Publications

Order by: publication date number of citations

• Studying dynamics in two-dimensional quantum lattices using tree tensor network states

  Benedikt Kloss, David R. Reichman, Yevgeny Bar Lev

  SciPost Phys. 9, 070 (2020) · published 11 November 2020 | Toggle abstract · pdf

  We analyze and discuss convergence properties of a numerically exact algorithm tailored to study the dynamics of interacting two-dimensional lattice systems. The method is based on the application of the time-dependent variational principle in a manifold of binary and quaternary Tree Tensor Network States. The approach is found to be competitive with existing matrix product state approaches. We discuss issues related to the convergence of the method, which could be relevant to a broader set of numerical techniques used for the study of two-dimensional systems.

  25 citations

• Quantum phases and transitions in spin chains with non-invertible symmetries

  Arkya Chatterjee, Ömer M. Aksoy, Xiao-Gang Wen

  SciPost Phys. 17, 115 (2024) · published 16 October 2024 | Toggle abstract · pdf

  Generalized symmetries often appear in the form of emergent symmetries in low energy effective descriptions of quantum many-body systems. Non-invertible symmetries are a particularly exotic class of generalized symmetries, in that they are implemented by transformations that do not form a group. Such symmetries appear in large families of gapless states of quantum matter and constrain their low-energy dynamics. To provide a UV-complete description of such symmetries, it is useful to construct lattice models that respect these symmetries exactly. In this paper, we discuss two families of one-dimensional lattice Hamiltonians with finite on-site Hilbert spaces: one with (invertible) $S_3$ symmetry and the other with non-invertible $\mathsf{Rep}(S_3)$ symmetry. Our models are largely analytically tractable and demonstrate all possible spontaneous symmetry breaking patterns of these symmetries. Moreover, we use numerical techniques to study the nature of continuous phase transitions between the different symmetry-breaking gapped phases associated with both symmetries. Both models have self-dual lines, where the models are enriched by so-called intrinsically non-invertible symmetries generated by Kramers-Wannier-like duality transformations. We provide explicit lattice operators that generate these non-invertible self-duality symmetries. We show that the enhanced symmetry at the self-dual lines is described by a 2+1d symmetry-topological-order (SymTO) of type $JK_4\boxtimes \overline{JK}_4$. The condensable algebras of the SymTO determine the allowed gapped and gapless states of the self-dual $S_3$-symmetric and $\mathsf{Rep}(S_3)$-symmetric models.

  25 citations

• Bootstrapping MN and tetragonal CFTs in three dimensions

  Andreas Stergiou

  SciPost Phys. 7, 010 (2019) · published 17 July 2019 | Toggle abstract · pdf

  Conformal field theories (CFTs) with MN and tetragonal global symmetry in $d=2+1$ dimensions are relevant for structural, antiferromagnetic and helimagnetic phase transitions. As a result, they have been studied in great detail with the $\varepsilon=4-d$ expansion and other field theory methods. The study of these theories with the nonperturbative numerical conformal bootstrap is initiated in this work. Bounds for operator dimensions are obtained and they are found to possess sharp kinks in the MN case, suggesting the existence of full-fledged CFTs. Based on the existence of a certain large-$N$ expansion in theories with MN symmetry, these are argued to be the CFTs predicted by the $\varepsilon$ expansion. In the tetragonal case no new kinks are found, consistently with the absence of such CFTs in the $\varepsilon$ expansion. Estimates for critical exponents are provided for a few cases describing phase transitions in actual physical systems. In two particular MN cases, corresponding to theories with global symmetry groups $O(2)^2\rtimes S_2$ and $O(2)^3\rtimes S_3$, a second kink is found. In the $O(2)^2\rtimes S_2$ case it is argued to be saturated by a CFT that belongs to a new universality class relevant for the structural phase transition of NbO$_2$ and paramagnetic-helimagnetic transitions of the rare-earth metals Ho and Dy. In the $O(2)^3\rtimes S_3$ case it is suggested that the CFT that saturates the second kink belongs to a new universality class relevant for the paramagnetic-antiferromagnetic phase transition of the rare-earth metal Nd.

