.

• Quantum current and holographic categorical symmetry

  Tian Lan, Jing-Ren Zhou

  SciPost Phys. 16, 053 (2024) · published 23 February 2024 | Toggle abstract · pdf

  We establish the formulation for quantum current. Given a symmetry group G, let $\mathcal{C}$:=Rep G be its representation category. Physically, symmetry charges are objects of $\mathcal{C}$ and symmetric operators are morphisms in $\mathcal{C}$. The addition of charges is given by the tensor product of representations. For any symmetric operator O crossing two subsystems, the exact symmetry charge transported by O can be extracted. The quantum current is defined as symmetric operators that can transport symmetry charges over an arbitrary long distance. A quantum current exactly corresponds to an object in the Drinfeld center $Z_1(\mathcal{C})$. The condition for quantum currents to be superconducting is also specified, which corresponds to condensation of anyons in one higher dimension. To express the local conservation, the internal hom must be used to compute the charge difference, and the framework of enriched category is inevitable. To illustrate these ideas, we develop a rigorous scheme of renormalization in one-dimensional lattice systems and analyse the fixed-point models. It is proved that in the fixed-point models, superconducting quantum currents form a Lagrangian algebra in $Z_1(\mathcal{C})$ and the boundary-bulk correspondence is verified in the enriched setting. Overall, the quantum current provides a natural physical interpretation to the holographic categorical symmetry.

• Vacuum-field-induced state mixing

  Diego Fernández de la Pradilla, Esteban Moreno, Johannes Feist

  SciPost Phys. 15, 252 (2023) · published 22 December 2023 | Toggle abstract · pdf

  By engineering the electromagnetic vacuum field, the induced Casimir-Polder shift (also known as Lamb shift) and spontaneous emission rates of individual atomic levels can be controlled. When the strength of these effects becomes comparable to the energy difference between two previously uncoupled atomic states, an environment-induced interaction between these states appears after tracing over the environment. This interaction has been previously studied for degenerate levels and simple geometries involving infinite, perfectly conducting half-spaces or free space. Here, we generalize these studies by developing a convenient description that permits the analysis of these non-diagonal perturbations to the atomic Hamiltonian in terms of an accurate non-Hermitian Hamiltonian. Applying this theory to a hydrogen atom close to a dielectric nanoparticle, we show strong vacuum-field-induced state mixing that leads to drastic modifications in both the energies and decay rates compared to conventional diagonal perturbation theory. In particular, contrary to the expected Purcell enhancement, we find a surprising decrease of decay rates within a considerable range of atom-nanoparticle separations. Furthermore, we quantify the large degree of mixing of the unperturbed eigenstates due to the non-diagonal perturbation. Our work opens new quantum state manipulation possibilities in emitters with closely spaced energy levels.

• The prediction of anyons: Its history and wider implications

  Gerald A. Goldin

  SciPost Phys. Proc. 14, 005 (2023) · published 23 November 2023 | Toggle abstract · pdf

  Prediction of "anyons," often attributed exclusively to Wilczek, came first from Leinaas and Myrheim in 1977, and independently from Goldin, Menikoff, and Sharp in 1980-81. In 2020, experimentalists successfully created anyonic excitations. This paper discusses why the possibility of quantum particles in two-dimensional space with intermediate exchange statistics eluded physicists for so long after bosons and fermions were understood. The history suggests ideas for the preparation of future researchers. I conclude by addressing failures to attribute scientific achievements accurately, both inadvertent and intentional. Such practices disproportionately hurt women and minorities in physics.

• Radiative asymptotic symmetries of 3D Einstein-Maxwell theory

  Jorrit Bosma, Marc Geiller, Sucheta Majumdar, Blagoje Oblak

  SciPost Phys. 16, 092 (2024) · published 3 April 2024 | Toggle abstract · pdf

  We study the null asymptotic structure of Einstein-Maxwell theory in three-dimensional (3D) spacetimes. Although devoid of bulk gravitational degrees of freedom, the system admits a massless photon and can therefore accommodate electromagnetic radiation. We derive fall-off conditions for the Maxwell field that contain both Coulombic and radiative modes with non-vanishing news. The latter produces non-integrability and fluxes in the asymptotic surface charges, and gives rise to a non-trivial 3D Bondi mass loss formula. The resulting solution space is thus analogous to a dimensional reduction of 4D pure gravity, with the role of gravitational radiation played by its electromagnetic cousin. We use this simplified setup to investigate choices of charge brackets in detail, and compute in particular the recently introduced Koszul bracket. When the latter is applied to Wald-Zoupas charges, which are conserved in the absence of news, it leads to the field-dependent central extension found earlier in [Class. Quantum Gravity 32, 245001 (2015)]. We also consider (Anti-)de Sitter asymptotics to further exhibit the analogy between this model and 4D gravity with leaky boundary conditions.

