Publications

Order by: publication date number of citations

• Interaction-induced strong zero modes in short quantum dot chains with time-reversal symmetry

  A. Mert Bozkurt, Sebastian Miles, Sebastiaan L. D. ten Haaf, Chun-Xiao Liu, Fabian Hassler, Michael Wimmer

  SciPost Phys. 18, 206 (2025) · published 25 June 2025 | Toggle abstract · pdf

  We theoretically explore the emergence of strong zero modes in a two-site chain consisting of two quantum dots coupled due to a central dot that mediates electron hopping and singlet superconducting pairing. In the presence of time-reversal symmetry, the on-site Coulomb interaction leads to a three-fold ground-state degeneracy when tuning the system to a sweet spot as a function of the inter-dot couplings. This degeneracy is protected against changes of the dot energies in the same way as "poor man's" Majorana bound states in short Kitaev chains. In the limit of strong interactions, this protection is maximal and the entire spectrum becomes triply degenerate, indicating the emergence of a "poor man's" version of a strong zero mode. We explain the degeneracy and protection by constructing corresponding Majorana Kramers-pair operators and $\mathbb{Z}_3$-parafermion operators. The strong zero modes share many properties of Majorana bound states in short Kitaev chains, including the stability of zero-bias peaks in the conductance and the behavior upon coupling to an additional quantum dot. However, they can be distinguished through finite-bias spectroscopy and the exhibit a different behavior when scaling to longer chains.

  1 citation

• The chiral SYK model in three-dimensional holography

  Alexander Altland, Dmitry Bagrets, Nele Callebaut, Konstantin Weisenberger

  SciPost Phys. 18, 205 (2025) · published 24 June 2025 | Toggle abstract · pdf

  A celebrated realization of the holographic principle posits an approximate duality between the $(0+1)$-dimensional quantum mechanical SYK model and two-dimensional Jackiw-Teitelboim gravity, mediated by the Schwarzian action as an effective low energy theory common to both systems. We here propose a generalization of this correspondence to one dimension higher. Starting from different microscopic realizations of effectively chiral $(1+1)$-dimensional generalizations of the SYK model, we derive a reduction to the Alekseev-Shatashvilli (AS)-action, a minimal extension of the Schwarzian action which has been proposed as the effective boundary action of three-dimensional gravity. In the bulk, we show how the same action describes fluctuations around the Euclidean BTZ black hole configuration, the dominant stationary solution of three-dimensional gravity. These two constructions allow us to match bulk and boundary coupling constants, and to compute observables. Specifically, we apply semiclassical techniques inspired by condensed matter physics to the computation of out-of-time-order correlation functions (OTOCs), demonstrating maximal chaos in the chiral SYK chain and its gravity dual.

  2 citations

• Non-linear photoconductivity of strongly driven graphene

  Lukas Broers, Ludwig Mathey

  SciPost Phys. 18, 199 (2025) · published 20 June 2025 | Toggle abstract · pdf

  We present the non-linear DC photoconductivity of graphene under strong infra-red (IR) radiation. The photoconductivity is obtained as the response to a strong DC electric field, with field strengths outside of the linear-response regime, while the IR radiation is described by a strong AC electric field. The conductivity displays two distinct regimes in which either the DC or the AC field dominates. We explore these regimes and associate them with the dynamics of driven Landau-Zener quenches in the case of a large DC field. In the limit of a large AC field, we describe the conductivity in a Floquet picture and compare the results to the closely related Tien-Gordon effect. We present analytical calculations for the non-linear differential photoconductivity, for both regimes based on the corresponding mechanisms. As part of this discussion of the non-equilibrium state of graphene, we present analytical estimates of the conductivity of undriven graphene as a function of temperature and DC bias field strength that show very good agreement with our simulations.

• On the relation between fractional charge and statistics

  Thors Hans Hansson, Rodrigo Arouca, Thomas Klein Kvorning

  SciPost Phys. 18, 197 (2025) · published 19 June 2025 | Toggle abstract · pdf

  We revisit an argument, originally given by Kivelson and Roček, for why the existence of fractional charge necessarily implies fractional statistics. In doing so, we resolve a contradiction in the original argument, and in the case of a $\nu = 1/m$ Laughlin holes, we also show that the standard relation between fractional charge and statistics is necessary by an argument based on a t'Hooft anomaly in a one-form global $\mathcal{Z}_m$ symmetry.

