Publications

Order by: publication date number of citations

• Conformal dispersion relations for defects and boundaries

  Lorenzo Bianchi, Davide Bonomi

  SciPost Phys. 15, 055 (2023) · published 8 August 2023 | Toggle abstract · pdf

  We derive a dispersion relation for two-point correlation functions in defect conformal field theories. The correlator is expressed as an integral over a (single) discontinuity that is controlled by the bulk channel operator product expansion (OPE). This very simple relation is particularly useful in perturbative settings where the discontinuity is determined by a subset of bulk operators. In particular, we apply it to holographic correlators of two chiral primary operators in $\mathcal{N}=4$ Super Yang-Mills theory in the presence of a supersymmetric Wilson line. With a very simple computation, we are able to reproduce and extend existing results. We also propose a second relation, which reconstructs the correlator from a double discontinuity, and is controlled by the defect channel OPE. Finally, for the case of codimension-one defects (boundaries and interfaces) we derive a dispersion relation which receives contributions from both OPE channels and we apply it to the boundary correlator in the O(N) critical model. We reproduce the order $\epsilon^2$ result in the $\epsilon$-expansion using as input a finite number of boundary CFT data.

  18 citations

• Statistical mechanics of coupled supercooled liquids in finite dimensions

  Benjamin Guiselin, Ludovic Berthier, Gilles Tarjus

  SciPost Phys. 12, 091 (2022) · published 14 March 2022 | Toggle abstract · pdf

  We study the statistical mechanics of supercooled liquids when the system evolves at a temperature $T$ with a field $\epsilon$ linearly coupled to its overlap with a reference configuration of the same liquid sampled at a temperature $T_0$. We use mean-field theory to fully characterize the influence of the reference temperature $T_0$, and we mainly study the case of a fixed, low-$T_0$ value in computer simulations. We numerically investigate the extended phase diagram in the $(\epsilon,T)$ plane of model glass-forming liquids in spatial dimensions $d=2$ and $d=3$, relying on umbrella sampling and reweighting techniques. For both $2d$ and $3d$ cases, a similar phenomenology with nontrivial thermodynamic fluctuations of the overlap is observed at low temperatures, but a detailed finite-size analysis reveals qualitatively distinct behaviors. We establish the existence of a first-order transition line for nonzero $\epsilon$ ending in a critical point in the universality class of the random-field Ising model (RFIM) in $d=3$. In $d=2$ instead, no phase transition is found in large enough systems at least down to temperatures below the extrapolated calorimetric glass transition temperature $T_g$. Our results confirm that glass-forming liquid samples of limited size display the thermodynamic fluctuations expected for finite systems undergoing a random first-order transition. They also support the relevance of the physics of the RFIM for supercooled liquids, which may then explain the qualitative difference between $2d$ and $3d$ glass-formers.

  18 citations

• An invitation to the principal series

  Tarek Anous, Jim Skulte

  SciPost Phys. 9, 028 (2020) · published 1 September 2020 | Toggle abstract · pdf

  Scalar unitary representations of the isometry group of $d$-dimensional de Sitter space $SO(1,d)$ are labeled by their conformal weights $\Delta$. A salient feature of de Sitter space is that scalar fields with sufficiently large mass compared to the de Sitter scale $1/\ell$ have complex conformal weights, and physical modes of these fields fall into the unitary continuous principal series representation of $SO(1,d)$. Our goal is to study these representations in $d=2$, where the relevant group is $SL(2,\mathbb{R})$. We show that the generators of the isometry group of dS$_2$ acting on a massive scalar field reproduce the quantum mechanical model introduced by de Alfaro, Fubini and Furlan (DFF) in the early/late time limit. Motivated by the ambient dS$_2$ construction, we review in detail how the DFF model must be altered in order to accommodate the principal series representation. We point out a difficulty in writing down a classical Lagrangian for this model, whereas the canonical Hamiltonian formulation avoids any problem. We speculate on the meaning of the various de Sitter invariant vacua from the point of view of this toy model and discuss some potential generalizations.

  18 citations

• Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters

  Jonas Richter, Tjark Heitmann, Robin Steinigeweg

  SciPost Phys. 9, 031 (2020) · published 3 September 2020 | Toggle abstract · pdf

  We study quantum quenches in the transverse-field Ising model defined on different lattice geometries such as chains, two- and three-leg ladders, and two-dimensional square lattices. Starting from fully polarized initial states, we consider the dynamics of the transverse and the longitudinal magnetization for quenches to weak, strong, and critical values of the transverse field. To this end, we rely on an efficient combination of numerical linked cluster expansions (NLCEs) and a forward propagation of pure states in real time. As a main result, we demonstrate that NLCEs comprising solely rectangular clusters provide a promising approach to study the real-time dynamics of two-dimensional quantum many-body systems directly in the thermodynamic limit. By comparing to existing data from the literature, we unveil that NLCEs yield converged results on time scales which are competitive to other state-of-the-art numerical methods.

