Publications

Order by: publication date number of citations

• Deconfined criticalities and dualities between chiral spin liquid, topological superconductor and charge density wave Chern insulator

  Xue-Yang Song, Ya-Hui Zhang

  SciPost Phys. 15, 215 (2023) · published 29 November 2023 | Toggle abstract · pdf

  We propose bi-critical and tri-critical theories between chiral spin liquid (CSL), topological superconductor (SC) and charge density wave (CDW) ordered Chern insulator with Chern number $C=2$ on square, triangular and Kagome lattices. The three CDW order parameters form a manifold of $S^2$ or $S^1$ depending on whether there is easy-plane anisotropy. The skyrmion defect of the CDW order carries physical charge $2e$ and its condensation leads to a topological superconductor. The CDW-SC transitions are in the same universality classes as the celebrated deconfined quantum critical points (DQCP) between Neel order and valence bond solid order on square lattice. Both SC and CDW order can be accessed from the CSL phase through a continuous phase transition. At the CSL-SC transition, there is still CDW order fluctuations although CDW is absent in both sides. We propose three different theories for the CSL-SC transition (and CSL to easy-plane CDW transition): a $U(1)$ theory with two bosons, a $U(1)$ theory with two Dirac fermions, and an $SU(2)$ theory with two bosons. Our construction offers a derivation of the duality between these three theories as well as a promising physical realization. The $SU(2)$ theory offers a unified framework for a series of fixed points with explicit $SO(5), O(4)$ or $SO(3)× O(2)$ symmetry. There is also a transparent duality transformation mapping SC order to easy-plane CDW order. The CSL-SC-CDW tri-critical points are invariant under this duality mapping and have an enlarged $SO(5)$ or $O(4)$ symmetry. The DQCPs between CDW and SC inherit the enlarged symmetry, emergent anomaly, and self-duality from the tri-critical point. Our analysis unifies the well-studied DQCP between symmetry breaking phases into a larger framework where they are proximate to a topologically ordered phase. Experimentally the theory demonstrates the possibility of a rich phase diagram and criticality through closing the Mott gap of a quantum spin liquid with projective symmetry group.

  4 citations

• Ground state topology of a four-terminal superconducting double quantum dot

  Lev Teshler, Hannes Weisbrich, Jonathan Sturm, Raffael L. Klees, Gianluca Rastelli, Wolfgang Belzig

  SciPost Phys. 15, 214 (2023) · published 29 November 2023 | Toggle abstract · pdf

  In recent years, various classes of systems were proposed to realize topological states of matter. One of them are multiterminal Josephson junctions where topological Andreev bound states are constructed in the synthetic space of superconducting phases. Crucially, the topology in these systems results in a quantized transconductance between two of its terminals comparable to the quantum Hall effect. In this work, we study a double quantum dot with four superconducting terminals and show that it has an experimentally accessible topological regime in which the non-trivial topology can be measured. We also include Coulomb repulsion between electrons which is usually present in experiments and show how the topological region can be maximized in parameter space.

  4 citations

• Interplay between chiral media and perfect electromagnetic conductor plates: Repulsive vs. attractive Casimir force transitions

  Thomas Oosthuyse, David Dudal

  SciPost Phys. 15, 213 (2023) · published 28 November 2023 | Toggle abstract · pdf

  We determine the Casimir energies and forces in a variety of potentially experimentally viable setups, consisting of parallel plates made of perfect electromagnetic conductors (PEMCs), which generalize perfect electric conductors (PECs) and perfect magnetic conductors (PMCs), and Weyl semimetals (WSMs). Where comparison is possible, our results agree with the Casimir forces calculated elsewhere in the literature, albeit with different methods. We find a multitude of known but also new cases where repulsive Casimir forces are in principle possible, but restricting the setup to PECs combined with the aforementioned WSM geometry, results in purely attractive Casimir forces.