  1 citation

• A minimal tensor network beyond free fermions

  Carolin Wille, Maksimilian Usoltcev, Jens Eisert, Alexander Altland

  SciPost Phys. 18, 196 (2025) · published 19 June 2025 | Toggle abstract · pdf

  This work proposes a minimal model extending the duality between classical statistical spin systems and fermionic systems beyond the case of free fermions. A Jordan-Wigner transformation applied to a two-dimensional tensor network maps the partition sum of a classical statistical mechanics model to a Grassmann variable integral, structurally similar to the path integral for interacting fermions in two dimensions. The resulting model is simple, featuring only two parameters: one governing spin-spin interaction (dual to effective hopping strength in the fermionic picture), the other measuring the deviation from the free fermion limit. Nevertheless, it exhibits a rich phase diagram, partially stabilized by elements of topology, and featuring three phases meeting at a multicritical point. Besides the interpretation as a spin and fermionic system, the model is closely related to loop gas and vertex models and can be interpreted as a parity-preserving (non-unitary) circuit. Its minimal construction makes it an ideal reference system for studying non-linearities in tensor networks and deriving results by means of duality.

  1 citation

• Fermionic non-invertible symmetries in (1+1)d: Gapped and gapless phases, transitions, and symmetry TFTs

  Lakshya Bhardwaj, Kansei Inamura, Apoorv Tiwari

  SciPost Phys. 18, 194 (2025) · published 18 June 2025 | Toggle abstract · pdf

  We study fermionic non-invertible symmetries in (1+1)d, which are generalized global symmetries that mix fermion parity symmetry with other invertible and non-invertible internal symmetries. Such symmetries are described by fermionic fusion supercategories, which are fusion $\pi$-supercategories with a choice of fermion parity. The aim of this paper is to flesh out the categorical Landau paradigm for fermionic symmetries. We use the formalism of Symmetry Topological Field Theory (SymTFT) to study possible gapped and gapless phases for such symmetries, along with possible deformations between these phases, which are organized into a Hasse phase diagram. The phases can be characterized in terms of sets of condensed, confined and deconfined generalized symmetry charges, reminiscent of notions familiar from superconductivity. Many of the gapless phases also serve as phase transitions between gapped phases. The associated fermionic conformal field theories (CFTs) can be obtained by performing generalized fermionic Kennedy-Tasaki (KT) transformations on bosonic CFTs describing simpler transitions. The fermionic non-invertible symmetries along with their charges and phases discussed here can be obtained from those of bosonic non-invertible symmetries via fermionization or Jordan-Wigner transformation, which is discussed in detail.

  8 citations

• Mode-Shell correspondence, a unifying phase space theory in topological physics - Part II: Higher-dimensional spectral invariants

  Lucien Jezequel, Pierre Delplace

  SciPost Phys. 18, 193 (2025) · published 18 June 2025 | Toggle abstract · pdf

  The mode-shell correspondence relates the number $\mathcal{I}_M$ of gapless modes in phase space to a topological \textit{shell invariant} $\mathcal{I}_S$ defined on a closed surface - the shell - surrounding those modes, namely $\mathcal{I}_M=\mathcal{I}_S$. In part I, we introduced the mode-shell correspondence for zero-modes of chiral symmetric Hamiltonians (class AIII). In this part II, we broaden the correspondence to arbitrary dimension and to both symmetry classes A and AIII. This allows us to include, in particular, $1D$-unidirectional edge modes of Chern insulators, $2D$ massless Dirac and $3D$-Weyl cones, within the same formalism. We provide an expression for $\mathcal{I}_M$ that only depends on the dimension of the dispersion relation of the gapless mode, and does not require a translation invariance. Then, we show that the topology of the shell (a circle, a sphere, a torus), that must account for the spreading of the gapless mode in phase space, yields specific expressions of the shell index. Semi-classical expressions of those shell indices are also derived and reduce to either Chern or winding numbers depending on the parity of the mode’s dimension. In that way, the mode-shell correspondence provides a unified and systematic topological description of both bulk and boundary gapless modes in any dimension, and in particular includes the bulk-boundary correspondence. We illustrate the generality of the theory by analyzing several models of semimetals and insulators, both on lattices and in the continuum, and also discuss weak and higher-order topological phases within this framework. Although this paper is a continuation of Part I, the content remains sufficiently independent to be mostly read separately.

• Cons-training tensor networks: Embedding and optimization over discrete linear constraints

  Javier Lopez-Piqueres, Jing Chen

  SciPost Phys. 18, 192 (2025) · published 17 June 2025 | Toggle abstract · pdf

  In this study, we introduce a novel family of tensor networks, termed constrained matrix product states (MPS), designed to incorporate exactly arbitrary discrete linear constraints, including inequalities, into sparse block structures. These tensor networks are particularly tailored for modeling distributions with support strictly over the feasible space, offering benefits such as reducing the search space in optimization problems, alleviating overfitting, improving training efficiency, and decreasing model size. Central to our approach is the concept of a quantum region, an extension of quantum numbers traditionally used in $U(1)$ symmetric tensor networks, adapted to capture any linear constraint, including the unconstrained scenario. We further develop a novel canonical form for these new MPS, which allow for the merging and factorization of tensor blocks according to quantum region fusion rules and permit optimal truncation schemes. Utilizing this canonical form, we apply an unsupervised training strategy to optimize arbitrary objective functions subject to discrete linear constraints. Our method's efficacy is demonstrated by solving the quadratic knapsack problem, achieving superior performance compared to a leading nonlinear integer programming solver. Additionally, we analyze the complexity and scalability of our approach, demonstrating its potential in addressing complex constrained combinatorial optimization problems.