• A differential-geometry approach to operator mixing in massless QCD-like theories and Poincaré-Dulac theorem

  Matteo Becchetti

  SciPost Phys. Proc. 7, 032 (2022) · published 21 June 2022 | Toggle abstract · pdf

  We review recent progress on operator mixing in the light of the theory of canonical forms for linear systems of differential equations and, in particular, of the Poincar\'e-Dulac theorem. We show that the matrix $A(g) = -\frac{\gamma(g)}{\beta(g)} =\frac{\gamma_0}{\beta_0}\frac{1}{g} + \cdots $ determines which different cases of operator mixing can occur, and we review their classification. We derive a sufficient condition for $A(g)$ to be set in the one-loop exact form $A(g) = \frac{\gamma_0}{\beta_0}\frac{1}{g}$. Finally, we discuss the consequences of the unitarity requirement in massless QCD-like theories, and we demonstrate that $\gamma_0$ is always diagonalizable if the theory is conformal invariant and unitary in its free limit at $g =0$.

• Optimal control strategies for parameter estimation of quantum systems

  Quentin Ansel, Etienne Dionis, Dominique Sugny

  SciPost Phys. 16, 013 (2024) · published 17 January 2024 | Toggle abstract · pdf

  Optimal control theory is an effective tool to improve parameter estimation of quantum systems. Different methods can be employed for the design of the control protocol. They can be based either on Quantum Fischer Information (QFI) maximization or selective control processes. We describe the similarities, differences, and advantages of these two approaches. A detailed comparative study is presented for estimating the parameters of a spin$-\tfrac{1}{2}$ system coupled to a bosonic bath. We show that the control mechanisms are generally equivalent, except when the decoherence is not negligible or when the experimental setup is not adapted to the QFI. In this latter case, the precision achieved with selective controls can be several orders of magnitude better than that given by the QFI.

• Thermalization of long range Ising model in different dynamical regimes: A full counting statistics approach

  Nishan Ranabhat, Mario Collura

  SciPost Phys. Core 7, 017 (2024) · published 5 April 2024 | Toggle abstract · pdf

  We study the thermalization of the transverse field Ising chain with a power law decaying interaction $\sim 1/r^{\alpha}$ following a global quantum quench of the transverse field in two different dynamical regimes. The thermalization behavior is quantified by comparing the full probability distribution function (PDF) of the evolving states with the corresponding thermal state given by the canonical Gibbs ensemble (CGE). To this end, we used the matrix product state (MPS)-based Time Dependent Variational Principle (TDVP) algorithm to simulate both real time evolution following a global quantum quench and the finite temperature density operator. We observe that thermalization is strongly suppressed in the region with strong confinement for all interaction strengths $\alpha$, whereas thermalization occurs in the region with weak confinement.

• Nonlinear response in diffusive systems

  Luca V. Delacrétaz, Ruchira Mishra

  SciPost Phys. 16, 047 (2024) · published 12 February 2024 | Toggle abstract · pdf

  Nonintegrable systems thermalize, leading to the emergence of fluctuating hydrodynamics. Typically, this hydrodynamics is diffusive. We use the effective field theory (EFT) of diffusion to compute higher-point functions of conserved densities. We uncover a simple scaling behavior of correlators at late times, and, focusing on three and four-point functions, derive the asymptotically exact universal scaling functions that characterize nonlinear response in diffusive systems. This allows for precision tests of thermalization beyond linear response in quantum and classical many-body systems. We confirm our predictions in a classical lattice gas.

• Seven-dimensional super Yang-Mills at negative coupling

  Joseph A. Minahan, Usman Naseer, Charles Thull

  SciPost Phys. 14, 028 (2023) · published 6 March 2023 | Toggle abstract · pdf

  We consider the partition function for Euclidean $SU(N)$ super Yang-Mills on a squashed seven-sphere. We show that the localization locus of the partition function has instanton membrane solutions wrapping the six ``fixed" three-spheres on the $\mathbb{S}^7$. The ADHM variables of these instantons are fields living on the membrane world volume. We compute their contribution by localizing the resulting three-dimensional supersymmetric field theory. In the round-sphere limit the individual instanton contributions are singular, but the singularities cancel when adding the contributions of all six three-spheres. The full partition function on the ${\mathbb S}^7$ is well-defined even when the square of the effective Yang-Mills coupling is negative. We show for an $SU(2)$ gauge theory in this regime that the bare negative tension of the instanton membranes is canceled off by contributions from the instanton partition function, indicating the existence of tensionless membranes. We provide evidence that this phase is distinct from the usual weakly coupled super Yang-Mills and, in fact, is gravitational.