Publications

Order by: publication date number of citations

• Pfaffian invariant identifies magnetic obstructed atomic insulators

  Isidora Araya Day, Anastasiia Varentcova, Daniel Varjas, Anton R. Akhmerov

  SciPost Phys. 15, 114 (2023) · published 25 September 2023 | Toggle abstract · pdf

  We derive a $\mathbb{Z}_4$ topological invariant that extends beyond symmetry eigenvalues and Wilson loops and classifies two-dimensional insulators with a $C_4 \mathcal{T}$ symmetry. To formulate this invariant, we consider an irreducible Brillouin zone and constrain the spectrum of the open Wilson lines that compose its boundary. We fix the gauge ambiguity of the Wilson lines by using the Pfaffian at high symmetry momenta. As a result, we distinguish the four $C_4 \mathcal{T}$-protected atomic insulators, each of which is adiabatically connected to a different atomic limit. We establish the correspondence between the invariant and the obstructed phases by constructing both the atomic limit Hamiltonians and a $C_4 \mathcal{T}$-symmetric model that interpolates between them. The phase diagram shows that $C_4 \mathcal{T}$ insulators allow $\pm 1$ and $2$ changes of the invariant, where the latter is overlooked by symmetry indicators.

  5 citations

• CDMFT+HFD: An extension of dynamical mean field theory for nonlocal interactions applied to the single band extended Hubbard model

  Sarbajaya Kundu, David Sénéchal

  SciPost Phys. Core 7, 033 (2024) · published 3 June 2024 | Toggle abstract · pdf

  We examine the phase diagram of the extended Hubbard model on a square lattice, for both attractive and repulsive nearest-neighbor interactions, using CDMFT+HFD, a combination of Cluster Dynamical Mean Field theory (CDMFT) and a Hartree-Fock mean-field decoupling of the inter-cluster extended interaction. For attractive non-local interactions, this model exhibits a region of phase separation near half-filling, in the vicinity of which we find islands of d-wave superconductivity, decaying rapidly as a function of doping, with disconnected regions of extended s-wave order at smaller (higher) electron densities. On the other hand, when the extended interaction is repulsive, a Mott insulating state at half-filling is destabilized by hole doping, in the strong-coupling limit, in favor of d-wave superconductivity. At the particle-hole invariant chemical potential, we find a first-order phase transition from antiferromagnetism (AF) to d-wave superconductivity as a function of the attractive nearest-neighbor interaction, along with a deviation of the density from the half-filled limit. A repulsive extended interaction instead favors charge-density wave (CDW) order at half-filling.

  5 citations

• Towards traversable wormholes from force-free plasmas

  Nabil Iqbal, Simon F. Ross

  SciPost Phys. 12, 086 (2022) · published 9 March 2022 | Toggle abstract · pdf

  The near-horizon region of magnetically charged black holes can have very strong magnetic fields. A useful low-energy effective theory for fluctuations of the fields, coupled to electrically charged particles, is force-free electrodynamics. The low energy collective excitations include a large number of Alfven wave modes, which have a massless dispersion relation along the field worldlines. We attempt to construct traversable wormhole solutions using the negative Casimir energy of the Alfven wave modes, analogously to the recent construction using charged massless fermions. The behaviour of massless scalars in the near-horizon region implies that the size of the wormholes is strongly restricted and cannot be made large, even though the force free description is valid in a larger regime.

  5 citations

• Counterdiabatic Hamiltonians for multistate Landau-Zener problem

  Kohji Nishimura, Kazutaka Takahashi

  SciPost Phys. 5, 029 (2018) · published 27 September 2018 | Toggle abstract · pdf

  We study the Landau-Zener transitions generalized to multistate systems. Based on the work by Sinitsyn et al. [Phys. Rev. Lett. 120, 190402 (2018)], we introduce the auxiliary Hamiltonians that are interpreted as the counterdiabatic terms. We find that the counterdiabatic Hamiltonians satisfy the zero curvature condition. The general structures of the auxiliary Hamiltonians are studied in detail and the time-evolution operator is evaluated by using a deformation of the integration contour and asymptotic forms of the auxiliary Hamiltonians. For several spin models with transverse field, we calculate the transition probability between the initial and final ground states and find that the method is useful to study nonadiabatic regime.

  5 citations

• Investigating finite-size effects in random matrices by counting resonances

  Anton Kutlin, Carlo Vanoni

  SciPost Phys. 18, 090 (2025) · published 12 March 2025 | Toggle abstract · pdf

  Resonance counting is an intuitive and widely used tool in Random Matrix Theory and Anderson Localization. Its undoubted advantage is its simplicity: in principle, it is easily applicable to any random matrix ensemble. On the downside, the notion of resonance is ill-defined, and the "number of resonances" does not have a direct mapping to any commonly used physical observable like the participation entropy, the fractal dimensions, or the gap ratios (r-parameter), restricting the method's predictive power to the thermodynamic limit only where it can be used for locating the Anderson localization transition. In this work, we reevaluate the notion of resonances and relate it to measurable quantities, building a foundation for the future application of the method to finite-size systems. To access the HTML version of the paper & discuss it with the authors, visit https://enabla.com/pub/558.