• The asymmetric Fermi surface of Bi2201

  Steef Smit, Kourosh L. Shirkoohi, Saumya Mukherjee, Sergio Barquero Pierantoni, Lewis Bawden, Erik van Heumen, Arnaud P. N. Tchiomo, Jans Henke, Jasper van Wezel, Yingkai Huang, Takeshi Kondo, Tsunehiro Takeuchi, Timur K. Kim, Cephise Cacho, Marta Zonno, Sergey Gorovikov, Stephen B. Dugdale, Jorge I. Facio, Mariia Roslova, Laura Folkers, Anna Isaeva, Nigel E. Hussey, Mark S. Golden

  SciPost Phys. 18, 191 (2025) · published 17 June 2025 | Toggle abstract · pdf

  High-resolution angle-resolved photoemission spectroscopy (ARPES) performed on the single-layered cuprate (Pb$_{1-y}$,Bi$_y$)$_2$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$ (Bi2201) reveals a 6-10% difference in the nodal $k_F$ vectors along the $\Gamma$Y and $\Gamma$X directions. This asymmetry is notably larger than the 2% orthorhombic distortion in the CuO$_2$ plane lattice constants determined using X-ray crystallography from the same samples. First principles calculations indicate that crystal-field splitting of the bands lies at the root of the $k_{F}$ asymmetry. Concomitantly, the nodal Fermi velocities for the $\Gamma$Y quadrant exceed those for $\Gamma$X by 4%. Momentum distribution curve widths for the two nodal dispersions are also anisotropic, showing identical energy dependencies, bar a scaling factor of $\sim$ 1.17$± 0.05$ between $\Gamma$Y and $\Gamma$X. Consequently, the imaginary part of the self-energy is found to be 10-20% greater along $\Gamma$Y than $\Gamma$X. These results emphasize the need to account for Fermi surface asymmetry in the analysis of ARPES data on Bi-based cuprate high temperature superconductors such as Bi2201. To illustrate this point, an orthorhombic tight-binding model (with twofold in-plane symmetry) was used to fit ARPES Fermi surface maps spanning all four quadrants of the Brillouin zone, and the ARPES-derived hole-doping (Luttinger count) was extracted. Comparison of the Luttinger count with one assuming four-fold in-plane symmetry strongly suggests the marked spread in previously-reported Fermi surface areas from ARPES on Bi2201 results from the differences in $k_F$ along $\Gamma$Y and $\Gamma$X. Using this analysis, a new, linear relationship emerges between the hole-doping derived from ARPES ($p_{\text{ARPES}}$) and that derived using the Presland ($p_{\text{Presland}}$) relation such that $p_{\text{ARPES}} = p_{\text{Presland}}+0.11$. The implications for this difference between the ARPES- and Presland-derived estimates for $p$ are discussed and possible future directions to elucidate the origin of this discrepancy are presented.

• Chapman-Enskog theory and crossover between diffusion and superdiffusion for nearly integrable quantum gases

  Maciej Łebek, Miłosz Panfil

  SciPost Phys. 18, 186 (2025) · published 12 June 2025 | Toggle abstract · pdf

  Integrable systems feature an infinite number of conserved charges and on hydrodynamic scales are described by generalised hydrodynamics (GHD). This description breaks down when the integrability is weakly broken and sufficiently large space-time-scales are probed. The emergent hydrodynamics depends then on the charges conserved by the perturbation. We focus on nearly-integrable Galilean-invariant systems with conserved particle number, momentum and energy. Basing on the Boltzmann approach to integrability-breaking we describe dynamics of the system with GHD equation supplemented with a collision term. The limit of large space-time-scales is addressed using Chapman-Enskog expansion adapted to the GHD equation. For length scales larger than $\sim \lambda^{-2}$, where $\lambda$ is integrability-breaking parameter, we recover Navier-Stokes equations and find transport coefficients: viscosity and thermal conductivity. At even larger length scales, this description crosses over to Kardar-Parisi-Zhang universality class, characteristic to generic non-integrable one-dimensional fluids. Employing nonlinear fluctuating hydrodynamics we estimate this crossover length scale as $ \sim \lambda^{-4}$.