Publications

Order by: publication date number of citations

• Scalar products and norm of Bethe vectors for integrable models based on $U_q(\widehat{\mathfrak{gl}}_{n})$

  A. Hutsalyuk, A. Liashyk, S. Z. Pakuliak, E. Ragoucy, N. A. Slavnov

  SciPost Phys. 4, 006 (2018) · published 30 January 2018 | Toggle abstract · pdf

  We obtain recursion formulas for the Bethe vectors of models with periodic boundary conditions solvable by the nested algebraic Bethe ansatz and based on the quantum affine algebra $U_q(\widehat{\mathfrak{gl}}_{n})$. We also present a sum formula for their scalar products. This formula describes the scalar product in terms of a sum over partitions of the Bethe parameters, whose factors are characterized by two highest coefficients. We provide different recursions for these highest coefficients. In addition, we show that when the Bethe vectors are on-shell, their norm takes the form of a Gaudin determinant.

  13 citations

• Active particles driven by competing spatially dependent self-propulsion and external force

  Lorenzo Caprini, Umberto Marini Bettolo Marconi, René Wittmann , Hartmut Löwen

  SciPost Phys. 13, 065 (2022) · published 23 September 2022 | Toggle abstract · pdf

  We investigate how the competing presence of a nonuniform motility landscape and an external confining field affects the properties of active particles. We employ the active Ornstein-Uhlenbeck particle (AOUP) model with a periodic swim-velocity profile to derive analytical approximations for the steady-state probability distribution of position and velocity, encompassing both the Unified Colored Noise Approximation and the theory of potential-free active particles with spatially dependent swim velocity recently developed. We test the theory by confining an active particle in a harmonic trap, which gives rise to interesting properties, such as a transition from a unimodal to a bimodal (and, eventually multimodal) spatial density, induced by decreasing the spatial period of the self propulsion. Correspondingly, the velocity distribution shows pronounced deviations from the Gaussian shape, even displaying a bimodal profile in the high-motility regions. We thus show that the interplay of two relatively simple physical fields can be employed to generate complex emerging behavior.

  13 citations

• Spectral and steady-state properties of fermionic random quadratic Liouvillians

  João Costa, Pedro Ribeiro, Andrea De Luca, Tomaž Prosen, Lucas Sá

  SciPost Phys. 15, 145 (2023) · published 9 October 2023 | Toggle abstract · pdf

  We study spectral and steady-state properties of generic Markovian dissipative systems described by quadratic fermionic Liouvillian operators of the Lindblad form. The Hamiltonian dynamics is modeled by a generic random quadratic operator, i.e., as a featureless superconductor of class D, whereas the Markovian dissipation is described by $M$ random linear jump operators. By varying the dissipation strength and the ratio of dissipative channels per fermion, $m=M/(2N_F)$, we find two distinct phases where the support of the single-particle spectrum has one or two connected components. In the strongly dissipative regime, this transition occurs for $m=1/2$ and is concomitant with a qualitative change in both the steady-state and the spectral gap that rules the large-time dynamics. Above this threshold, the spectral gap and the steady-state purity qualitatively agree with the fully generic (i.e., non-quadratic) case studied recently. Below $m=1/2$, the spectral gap closes in the thermodynamic limit and the steady-state decouples into an ergodic and a nonergodic sector yielding a non-monotonic steady-state purity as a function of the dissipation strength. Our results show that some of the universal features previously observed for fully random Liouvillians are generic for a sufficiently large number of jump operators. On the other hand, if the number of dissipation channels is decreased the system can exhibit nonergodic features, rendering it possible to suppress dissipation in protected subspaces even in the presence of strong system-environment coupling.

  13 citations

• On the quark spectral function in QCD

  Jan Horak, Jan M. Pawlowski, Nicolas Wink

  SciPost Phys. 15, 149 (2023) · published 10 October 2023 | Toggle abstract · pdf

  We calculate the spectral function of light quark flavours in 2+1 flavour vacuum QCD in the isospin-symmetric approximation. We employ spectral Dyson-Schwinger equations and compute the non-perturbative quark propagator directly in real-time, using recent spectral reconstruction results from Gaussian process regression of gluon propagator data in 2+1 flavour lattice QCD. Our results feature a pole-like peak structure at time-like momenta larger than the propagator's gapping scale as well as a negative scattering continuum, which we exploit assuming an analytic pole-tail split during the iterative solution. The computation is augmented with a general discussion of the impact of the quark-gluon vertex and the gluon propagator on the analytic structure of the quark propagator. In particular, we investigate under which conditions the quark propagator shows unphysical complex poles. Our results offer a wide range of applications, encompassing the ab-initio calculation of transport as well as resonance properties in QCD.

  13 citations

• Boundary signature of singularity in the presence of a shock wave

  Gary T. Horowitz, Henry Leung, Leonel Queimada, Ying Zhao

  SciPost Phys. 16, 060 (2024) · published 28 February 2024 | Toggle abstract · pdf

  Matter falling into a Schwarzschild-AdS black hole from the left causes increased focussing of ingoing geodesics from the right, and, as a consequence, they reach the singularity sooner. In a standard Penrose diagram, the singularity "bends down". We show how to detect this feature of the singularity holographically, using a boundary two-point function. We model the matter with a shock wave, and show that this bending down of the singularity can be read off from a novel analytic continuation of the boundary two-point function. Along the way, we obtain a generalization of the recently proposed thermal product formula for two-point correlators.

