Publications

Order by: publication date number of citations

• Navigating through the O(N) archipelago

  Benoit Sirois

  SciPost Phys. 13, 081 (2022) · published 4 October 2022 | Toggle abstract · pdf

  A novel method for finding allowed regions in the space of CFT-data, coined navigator method, was recently proposed in arXiv:2104.09518. Its efficacy was demonstrated in the simplest example possible, i.e. that of the mixed-correlator study of the 3D Ising Model. In this paper, we would like to show that the navigator method may also be applied to the study of the family of $d$-dimensional $O(N)$ models. We will aim to follow these models in the $(d,N)$ plane. We will see that the "sailing" from island to island can be understood in the context of the navigator as a parametric optimization problem, and we will exploit this fact to implement a simple and effective path-following algorithm. By sailing with the navigator through the $(d,N)$ plane, we will provide estimates of the scaling dimensions $(\Delta_{\phi},\Delta_{s},\Delta_{t})$ in the entire range $(d,N) \in [3,4] \times [1,3]$. We will show that to our level of precision, we cannot see the non-unitary nature of the $O(N)$ models due to the fractional values of $d$ or $N$ in this range. We will also study the limit $N \xrightarrow[]{} 1$, and see that we cannot find any solution to the unitary mixed-correlator crossing equations below $N=1$.

  8 citations

• Integrability of open boundary driven quantum circuits

  Chiara Paletta, Tomaž Prosen

  SciPost Phys. 18, 027 (2025) · published 22 January 2025 | Toggle abstract · pdf

  In this paper, we address the problem of Yang-Baxter integrability of doubled quantum circuit of qubits (spins 1/2) with open boundary conditions where the two circuit replicas are only coupled at the left or right boundary. We investigate the cases where the bulk is given by elementary six vertex unitary gates of either the free fermionic XX type or interacting XXZ type. By using the Sklyanin's construction of reflection algebra, we obtain the most general solutions of the boundary Yang-Baxter equation for such a setup. We use this solution to build, from the transfer matrix formalism, integrable circuits with two step discrete time Floquet (aka brickwork) dynamics. We prove that, only if the bulk is a free-model, the boundary matrices are in general non-factorizable, and for particular choice of free parameters yield non-trivial unitary dynamics with boundary interaction between the two chains. Then, we consider the limit of continuous time evolution and we give the interpretation of a restricted set of the boundary terms in the Lindbladian setting. Specifically, for a particular choice of free parameters, the solutions correspond to an open quantum system dynamics with the source terms representing injecting or removing particles from the boundary of the spin chain.

  8 citations

• Correlation functions by separation of variables: the XXX spin chain

  Giuliano Niccoli, Hai Pei, Véronique Terras

  SciPost Phys. 10, 006 (2021) · published 12 January 2021 | Toggle abstract · pdf

  We explain how to compute correlation functions at zero temperature within the framework of the quantum version of the Separation of Variables (SoV) in the case of a simple model: the XXX Heisenberg chain of spin 1/2 with twisted (quasi-periodic) boundary conditions. We first detail all steps of our method in the case of anti-periodic boundary conditions. The model can be solved in the SoV framework by introducing inhomogeneity parameters. The action of local operators on the eigenstates are then naturally expressed in terms of multiple sums over these inhomogeneity parameters. We explain how to transform these sums over inhomogeneity parameters into multiple contour integrals. Evaluating these multiple integrals by the residues of the poles outside the integration contours, we rewrite this action as a sum involving the roots of the Baxter polynomial plus a contribution of the poles at infinity. We show that the contribution of the poles at infinity vanishes in the thermodynamic limit, and that we recover in this limit for the zero-temperature correlation functions the multiple integral representation that had been previously obtained through the study of the periodic case by Bethe Ansatz or through the study of the infinite volume model by the q-vertex operator approach. We finally show that the method can easily be generalized to the case of a more general non-diagonal twist: the corresponding weights of the different terms for the correlation functions in finite volume are then modified, but we recover in the thermodynamic limit the same multiple integral representation than in the periodic or anti-periodic case, hence proving the independence of the thermodynamic limit of the correlation functions with respect to the particular form of the boundary twist.