  5 citations

• Functional renormalisation group approach to shell models of turbulence

  Côme Fontaine, Malo Tarpin, Freddy Bouchet, Léonie Canet

  SciPost Phys. 15, 212 (2023) · published 28 November 2023 | Toggle abstract · pdf

  Shell models are simplified models of hydrodynamic turbulence, retaining only some essential features of the original equations, such as the non-linearity, symmetries and quadratic invariants. Yet, they were shown to reproduce the most salient properties of developed turbulence, in particular universal statistics and multi-scaling. We set up the functional renormalisation group (FRG) formalism to study generic shell models. In particular, we formulate an inverse RG flow, which consists in integrating out fluctuation modes from the large scales (small wavenumbers) to the small scales (large wavenumbers), which is physically grounded and has long been advocated in the context of turbulence. Focusing on the Sabra shell model, we study the effect of both a large-scale forcing, and a power-law forcing exerted at all scales. We show that these two types of forcing yield different fixed points, and thus correspond to distinct universality classes, characterised by different scaling exponents. We find that the power-law forcing leads to dimensional (K41-like) scaling, while the large-scale forcing entails anomalous scaling.

  2 citations

• Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree

  Ankita Chakrabarti, Cyril Martins, Nicolas Laflorencie, Bertrand Georgeot, Éric Brunet, Gabriel Lemarié

  SciPost Phys. 15, 211 (2023) · published 28 November 2023 | Toggle abstract · pdf

  We study the random transverse field Ising model on a finite Cayley tree. This enables us to probe key questions arising in other important disordered quantum systems, in particular the Anderson transition and the problem of dirty bosons on the Cayley tree, or the emergence of non-ergodic properties in such systems. We numerically investigate this problem building on the cavity mean-field method complemented by state-of-the art finite-size scaling analysis. Our numerics agree very well with analytical results based on an analogy with the traveling wave problem of a branching random walk in the presence of an absorbing wall. Critical properties and finite-size corrections for the zero-temperature paramagnetic-ferromagnetic transition are studied both for constant (independent of the system volume) and algebraically vanishing (scaling as an inverse power law with the system volume) boundary conditions. In the later case, we reveal a regime which is reminiscent of the non-ergodic delocalized phase observed in other systems, thus shedding some light on critical issues in the context of disordered quantum systems, such as Anderson transitions, the many-body localization or disordered bosons in infinite dimensions.

  1 citation

• Horizon strings as 3D black hole microstates

  Arjun Bagchi, Daniel Grumiller, Mohammad Mehdi Sheikh-Jabbari

  SciPost Phys. 15, 210 (2023) · published 27 November 2023 | Toggle abstract · pdf

  We propose that 3d black holes are an ensemble of tensionless null string states. These microstates typically have non-zero winding. We evaluate their partition function in the limit of large excitation numbers and show that their combinatorics reproduces the Bekenstein-Hawking entropy and its semiclassical logarithmic corrections.

  8 citations

• A convenient Keldysh contour for thermodynamically consistent perturbative and semiclassical expansions

  Vasco Cavina, Sadeq S. Kadijani, Massimiliano Esposito, Thomas L. Schmidt

  SciPost Phys. 15, 209 (2023) · published 27 November 2023 | Toggle abstract · pdf

  The work fluctuation theorem (FT) is a symmetry connecting the moment generating functions (MGFs) of the work extracted in a given process and in its time-reversed counterpart. We show that, equivalently, the FT for work in isolated quantum systems can be expressed as an invariance property of a modified Keldysh contour. Modified contours can be used as starting points of perturbative and path integral approaches to quantum thermodynamics, as recently pointed out in the literature. After reviewing the derivation of the contour-based perturbation theory, we use the symmetry of the modified contour to show that the theory satisfies the FT at every order. Furthermore, we extend textbook diagrammatic techniques to the computation of work MGFs, showing that the contributions of the different Feynman diagrams can be added to obtain a general expression of the work statistics in terms of a sum of independent rescaled Poisson processes. In this context, the FT takes the form of a detailed balance condition linking every Feynman diagram with its time-reversed variant. In the second part, we study path integral approaches to the calculation of the MGF, and discuss how the arbitrariness in the choice of the contour impacts the final form of the path integral action. In particular, we show how using a symmetrized contour makes it possible to easily generalize the Keldysh rotation in the context of work statistics, a procedure paving the way to a semiclassical expansion of the work MGF. Furthermore, we use our results to discuss a generalization of the detailed balance conditions at the level of the quantum trajectories.

