Publications

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• On quantum separation of variables beyond fundamental representations

  Jean Michel Maillet, Giuliano Niccoli

  SciPost Phys. 10, 026 (2021) · published 4 February 2021 | Toggle abstract · pdf

  We describe the extension, beyond fundamental representations of the Yang-Baxter algebra, of our new construction of separation of variables bases for quantum integrable lattice models. The key idea underlying our approach is to use the commuting conserved charges of the quantum integrable models to generate bases in which their spectral problem is separated, i.e. in which the wave functions are factorized in terms of specific solutions of a functional equation. For the so-called "non-fundamental" models we construct two different types of SoV bases. The first is given from the fundamental quantum Lax operator having isomorphic auxiliary and quantum spaces and that can be obtained by fusion of the original quantum Lax operator. The construction essentially follows the one we used previously for fundamental models and allows us to derive the simplicity and diagonalizability of the transfer matrix spectrum. Then, starting from the original quantum Lax operator and using the full tower of the fused transfer matrices, we introduce a second type of SoV bases for which the proof of the separation of the transfer matrix spectrum is naturally derived. We show that, under some special choice, this second type of SoV bases coincides with the one associated to Sklyanin's approach. Moreover, we derive the finite difference type (quantum spectral curve) functional equation and the set of its solutions defining the complete transfer matrix spectrum. This is explicitly implemented for the integrable quantum models associated to the higher spin representations of the general quasi-periodic Y(gl2) Yang-Baxter algebra. Our SoV approach also leads to the construction of a Q-operator in terms of the fused transfer matrices. Finally, we show that the Q-operator family can be equivalently used as the family of commuting conserved charges enabling to construct our SoV bases.

  6 citations

• Shape of a sound wave in a weakly-perturbed Bose gas

  Oleksandr V. Marchukov, Artem G. Volosniev

  SciPost Phys. 10, 025 (2021) · published 3 February 2021 | Toggle abstract · pdf

  We employ the Gross-Pitaevskii equation to study acoustic emission generated in a uniform Bose gas by a static impurity. The impurity excites a sound-wave packet, which propagates through the gas. We calculate the shape of this wave packet in the limit of long wave lengths, and argue that it is possible to extract properties of the impurity by observing this shape. We illustrate here this possibility for a Bose gas with a trapped impurity atom -- an example of a relevant experimental setup. Presented results are general for all one-dimensional systems described by the nonlinear Schr\"odinger equation and can also be used in nonatomic systems, e.g., to analyze light propagation in nonlinear optical media. Finally, we calculate the shape of the sound-wave packet for a three-dimensional Bose gas assuming a spherically symmetric perturbation.

  3 citations

• $T\bar T$ and the mirage of a bulk cutoff

  Monica Guica, Ruben Monten

  SciPost Phys. 10, 024 (2021) · published 1 February 2021 | Toggle abstract · pdf

  We use the variational principle approach to derive the large $N$ holographic dictionary for two-dimensional $T\bar T$-deformed CFTs, for both signs of the deformation parameter. The resulting dual gravitational theory has mixed boundary conditions for the non-dynamical graviton; the boundary conditions for matter fields are undeformed. When the matter fields are turned off and the deformation parameter is negative, the mixed boundary conditions for the metric at infinity can be reinterpreted on-shell as Dirichlet boundary conditions at finite bulk radius, in agreement with a previous proposal by McGough, Mezei and Verlinde. The holographic stress tensor of the deformed CFT is fixed by the variational principle, and in pure gravity it coincides with the Brown-York stress tensor on the radial bulk slice with a particular cosmological constant counterterm contribution. In presence of matter fields, the connection between the mixed boundary conditions and the radial "bulk cutoff" is lost. Only the former correctly reproduce the energy of the bulk configuration, as expected from the fact that a universal formula for the deformed energy can only depend on the universal asymptotics of the bulk solution, rather than the details of its interior. The asymptotic symmetry group associated with the mixed boundary conditions consists of two commuting copies of a state-dependent Virasoro algebra, with the same central extension as in the original CFT.

