Publications

Order by: publication date number of citations

• Electrostatic solution of massless quenches in Luttinger liquids

  Paola Ruggiero, Pasquale Calabrese, Thierry Giamarchi, Laura Foini

  SciPost Phys. 13, 111 (2022) · published 18 November 2022 | Toggle abstract · pdf

  The study of non-equilibrium dynamics of many-body systems after a quantum quench received a considerable boost and a deep theoretical understanding from the path integral formulation in imaginary time. However, the celebrated problem of a quench in the Luttinger parameter of a one dimensional quantum critical system (massless quench) has so far only been solved in the real-time Heisenberg picture. In order to bridge this theoretical gap and to understand on the same ground massive and massless quenches, we study the problem of a gaussian field characterized by a coupling parameter $K$ within a strip and a different one $K_0$ in the remaining two semi-infinite planes. We give a fully analytical solution using the electrostatic analogy with the problem of a dielectric material within a strip surrounded by an infinite medium of different dielectric constant, and exploiting the method of charge images. After analytic continuation, this solution allows us to obtain all the correlation functions after the quench within a path integral approach in imaginary time, thus recovering and generalizing the results in real time. Furthermore, this imaginary-time approach establishes a remarkable connection between the quench and the famous problem of the conductivity of a Tomonaga-Luttinger liquid coupled to two semi-infinite leads: the two are in fact related by a rotation of the spacetime coordinates.

  6 citations

• Density resolved wave packet spreading in disordered Gross-Pitaevskii lattices

  Yagmur Kati, Xiaoquan Yu, Sergej Flach

  SciPost Phys. Core 3, 006 (2020) · published 8 October 2020 | Toggle abstract · pdf

  We perform novel energy and norm density resolved wave packet spreading studies in the disordered Gross-Pitaevskii (GP) lattice to confine energy density fluctuations. We map the locations of GP regimes of weak and strong chaos subdiffusive spreading in the 2D density control parameter space and observe strong chaos spreading over several decades. We obtain a renormalization of the ground state due to disorder, which allows for a new disorder-induced phase of disconnected insulating puddles of matter due to Lifshits tails. Inside this Lifshits phase, the wave packet spreading is substantially slowed down.

  6 citations

• Extreme boundary conditions and random tilings

  Jean-Marie Stéphan

  SciPost Phys. Lect. Notes 26 (2021) · published 12 March 2021 | Toggle abstract · pdf

  Standard statistical mechanical or condensed matter arguments tell us that bulk properties of a physical system do not depend too much on boundary conditions. Random tilings of large regions provide counterexamples to such intuition, as illustrated by the famous 'arctic circle theorem' for dimer coverings in two dimensions. In these notes, I discuss such examples in the context of critical phenomena, and their relation to 1+1d quantum particle models. All those turn out to share a common feature: they are inhomogeneous, in the sense that local densities now depend on position in the bulk. I explain how such problems may be understood using variational (or hydrodynamic) arguments, how to treat long range correlations, and how non trivial edge behavior can occur. While all this is done on the example of the dimer model, the results presented here have much greater generality. In that sense the dimer model serves as an opportunity to discuss broader methods and results. [These notes require only a basic knowledge of statistical mechanics.]

  6 citations

• The bosonic skin effect: Boundary condensation in asymmetric transport

  Louis Garbe, Yuri Minoguchi, Julian Huber, Peter Rabl

  SciPost Phys. 16, 029 (2024) · published 25 January 2024 | Toggle abstract · pdf

  We study the incoherent transport of bosonic particles through a one dimensional lattice with different left and right hopping rates, as modelled by the asymmetric simple inclusion process (ASIP). Specifically, we show that as the current passing through this system increases, a transition occurs, which is signified by the appearance of a characteristic zigzag pattern in the stationary density profile near the boundary. In this highly unusual transport phase, the local particle distribution alternates on every site between a thermal distribution and a Bose-condensed state with broken $U(1)$-symmetry. Furthermore, we show that the onset of this phase is closely related to the so-called non-Hermitian skin effect and coincides with an exceptional point in the spectrum of density fluctuations. Therefore, this effect establishes a direct connection between quantum transport, non-equilibrium condensation phenomena and non-Hermitian topology, which can be probed in cold-atom experiments or in systems with long-lived photonic, polaritonic and plasmonic excitations.

  6 citations

• A plane defect in the 3d O(N) model

  Abijith Krishnan, Max A. Metlitski

  SciPost Phys. 15, 090 (2023) · published 12 September 2023 | Toggle abstract · pdf

  It was recently found that the classical 3d O$(N)$ model in the semi-infinite geometry can exhibit an "extraordinary-log" boundary universality class, where the spin-spin correlation function on the boundary falls off as $\langle \vec{S}(x) \cdot \vec{S}(0)\rangle \sim \frac{1}{(\log x)^q}$. This universality class exists for a range $2 ≤ N < N_c$ {and Monte-Carlo simulations and conformal bootstrap} indicate $N_c > 3$. In this work, we extend this {result} to the 3d O$(N)$ model in an infinite geometry with a plane defect. We use renormalization group (RG) to show that in this case the extraordinary-log universality class is present for any finite $N ≥ 2$. We additionally show, {in agreement with our RG analysis}, that the line of defect fixed points which is present at $N = ∞$ is lifted to the ordinary, special (no defect) and extraordinary-log universality classes by $1/N$ corrections. We study the "central charge" $a$ for the $O(N)$ model in the boundary and interface geometries and provide a non-trivial detailed check of an $a$-theorem by Jensen and O'Bannon. Finally, we revisit the problem of the O$(N)$ model in the semi-infinite geometry. We find evidence that at $N = N_c$ the extraordinary and special fixed points annihilate and only the ordinary fixed point is left for $N > N_c$.