  13 citations

• Tensor network representations from the geometry of entangled states

  Matthias Christandl, Angelo Lucia, Péter Vrana, Albert H. Werner

  SciPost Phys. 9, 042 (2020) · published 30 September 2020 | Toggle abstract · pdf

  Tensor network states provide successful descriptions of strongly correlated quantum systems with applications ranging from condensed matter physics to cosmology. Any family of tensor network states possesses an underlying entanglement structure given by a graph of maximally entangled states along the edges that identify the indices of the tensors to be contracted. Recently, more general tensor networks have been considered, where the maximally entangled states on edges are replaced by multipartite entangled states on plaquettes. Both the structure of the underlying graph and the dimensionality of the entangled states influence the computational cost of contracting these networks. Using the geometrical properties of entangled states, we provide a method to construct tensor network representations with smaller effective bond dimension. We illustrate our method with the resonating valence bond state on the kagome lattice.

  13 citations

• Many-body open quantum systems

  Rosario Fazio, Jonathan Keeling, Leonardo Mazza, Marco Schirò

  SciPost Phys. Lect. Notes 99 (2025) · published 14 August 2025 | Toggle abstract · pdf

  These lecture notes discuss the recent theoretical advances in the understanding of open quantum many-body physics in platforms where both dissipative and coherent processes can be tuned and controlled to a high degree. We start by reviewing the theoretical frameworks and methods used to describe and tackle open quantum many-body systems. We then discuss the use of dissipative processes to engineer many-body stationary states with desired properties and the emergence of dissipative phase transitions arising out of the competition between coherent evolution and dissipation. We review the dynamics of open quantum many body systems in the presence of correlated many-body dissipative processes, such as heating and many-body losses. Finally we provide a different perspective on open quantum many-body systems by looking at stochastic quantum trajectories, relevant for the case in which the environment represents a monitoring device, and the associated measurement-induced phase transitions.

  13 citations

• Boundary states of three dimensional topological order and the deconfined quantum critical point

  Wenjie Ji, Nathanan Tantivasadakarn, Cenke Xu

  SciPost Phys. 15, 231 (2023) · published 7 December 2023 | Toggle abstract · pdf

  We study the boundary states of the archetypal three dimensional topological order, i.e. the three dimensional $\mathbb{Z}_2$ toric code. There are three distinct elementary types of boundary states that we will consider in this work. In the phase diagram that includes the three elementary boundaries there may exist a multi-critical point, which is captured by the so-called deconfined quantum critical point (DQCP) with an "easy-axis" anisotropy. Moreover, there is an emergent $\mathbb{Z}_{2,d}$ symmetry that swaps two of the boundary types, and it becomes part of the global symmetry of the DQCP. The emergent $\mathbb{Z}_{2,d}$ (where d represents "defect") symmetry on the boundary is originated from a type of surface defect in the bulk. We further find a gapped boundary with a surface topological order that is invariant under the emergent symmetry.

  13 citations

• Many-body chaos near a thermal phase transition

  Alexander Schuckert, Michael Knap

  SciPost Phys. 7, 022 (2019) · published 19 August 2019 | Toggle abstract · pdf

  We study many-body chaos in a (2+1)D relativistic scalar field theory at high temperatures in the classical statistical approximation, which captures the quantum critical regime and the thermal phase transition from an ordered to a disordered phase. We evaluate out-of-time ordered correlation functions (OTOCs) and find that the associated Lyapunov exponent increases linearly with temperature in the quantum critical regime, and approaches the non-interacting limit algebraically in terms of a fluctuation parameter. OTOCs spread ballistically in all regimes, also at the thermal phase transition, where the butterfly velocity is maximal. Our work contributes to the understanding of the relation between quantum and classical many-body chaos and our method can be applied to other field theories dominated by classical modes at long wavelengths.

  13 citations

• From ray tracing to waves of topological origin in continuous media

  Antoine Venaille, Yohei Onuki, Nicolas Perez, Armand Leclerc

  SciPost Phys. 14, 062 (2023) · published 5 April 2023 | Toggle abstract · pdf

  Continuous media commonly support a discrete number of wave modes that are trapped along interfaces defined by spatially varying parameters. In the case of multicomponent wave problems, those trapped modes fill a frequency gap between different wave bands. When they are robust against continuous deformations of parameters, such waves are said to be of topological origin. It has been realized over the last decades that waves of topological origin can be predicted by computing a single topological invariant, the first Chern number, in a dual bulk wave problem that is much simpler to solve than the original wave equation involving spatially varying coefficients. The correspondence between the simple bulk problem and the more complicated interface problem is usually justified by invoking an abstract index theorem. Here, by applying ray tracing machinery to the paradigmatic example of equatorial shallow water waves, we propose a physical interpretation of this correspondence. We first compute ray trajectories in the phase space given by position and wavenumber of the wave packet, using Wigner-Weyl transforms. We then apply a quantization condition to describe the spectral properties of the original wave operator. This bridges the gap between previous work by Littlejohn and Flynn showing manifestation of Berry curvature in ray tracing equations, and more recent studies that computed the Chern number of flow models by integrating the Berry curvature over a closed surface in parameter space. We find that an integral of Berry curvature over this closed surface emerges naturally from the quantization condition, which allows us to recover the bulk-interface correspondence.

  13 citations