  18 citations

• Gapless chiral spin liquid from coupled chains on the kagome lattice

  Rodrigo G. Pereira, Samuel Bieri

  SciPost Phys. 4, 004 (2018) · published 24 January 2018 | Toggle abstract · pdf

  Using a perturbative renormalization group approach, we show that the extended ($J_1$-$J_2$-$J_d$) Heisenberg model on the kagome lattice with a staggered chiral interaction ($J_\chi$) can exhibit a gapless chiral quantum spin liquid phase. Within a coupled-chains construction, this phase can be understood as a chiral sliding Luttinger liquid with algebraic decay of spin correlations along the chain directions. We calculate the low-energy properties of this gapless chiral spin liquid using the effective field theory and show that they are compatible with the predictions from parton mean-field theories with symmetry-protected line Fermi surfaces. These results may be relevant to the state observed in the kapellasite material.

  18 citations

• Adaptive numerical solution of Kadanoff-Baym equations

  Francisco Meirinhos, Michael Kajan, Johann Kroha, Tim Bode

  SciPost Phys. Core 5, 030 (2022) · published 27 May 2022 | Toggle abstract · pdf

  A time-stepping scheme with adaptivity in both the step size and the integration order is presented in the context of non-equilibrium dynamics described via Kadanoff-Baym equations. The accuracy and effectiveness of the algorithm are analysed by obtaining numerical solutions of exactly solvable models. We find a significant reduction in the number of time-steps compared to fixed-step methods. Due to the at least quadratic scaling of Kadanoff-Baym equations, reducing the amount of steps can dramatically increase the accessible integration time, opening the door for the study of long-time dynamics in interacting systems. A selection of illustrative examples is provided, among them interacting and open quantum systems as well as classical stochastic processes. An open-source implementation of our algorithm in the scientific-computing language Julia is made available.

  18 citations

• Quantum robustness and phase transitions of the 3D Toric Code in a field

  David A. Reiss, Kai Phillip Schmidt

  SciPost Phys. 6, 078 (2019) · published 27 June 2019 | Toggle abstract · pdf

  We study the robustness of 3D intrinsic topogical order under external perturbations by investigating the paradigmatic microscopic model, the 3D toric code in an external magnetic field. Exact dualities as well as variational calculations reveal a ground-state phase diagram with first and second-order quantum phase transitions. The variational approach can be applied without further approximations only for certain field directions. In the general field case, an approximative scheme based on an expansion of the variational energy in orders of the variational parameters is developed. For the breakdown of the 3D intrinsic topological order, it is found that the (im-)mobility of the quasiparticle excitations is crucial in contrast to their fractional statistics.

  18 citations

• Introduction to quantum error correction and fault tolerance

  Steven M. Girvin

  SciPost Phys. Lect. Notes 70 (2023) · published 12 June 2023 | Toggle abstract · pdf

  These lecture notes from the 2019 Les Houches Summer School on "Quantum Information Machines" are intended to provide an introduction to classical and quantum error correction with bits and qubits, and with continuous variable systems (harmonic oscillators). The focus on the latter will be on practical examples that can be realized today or in the near future with a modular architecture based on superconducting electrical circuits and microwave photons. The goal and vision is "hardware-efficient" quantum error correction that does not require exponentially large hardware overhead in order to achieve practical and useful levels of fault tolerance and circuit depth.

  18 citations

• Logarithmic, noise-induced dynamics in the Anderson insulator

  Talía L. M. Lezama, Yevgeny Bar Lev

  SciPost Phys. 12, 174 (2022) · published 25 May 2022 | Toggle abstract · pdf

  We study the dynamical behavior of the one-dimensional Anderson insulator in the presence of a local noise. We show that the noise induces logarithmically slow energy and entanglement growth, until the system reaches an infinite-temperature state, where both quantities saturate to extensive values. The saturation value of the entanglement entropy approaches the average entanglement entropy over all possible product states. At infinite temperature, we find that a density excitation spreads logarithmically with time, without any signs of asymptotic diffusive behavior. In addition, we provide a theoretical picture which qualitatively reproduces the phenomenology of particle transport.

  18 citations

• Entanglement entropy from entanglement contour: higher dimensions

  Muxin Han, Qiang Wen

  SciPost Phys. Core 5, 020 (2022) · published 12 April 2022 | Toggle abstract · pdf

  We study the entanglement contour and partial entanglement entropy (PEE) in quantum field theories in 3 and higher dimensions. The entanglement entropy is evaluated from a certain limit of the PEE with a geometric regulator. In the context of the entanglement contour, we classify the geometric regulators, study their difference from the UV regulators. Furthermore, for spherical regions in conformal field theories (CFTs) we find the exact relation between the UV and geometric cutoff, which clarifies some subtle points in the previous literature. We clarify a subtle point of the additive linear combination (ALC) proposal for PEE in higher dimensions. The subset entanglement entropies in the ALC proposal should all be evaluated as a limit of the PEE while excluding a fixed class of local-short-distance correlation. Unlike the 2-dimensional configurations, naively plugging the entanglement entropy calculated with a UV cutoff will spoil the validity of the ALC proposal. We derive the entanglement contour function for spherical regions, annuli and spherical shells in the vacuum state of general-dimensional CFTs on a hyperplane.

  18 citations