  81 citations

• Improved neural network Monte Carlo simulation

  I-Kai Chen, Matthew D. Klimek, Maxim Perelstein

  SciPost Phys. 10, 023 (2021) · published 29 January 2021 | Toggle abstract · pdf

  The algorithm for Monte Carlo simulation of parton-level events based on an Artificial Neural Network (ANN) proposed in arXiv:1810.11509 is used to perform a simulation of $H\to 4\ell$ decay. Improvements in the training algorithm have been implemented to avoid numerical instabilities. The integrated decay width evaluated by the ANN is within 0.7% of the true value and unweighting efficiency of 26% is reached. While the ANN is not automatically bijective between input and output spaces, which can lead to issues with simulation quality, we argue that the training procedure naturally prefers bijective maps, and demonstrate that the trained ANN is bijective to a very good approximation.

  29 citations

• Symmetries of the black hole interior and singularity regularization

  Marc Geiller, Etera R. Livine, Francesco Sartini

  SciPost Phys. 10, 022 (2021) · published 29 January 2021 | Toggle abstract · pdf

  We reveal an $\mathfrak{iso}(2,1)$ Poincar\'e algebra of conserved charges associated with the dynamics of the interior of black holes. The action of these Noether charges integrates to a symmetry of the gravitational system under the Poincar\'e group ISO$(2,1)$, which allows to describe the evolution of the geometry inside the black hole in terms of geodesics and horocycles of AdS${}_2$. At the Lagrangian level, this symmetry corresponds to M\"obius transformations of the proper time together with translations. Remarkably, this is a physical symmetry changing the state of the system, which also naturally forms a subgroup of the much larger $\textrm{BMS}_{3}=\textrm{Diff}(S^1)\ltimes\textrm{Vect}(S^1)$ group, where $S^1$ is the compactified time axis. It is intriguing to discover this structure for the black hole interior, and this hints at a fundamental role of BMS symmetry for black hole physics. The existence of this symmetry provides a powerful criterion to discriminate between different regularization and quantization schemes. Following loop quantum cosmology, we identify a regularized set of variables and Hamiltonian for the black hole interior, which allows to resolve the singularity in a black-to-white hole transition while preserving the Poincar\'e symmetry on phase space. This unravels new aspects of symmetry for black holes, and opens the way towards a rigorous group quantization of the interior.

  21 citations

• Logarithmic CFT at generic central charge: from Liouville theory to the $Q$-state Potts model

  Rongvoram Nivesvivat, Sylvain Ribault

  SciPost Phys. 10, 021 (2021) · published 29 January 2021 | Toggle abstract · pdf

  Using derivatives of primary fields (null or not) with respect to the conformal dimension, we build infinite families of non-trivial logarithmic representations of the conformal algebra at generic central charge, with Jordan blocks of dimension $2$ or $3$. Each representation comes with one free parameter, which takes fixed values under assumptions on the existence of degenerate fields. This parameter can be viewed as a simpler, normalization-independent redefinition of the logarithmic coupling. We compute the corresponding non-chiral conformal blocks, and show that they appear in limits of Liouville theory four-point functions. As an application, we describe the logarithmic structures of the critical two-dimensional $O(n)$ and $Q$-state Potts models at generic central charge. The validity of our description is demonstrated by semi-analytically bootstrapping four-point connectivities in the $Q$-state Potts model to arbitrary precision. Moreover, we provide numerical evidence for the Delfino--Viti conjecture for the three-point connectivity. Our results hold for generic values of $Q$ in the complex plane and beyond.

  22 citations

• Hidden symmetries, the Bianchi classification and geodesics of the quantum geometric ground-state manifolds

  Diego Liska, Vladimir Gritsev

  SciPost Phys. 10, 020 (2021) · published 28 January 2021 | Toggle abstract · pdf

  We study the Killing vectors of the quantum ground-state manifold of a parameter-dependent Hamiltonian. We find that the manifold may have symmetries that are not visible at the level of the Hamiltonian and that different quantum phases of matter exhibit different symmetries. We propose a Bianchi-based classification of the various ground-state manifolds using the Lie algebra of the Killing vector fields. Moreover, we explain how to exploit these symmetries to find geodesics and explore their behaviour when crossing critical lines. We briefly discuss the relation between geodesics, energy fluctuations and adiabatic preparation protocols. Our primary example is the anisotropic transverse-field Ising model. We also analyze the Ising limit and find analytic solutions to the geodesic equations for both cases.