  6 citations

• On the generalizability of artificial neural networks in spin models

  Hon Man Yau, Nan Su

  SciPost Phys. Core 5, 032 (2022) · published 8 June 2022 | Toggle abstract · pdf

  The applicability of artificial neural networks (ANNs) is typically limited to the models they are trained with and little is known about their generalizability, which is a pressing issue in the practical application of trained ANNs to unseen problems. Here, by using the task of identifying phase transitions in spin models, we establish a systematic generalizability such that simple ANNs trained with the two-dimensional ferromagnetic Ising model can be applied to the ferromagnetic q-state Potts model in different dimensions for q>=2. The same scheme can be applied to the highly nontrivial antiferromagnetic q-state Potts model. We demonstrate that similar results can be obtained by reducing the exponentially large state space spanned by the training data to one that comprises only three representative configurations artificially constructed through symmetry considerations. We expect our findings to simplify and accelerate the development of machine learning-assisted tasks in spin-model related disciplines in physics and materials science.

  6 citations

• Crystal gravity

  Jan Zaanen, Floris Balm, Aron J. Beekman

  SciPost Phys. 13, 039 (2022) · published 30 August 2022 | Toggle abstract · pdf

  We address a subject that could have been analyzed century ago: how does the universe of general relativity look like when it would have been filled with solid matter? Solids break spontaneously the translations and rotations of space itself. Only rather recently it was realized in various context that the order parameter of the solid has a relation to Einsteins dynamical space time which is similar to the role of a Higgs field in a Yang-Mills gauge theory. Such a "crystal gravity" is therefore like the Higgs phase of gravity. The usual Higgs phases are characterized by a special phenomenology. A case in point is superconductivity exhibiting phenomena like the Type II phase, characterized by the emergence of an Abrikosov lattice of quantized magnetic fluxes absorbing the external magnetic field. What to expect in the gravitational setting? The theory of elasticity is the universal effective field theory associated with the breaking of space translations and rotations having a similar status as the phase action describing a neutral superfluid. A geometrical formulation appeared in its long history, similar in structure to general relativity, which greatly facilitates the marriage of both theories. With as main limitation that we focus entirely on stationary circumstances -- the dynamical theory is greatly complicated by the lack of Lorentz invariance -- we will present a first exploration of a remarkably rich and often simple physics of "Higgsed gravity".

  6 citations

• Extreme value statistics of edge currents in Markov jump processes and their use for entropy production estimation

  Izaak Neri, Matteo Polettini

  SciPost Phys. 14, 131 (2023) · published 25 May 2023 | Toggle abstract · pdf

  The infimum of an integrated current is its extreme value against the direction of its average flow. Using martingale theory, we show that the infima of integrated edge currents in time-homogeneous Markov jump processes are geometrically distributed, with a mean value determined by the effective affinity measured by a marginal observer that only sees the integrated edge current. In addition, we show that a marginal observer can estimate a fraction of the average entropy production rate in the underlying nonequilibrium process from the extreme value statistics in the integrated edge current. The estimated average rate of dissipation obtained in this way equals the above mentioned effective affinity times the average edge current. Moreover, we show that estimates of dissipation based on extreme value statistics can be significantly more accurate than those based on thermodynamic uncertainty ratios, as well as those based on a naive estimator obtained by neglecting nonMarkovian correlations in the Kullback-Leibler divergence of the trajectories of the integrated edge current.

  6 citations

• 3D Ising CFT and exact diagonalization on icosahedron: The power of conformal perturbation theory

  Bing-Xin Lao, Slava Rychkov

  SciPost Phys. 15, 243 (2023) · published 18 December 2023 | Toggle abstract · pdf

  We consider the transverse field Ising model in (2+1)D, putting 12 spins at the vertices of the regular icosahedron. The model is tiny by the exact diagonalization standards, and breaks rotation invariance. Yet we show that it allows a meaningful comparison to the 3D Ising CFT on $\mathbb{R}× S^2$, by including effective perturbations of the CFT Hamiltonian with a handful of local operators. This extreme example shows the power of conformal perturbation theory in understanding finite N effects in models on regularized $S^2$. Its ideal arena of application should be the recently proposed models of fuzzy sphere regularization.

  5 citations

• Entanglement gap, corners, and symmetry breaking

  Vincenzo Alba

  SciPost Phys. 10, 056 (2021) · published 8 March 2021 | Toggle abstract · pdf

  We investigate the finite-size scaling of the lowest entanglement gap $\delta\xi$ in the ordered phase of the two-dimensional quantum spherical model (QSM). The entanglement gap decays as $\delta\xi=\Omega/\sqrt{L\ln(L)}$. This is in contrast with the purely logarithmic behaviour as $\delta\xi=\pi^2/\ln(L)$ at the critical point. The faster decay in the ordered phase reflects the presence of magnetic order. We analytically determine the constant $\Omega$, which depends on the low-energy part of the model dispersion and on the geometry of the bipartition. In particular, we are able to compute the corner contribution to $\Omega$, at least for the case of a square corner.

  5 citations