  2 citations

• Estimation of the geometric measure of entanglement with Wehrl moments through artificial neural networks

  Jérôme Denis, François Damanet, John Martin

  SciPost Phys. 15, 208 (2023) · published 27 November 2023 | Toggle abstract · pdf

  In recent years, artificial neural networks (ANNs) have become an increasingly popular tool for studying problems in quantum theory, and in particular entanglement theory. In this work, we analyse to what extent ANNs can accurately predict the geometric measure of entanglement of symmetric multiqubit states using only a limited number of Wehrl moments (moments of the Husimi function of the state) as input, which represents partial information about the state. We consider both pure and mixed quantum states. We compare the results we obtain by training ANNs with the informed use of convergence acceleration methods. We find that even some of the most powerful convergence acceleration algorithms do not compete with ANNs when given the same input data, provided that enough data is available to train these ANNs. We also provide an experimental protocol for measuring Wehrl moments, which is state-independent. More generally, this work opens up perspectives for the estimation of entanglement measures and other SU(2)-invariant quantities, such as the Wehrl entropy, in a way that is more accessible in experiments than by means of full state tomography.

• Parity and spin CFT with boundaries and defects

  Ingo Runkel, Lóránt Szegedy, Gérard M. T. Watts

  SciPost Phys. 15, 207 (2023) · published 27 November 2023 | Toggle abstract · pdf

  This paper is a follow-up to [J. High Energy Phys. 06, 025 (2020)] in which two-dimensional conformal field theories in the presence of spin structures are studied. In the present paper we define four types of CFTs, distinguished by whether they need a spin structure or not in order to be well-defined, and whether their fields have parity or not. The cases of spin dependence without parity, and of parity without the need of a spin structure, have not, to our knowledge, been investigated in detail so far. We analyse these theories by extending the description of CFT correlators via three-dimensional topological field theory developed in [Nucl. Phys. B 646, 353 (2002)] to include parity and spin. In each of the four cases, the defining data are a special Frobenius algebra $F$ in a suitable ribbon fusion category, such that the Nakayama automorphism of $F$ is the identity (oriented case) or squares to the identity (spin case). We use the TFT to define correlators in terms of $F$ and we show that these satisfy the relevant factorisation and single-valuedness conditions. We allow for world sheets with boundaries and topological line defects, and we specify the categories of boundary labels and the fusion categories of line defect labels for each of the four types. The construction can be understood in terms of topological line defects as gauging a possibly non-invertible symmetry. We analyse the case of a $\mathbb{Z}_2$-symmetry in some detail and provide examples of all four types of CFT, with Bershadsky-Polyakov models illustrating the two new types.

  5 citations

• Thermal pure matrix product state in two dimensions: Tracking thermal equilibrium from paramagnet down to the Kitaev honeycomb spin liquid state

  Matthias Gohlke, Atsushi Iwaki, Chisa Hotta

  SciPost Phys. 15, 206 (2023) · published 24 November 2023 | Toggle abstract · pdf

  We present the first successful application of the matrix product state (MPS) representing a thermal quantum pure state (TPQ) in equilibrium in two spatial dimensions over almost the entire temperature range. We use the Kitaev honeycomb model as a prominent example hosting a quantum spin liquid (QSL) ground state to target the two specific-heat peaks previously solved nearly exactly using the free Majorana fermionic description. Starting from the high-temperature random state, our TPQ-MPS framework on a cylinder precisely reproduces these peaks, showing that the quantum many-body description based on spins can still capture the emergent itinerant Majorana fermions in a ${\mathbb Z}_2$ gauge field. The truncation process efficiently discards the high-energy states, eventually reaching the long-range entangled topological state approaching the exact ground state for a given finite size cluster. An advantage of TPQ-MPS over exact diagonalization or purification-based methods is its lowered numerical cost coming from a reduced effective Hilbert space even at finite temperature.

  1 citation