  4 citations

• Finite-temperature symmetric tensor network for spin-1/2 Heisenberg antiferromagnets on the square lattice

  Didier Poilblanc, Matthieu Mambrini, Fabien Alet

  SciPost Phys. 10, 019 (2021) · published 28 January 2021 | Toggle abstract · pdf

  Within the tensor network framework, the (positive) thermal density operator can be approximated by a double layer of infinite Projected Entangled Pair Operator (iPEPO) coupled via ancilla degrees of freedom. To investigate the thermal properties of the spin-1/2 Heisenberg model on the square lattice, we introduce a family of fully spin-$SU(2)$ and lattice-$C_{4v}$ symmetric on-site tensors (of bond dimensions $D=4$ or $D=7$) and a plaquette-based Trotter-Suzuki decomposition of the imaginary-time evolution operator. A variational optimization is performed on the plaquettes, using a full (for $D=4$) or simple (for $D=7$) environment obtained from the single-site Corner Transfer Matrix Renormalization Group fixed point. The method is benchmarked by a comparison to quantum Monte Carlo in the thermodynamic limit. Although the iPEPO spin correlation length starts to deviate from the exact exponential growth for inverse-temperature $\beta \gtrsim 2$, the behavior of various observables turns out to be quite accurate once plotted w.r.t the inverse correlation length. We also find that a direct $T=0$ variational energy optimization provides results in full agreement with the $\beta\rightarrow\infty$ limit of finite-temperature data, hence validating the imaginary-time evolution procedure. Extension of the method to frustrated models is described and preliminary results are shown.

  14 citations

• Counting D1-D5-P microstates in supergravity

  Daniel R. Mayerson, Masaki Shigemori

  SciPost Phys. 10, 018 (2021) · published 27 January 2021 | Toggle abstract · pdf

  We quantize the D1-D5-P microstate geometries known as superstrata directly in supergravity. We use Rychkov's consistency condition [hep-th/0512053] which was derived for the D1-D5 system; for superstrata, this condition turns out to be strong enough to fix the symplectic form uniquely. For the $(1,0,n)$ superstrata, we further confirm this quantization by a bona-fide explicit computation of the symplectic form using the semi-classical covariant quantization method in supergravity. We use the resulting quantizations to count the known supergravity superstrata states, finding agreement with previous countings that the number of these states grows parametrically smaller than those of the corresponding black hole.

  12 citations

• Approaching the Tsirelson bound with a Sagnac source of polarization-entangled photons

  Sandra Meraner, Robert J. Chapman, Stefan Frick, Robert Keil, Maximilian Prilmüller, Gregor Weihs

  SciPost Phys. 10, 017 (2021) · published 26 January 2021 | Toggle abstract · pdf

  High-fidelity polarization-entangled photons are a powerful resource for quantum communication, distributing entanglement and quantum teleportation. The Bell-CHSH inequality $S\leq2$ is violated by bipartite entanglement and only maximally entangled states can achieve $S=2\sqrt{2}$, the Tsirelson bound. Spontaneous parametric down-conversion sources can produce entangled photons with correlations close to the Tsirelson bound. Sagnac configurations offer intrinsic stability, compact footprint and high collection efficiency, however, there is often a trade off between source brightness and entanglement visibility. Here, we present a Sagnac polarization-entangled source with $2\sqrt{2}-S=(5.65\pm0.57\times10^{-3})$, on-par with the highest $S$ parameters recorded, while generating and detecting $(4660\pm70)pairs/s/mW$, which is a substantially higher brightness than previously reported for Sagnac sources and around two orders of magnitude brighter than for traditional cone sources with the highest $S$ parameters. Our source records $0.9953\pm0.0003$ concurrence and $0.99743\pm0.00014$ fidelity to an ideal Bell state. By studying systematic errors in Sagnac sources, we identify that the precision of the collection focal point inside the crystal plays the largest role in reducing the $S$ parameter in our experiment. We provide a pathway that could enable the highest $S$ parameter recorded with a Sagnac source to-date while maintaining very high brightness.

  7 citations