  8 citations

• Non-parametric learning critical behavior in Ising partition functions: PCA entropy and intrinsic dimension

  Rajat K. Panda, Roberto Verdel, Alex Rodriguez, Hanlin Sun, Ginestra Bianconi, Marcello Dalmonte

  SciPost Phys. Core 6, 086 (2023) · published 14 December 2023 | Toggle abstract · pdf

  We provide and critically analyze a framework to learn critical behavior in classical partition functions through the application of non-parametric methods to data sets of thermal configurations. We illustrate our approach in phase transitions in 2D and 3D Ising models. First, we extend previous studies on the intrinsic dimension of 2D partition function data sets, by exploring the effect of volume in 3D Ising data. We find that as opposed to 2D systems for which this quantity has been successfully used in unsupervised characterizations of critical phenomena, in the 3D case its estimation is far more challenging. To circumvent this limitation, we then use the principal component analysis (PCA) entropy, a "Shannon entropy" of the normalized spectrum of the covariance matrix. We find a striking qualitative similarity to the thermodynamic entropy, which the PCA entropy approaches asymptotically. The latter allows us to extract-through a conventional finite-size scaling analysis with modest lattice sizes-the critical temperature with less than 1% error for both 2D and 3D models while being computationally efficient. The PCA entropy can readily be applied to characterize correlations and critical phenomena in a huge variety of many-body problems and suggests a (direct) link between easy-to-compute quantities and entropies.

  8 citations

• Skating on slippery ice

  J. M. J. van Leeuwen

  SciPost Phys. 3, 042 (2017) · published 23 December 2017 | Toggle abstract · pdf

  The friction of a stationary moving skate on smooth ice is investigated, in particular in relation to the formation of a thin layer of water between skate and ice. It is found that the combination of ploughing and sliding gives a friction force that is rather insensitive for parameters such as velocity and temperature. The weak dependence originates from the pressure adjustment inside the water layer. For instance, high velocities, which would give rise to high friction, also lead to large pressures, which, in turn, decrease the contact zone and so lower the friction. The theory is a combination and completion of two existing but conflicting theories on the formation of the water layer.

  8 citations

• Quantum eigenstates from classical Gibbs distributions

  Pieter W. Claeys, Anatoli Polkovnikov

  SciPost Phys. 10, 014 (2021) · published 22 January 2021 | Toggle abstract · pdf

  We discuss how the language of wave functions (state vectors) and associated non-commuting Hermitian operators naturally emerges from classical mechanics by applying the inverse Wigner-Weyl transform to the phase space probability distribution and observables. In this language, the Schr\"odinger equation follows from the Liouville equation, with $\hbar$ now a free parameter. Classical stationary distributions can be represented as sums over stationary states with discrete (quantized) energies, where these states directly correspond to quantum eigenstates. Interestingly, it is now classical mechanics which allows for apparent negative probabilities to occupy eigenstates, dual to the negative probabilities in Wigner's quasiprobability distribution. These negative probabilities are shown to disappear when allowing sufficient uncertainty in the classical distributions. We show that this correspondence is particularly pronounced for canonical Gibbs ensembles, where classical eigenstates satisfy an integral eigenvalue equation that reduces to the Schr\"odinger equation in a saddle-point approximation controlled by the inverse temperature. We illustrate this correspondence by showing that some paradigmatic examples such as tunneling, band structures, Berry phases, Landau levels, level statistics and quantum eigenstates in chaotic potentials can be reproduced to a surprising precision from a classical Gibbs ensemble, without any reference to quantum mechanics and with all parameters (including $\hbar$) on the order of unity.