  5 citations

• Dynamics of parafermionic states in transport measurements

  Ida Egholm Nielsen, Jens Schulenborg, Reinhold Egger, Michele Burrello

  SciPost Phys. 15, 189 (2023) · published 8 November 2023 | Toggle abstract · pdf

  Advances in hybrid fractional quantum Hall (FQH)-superconductor platforms pave the way for realisation of parafermionic modes. We analyse signatures of these non-abelian anyons in transport measurements across devices with $\mathbb{Z}_6$ parafermions (PFs) coupled to an external electrode. Simulating the dynamics of these open systems by a stochastic quantum jump method, we show that a current readout over sufficiently long times constitutes a projective measurement of the fractional charge shared by two PFs. Interaction of these topological modes with the FQH environment, however, may cause poisoning events affecting this degree of freedom which we model by jump operators that describe incoherent coupling of PFs with FQH edge modes. We analyse how this gives rise to a characteristic three-level telegraph noise in the current, constituting a very strong signature of PFs. We discuss also other forms of poisoning and noise caused by interaction with fractional quasiparticles in the bulk of the Hall system. We conclude our work with an analysis of four-PF devices, in particular on how the PF fusion algebra can be observed in electrical transport experiments.

  5 citations

• A splash in a one-dimensional cold gas

  Subhadip Chakraborti, Abhishek Dhar, P. L. Krapivsky

  SciPost Phys. 13, 074 (2022) · published 29 September 2022 | Toggle abstract · pdf

  We consider a set of hard point particles distributed uniformly with a specified density on the positive half-line and all initially at rest. The particle masses alternate between two values, $m$ and $M$. The particles interact via collisions that conserve energy and momentum. We study the cascade of activity that results when the left-most particle is given a positive velocity. At long times we find that this leads to two fascinating features in the observed dynamics. First, in the bulk of the gas, a shock front develops separating the cold gas from a thermalized region. The shock-front travels sub-ballistically, with the bulk described by self-similar solutions of Euler hydrodynamics. Second, there is a splash region formed by the recoiled particles which move ballistically with negative velocities. The splash region is completely non-hydrodynamic and we propose two conjectures for the long time particle dynamics in this region. We provide a detailed analytic understanding of these coexisting regimes. These are supported by the results of molecular dynamics simulations.

  5 citations

• Quantum chaos in perturbative super-Yang-Mills Theory

  Tristan McLoughlin, Raul Pereira, Anne Spiering

  SciPost Phys. 14, 049 (2023) · published 27 March 2023 | Toggle abstract · pdf

  We provide numerical evidence that the perturbative spectrum of anomalous dimensions in maximally supersymmetric $SU(N)$ Yang-Mills theory is chaotic at finite values of $N$. We calculate the probability distribution of one-loop level spacings for subsectors of the theory and show that for large $N$ it is given by the Poisson distribution of integrable models, while at finite values it is the Wigner-Dyson distribution of the Gaussian orthogonal ensemble random matrix theory. We extend these results to two-loop order and to a one-parameter family of deformations. We further study the spectral rigidity for these models and show that it is also well described by random matrix theory. Finally we demonstrate that the finite-$N$ eigenvectors possess properties of chaotic states.

  5 citations

• Pymablock: An algorithm and a package for quasi-degenerate perturbation theory

  Isidora Araya Day, Sebastian Miles, Hugo K. Kerstens, Daniel Varjas, Anton R. Akhmerov

  SciPost Phys. Codebases 50 (2025) · published 12 February 2025 | Toggle abstract · pdf

  A common technique in the study of complex quantum-mechanical systems is to reduce the number of degrees of freedom in the Hamiltonian by using quasi-degenerate perturbation theory. While the Schrieffer-Wolff transformation achieves this and constructs an effective Hamiltonian, its scaling is suboptimal, it is limited to two subspaces, and implementing it efficiently is both challenging and error-prone. We introduce an algorithm for constructing an equivalent effective Hamiltonian as well as a Python package, Pymablock, that implements it. Our algorithm combines an optimal asymptotic scaling and the ability to handle any number of subspaces with a range of other improvements. The package supports numerical and analytical calculations of any order and it is designed to be interoperable with any other packages for specifying the Hamiltonian. We demonstrate how the package handles constructing a k.p model, analyses a superconducting qubit, and computes the low-energy spectrum of a large tight-binding model. We also compare its performance with reference calculations and demonstrate its efficiency.

  5 citations

• Correlations of quantum curvature and variance of Chern numbers

  Omri Gat, Michael Wilkinson

  SciPost Phys. 10, 149 (2021) · published 21 June 2021 | Toggle abstract · pdf

  We analyse the correlation function of the quantum curvature in complex quantum systems, using a random matrix model to provide an exemplar of a universal correlation function. We show that the correlation function diverges as the inverse of the distance at small separations. We also define and analyse a correlation function of mixed states, showing that it is finite but singular at small separations. A scaling hypothesis on a universal form for both types of correlations is supported by Monte-Carlo simulations. We relate the correlation function of the curvature to the variance of Chern integers which can describe quantised Hall conductance.

  5 citations