  25 citations

• Ruling out light axions: The writing is on the wall

  Konstantin A. Beyer, Subir Sarkar

  SciPost Phys. 15, 003 (2023) · published 10 July 2023 | Toggle abstract · pdf

  We revisit the domain wall problem for QCD axion models with more than one quark charged under the Peccei-Quinn symmetry. Symmetry breaking during or after inflation results in the formation of a domain wall network which would cause cosmic catastrophe if it comes to dominate the Universe. The network may be made unstable by invoking a "tilt" in the axion potential due to Planck scale suppressed non-renormalisable operators. Alternatively the random walk of the axion field during inflation can generate a "bias" favouring one of the degenerate vacua, but we find that this mechanism is in practice irrelevant. Consideration of the axion abundance generated by the decay of the wall network then requires the Peccei-Quinn scale to be rather low - thus e.g. ruling out the DFSZ axion with mass below $\sim$ 11 meV, where most experimental searches are in fact focused.

  25 citations

• Genuine multipartite entanglement in time

  Simon Milz, Cornelia Spee, Zhen-Peng Xu, Felix A. Pollock, Kavan Modi, Otfried Gühne

  SciPost Phys. 10, 141 (2021) · published 11 June 2021 | Toggle abstract · pdf

  While spatial quantum correlations have been studied in great detail, much less is known about the genuine quantum correlations that can be exhibited by temporal processes. Employing the quantum comb formalism, processes in time can be mapped onto quantum states, with the crucial difference that temporal correlations have to satisfy causal ordering, while their spatial counterpart is not constrained in the same way. Here, we exploit this equivalence and use the tools of multipartite entanglement theory to provide a comprehensive picture of the structure of correlations that (causally ordered) temporal quantum processes can display. First, focusing on the case of a process that is probed at two points in time -- which can equivalently be described by a tripartite quantum state -- we provide necessary as well as sufficient conditions for the presence of bipartite entanglement in different splittings. Next, we connect these scenarios to the previously studied concepts of quantum memory, entanglement breaking superchannels, and quantum steering, thus providing both a physical interpretation for entanglement in temporal quantum processes, and a determination of the resources required for its creation. Additionally, we construct explicit examples of W-type and GHZ-type genuinely multipartite entangled two-time processes and prove that genuine multipartite entanglement in temporal processes can be an emergent phenomenon. Finally, we show that genuinely entangled processes across multiple times exist for any number of probing times.

  25 citations

• $q$th-root non-Hermitian Floquet topological insulators

  Longwen Zhou, Raditya Weda Bomantara, Shenlin Wu

  SciPost Phys. 13, 015 (2022) · published 8 August 2022 | Toggle abstract · pdf

  Floquet phases of matter have attracted great attention due to their dynamical and topological nature that are unique to nonequilibrium settings. In this work, we introduce a generic way of taking any integer $q$th-root of the evolution operator $U$ that describes Floquet topological matter. We further apply our $q$th-rooting procedure to obtain $2^n$th- and $3^n$th-root first- and second-order non-Hermitian Floquet topological insulators (FTIs). There, we explicitly demonstrate the presence of multiple edge and corner modes at fractional quasienergies $±(0, 1,...2^n)π/2^n$ and $±(0, 1,..., 3^n)π/3^n$, whose numbers are highly controllable and capturable by the topological invariants of their parent systems. Notably, we observe non-Hermiticity induced fractional-quasienergy corner modes and the coexistence of non-Hermitian skin effect with fractional-quasienergy edge states. Our findings thus establish a framework of constructing an intriguing class of topological matter in Floquet open systems.