  8 citations

• Jacobi-Lie T-plurality

  Jose J. Fernandez-Melgarejo, Yuho Sakatani

  SciPost Phys. 11, 038 (2021) · published 23 August 2021 | Toggle abstract · pdf

  We propose a Leibniz algebra, to be called DD$^+$, which is a generalization of the Drinfel'd double. We find that there is a one-to-one correspondence between a DD$^+$ and a Jacobi-Lie bialgebra, extending the known correspondence between a Lie bialgebra and a Drinfel'd double. We then construct generalized frame fields $E_A{}^M\in\text{O}(D,D)\times\mathbb{R}^+$ satisfying the algebra ${\cal L}_{E_A}E_B = - X_{AB}{}^C\,E_C$, where $X_{AB}{}^C$ are the structure constants of the DD$^+$ and ${\cal L}$ is the generalized Lie derivative in double field theory. Using the generalized frame fields, we propose the Jacobi-Lie $T$-plurality and show that it is a symmetry of double field theory. We present several examples of the Jacobi-Lie $T$-plurality with or without Ramond-Ramond fields and the spectator fields.

  8 citations

• High-energy resummation in inclusive hadroproduction of Higgs plus jet

  Francesco Giovanni Celiberto, Dmitry Yu. Ivanov, Mohammed. M. A. Mohammed, Alessandro Papa

  SciPost Phys. Proc. 8, 039 (2022) · published 12 July 2022 | Toggle abstract · pdf

  Using the standard Balitsky-Fadin-Kuraev-Lipatov (BFKL) approach, with partial inclusion of next-to-leading order effects, we propose the inclusive hadroproduction of a Higgs boson and of a jet, featuring large transverse momenta and well separated in rapidity, as a new channel to probe the BFKL dynamics. Predictions are presented for cross-sections and azimuthal angle correlations in different kinematics configurations for the final-state transverse momenta. We find that the large energy scales provided by the emission of a Higgs boson stabilize the BFKL series.

  8 citations

• Integrability and quench dynamics in the spin-1 central spin XX model

  Long-Hin Tang, David M. Long, Anatoli Polkovnikov, Anushya Chandran, Pieter W. Claeys

  SciPost Phys. 15, 030 (2023) · published 26 July 2023 | Toggle abstract · pdf

  Central spin models provide an idealized description of interactions between a central degree of freedom and a mesoscopic environment of surrounding spins. We show that the family of models with a spin-1 at the center and XX interactions of arbitrary strength with surrounding spins is integrable. Specifically, we derive an extensive set of conserved quantities and obtain the exact eigenstates using the Bethe ansatz. As in the homogenous limit, the states divide into two exponentially large classes: bright states, in which the spin-1 is entangled with its surroundings, and dark states, in which it is not. On resonance, the bright states further break up into two classes depending on their weight on states with central spin polarization zero. These classes are probed in quench dynamics wherein they prevent the central spin from reaching thermal equilibrium. In the single spin-flip sector we explicitly construct the bright states and show that the central spin exhibits oscillatory dynamics as a consequence of the semilocalization of these eigenstates. We relate the integrability to the closely related class of integrable Richardson-Gaudin models, and conjecture that the spin-$s$ central spin XX model is integrable for any $s$.

  8 citations

• Evidence of $\phi_0$-Josephson junction from skewed diffraction patterns in Sn-InSb nanowires

  B. Zhang, Z. Li, V. Aguilar, P. Zhang, M. Pendharkar, C. Dempsey, J. S. Lee, S. D. Harrington, S. Tan, J. S. Meyer, M. Houzet, C. J. Palmstrom, S. M. Frolov

  SciPost Phys. 18, 013 (2025) · published 13 January 2025 | Toggle abstract · pdf

  We study Josephson junctions based on InSb nanowires with Sn shells. We observe skewed critical current diffraction patterns: the maxima in forward and reverse current bias are at different magnetic flux, with a displacement of 20-40 mT. The skew is greatest when the external field is nearly perpendicular to the nanowire, in the substrate plane. This orientation suggests that spin-orbit interaction plays a role. We develop a phenomenological model and perform tight-binding calculations, both methods reproducing the essential features of the experiment. The effect modeled is the $\phi_0$-Josephson junction with higher-order Josephson harmonics. The system is of interest for Majorana studies: the effects are either precursor to or concomitant with topological superconductivity. Current-phase relations that lack inversion symmetry can also be used to design quantum circuits with engineered nonlinearity.

  8 citations