  25 citations

• $\nu$-flows: Conditional neutrino regression

  Matthew Leigh, John Andrew Raine, Knut Zoch, Tobias Golling

  SciPost Phys. 14, 159 (2023) · published 16 June 2023 | Toggle abstract · pdf

  We present $\nu$-Flows, a novel method for restricting the likelihood space of neutrino kinematics in high-energy collider experiments using conditional normalising flows and deep invertible neural networks. This method allows the recovery of the full neutrino momentum which is usually left as a free parameter and permits one to sample neutrino values under a learned conditional likelihood given event observations. We demonstrate the success of $\nu$-Flows in a case study by applying it to simulated semileptonic $t\bar{t}$ events and show that it can lead to more accurate momentum reconstruction, particularly of the longitudinal coordinate. We also show that this has direct benefits in a downstream task of jet association, leading to an improvement of up to a factor of 1.41 compared to conventional methods.

  25 citations

• Euler-scale dynamical correlations in integrable systems with fluid motion

  Frederik S. Møller, Gabriele Perfetto, Benjamin Doyon, Jörg Schmiedmayer

  SciPost Phys. Core 3, 016 (2020) · published 22 December 2020 | Toggle abstract · pdf

  We devise an iterative scheme for numerically calculating dynamical two-point correlation functions in integrable many-body systems, in the Eulerian scaling limit. Expressions for these were originally derived in Ref. [1] by combining the fluctuation-dissipation principle with generalized hydrodynamics. Crucially, the scheme is able to address non-stationary, inhomogeneous situations, when motion occurs at the Euler-scale of hydrodynamics. In such situations, in interacting systems, the simple correlations due to fluid modes propagating with the flow receive subtle corrections, which we test. Using our scheme, we study the spreading of correlations in several integrable models from inhomogeneous initial states. For the classical hard-rod model we compare our results with Monte-Carlo simulations and observe excellent agreement at long time-scales, thus providing the first demonstration of validity for the expressions derived in Ref. [1]. We also observe the onset of the Euler-scale limit for the dynamical correlations.

  25 citations

• On the Euclidean action of de Sitter black holes and constrained instantons

  Edward K. Morvan, Jan Pieter van der Schaar, Manus R. Visser

  SciPost Phys. 14, 022 (2023) · published 23 February 2023 | Toggle abstract · pdf

  We compute the on-shell Euclidean action of Schwarzschild-de Sitter black holes, and take their contributions in the gravitational path integral into account using the formalism of constrained instantons. Although Euclidean de Sitter black hole geometries have conical singularities for generic masses, their on-shell action is finite and is shown to be independent of the Euclidean time periodicity and equal to minus the sum of the black hole and cosmological horizon entropy. We apply this result to compute the probability for a nonrotating, neutral arbitrary mass black hole to nucleate spontaneously in empty de Sitter space, which separates into a constant and a "non-perturbative" contribution, the latter corresponding to the proper saddle-point instanton in the Nariai limit. We also speculate on some further applications of our results, most notably as potential non-perturbative corrections to correlators in the de Sitter vacuum.

  25 citations

• Unsupervised and supervised learning of interacting topological phases from single-particle correlation functions

  Simone Tibaldi, Giuseppe Magnifico, Davide Vodola, Elisa Ercolessi

  SciPost Phys. 14, 005 (2023) · published 19 January 2023 | Toggle abstract · pdf

  The recent advances in machine learning algorithms have boosted the application of these techniques to the field of condensed matter physics, in order e.g. to classify the phases of matter at equilibrium or to predict the real-time dynamics of a large class of physical models. Typically in these works, a machine learning algorithm is trained and tested on data coming from the same physical model. Here we demonstrate that unsupervised and supervised machine learning techniques are able to predict phases of a non-exactly solvable model when trained on data of a solvable model. In particular, we employ a training set made by single-particle correlation functions of a non-interacting quantum wire and by using principal component analysis, k-means clustering, t-distributed stochastic neighbor embedding and convolutional neural networks we reconstruct the phase diagram of an interacting superconductor. We show that both the principal component analysis and the convolutional neural networks trained on the data of the non-interacting model can identify the topological phases of the interacting model. Our findings indicate that non-trivial phases of matter emerging from the presence of interactions can be identified by means of unsupervised and supervised techniques applied to data of non-interacting systems.

  25 citations