Publications

Order by: publication date number of citations

• Knizhnik-Zamolodchikov equations and integrable hyperbolic Landau-Zener models

  Suvendu Barik, Lieuwe Bakker, Vladimir Gritsev, Emil A. Yuzbashyan

  SciPost Phys. 18, 212 (2025) · published 27 June 2025 | Toggle abstract · pdf

  We study the relationship between integrable Landau-Zener (LZ) models and Knizhnik-Zamolodchikov (KZ) equations. The latter are originally equations for the correlation functions of two-dimensional conformal field theories, but can also be interpreted as multi-time Schrödinger equations. The general LZ problem is to find probabilities of tunneling from eigenstates at $t=t_\text{in}$ to eigenstates at $t\to+∞$ for an $N× N$ time-dependent Hamiltonian $\hat H(t)$. A number of such problems are exactly solvable in the sense that their tunneling probabilities are elementary functions of Hamiltonian parameters. Recently, it has been proposed that exactly solvable LZ models of this type map to KZ equations. Here we use this connection to identify and solve a class of integrable LZ models with hyperbolic time dependence, $\hat H(t)=\hat A+\hat B/t$, for $N=2, 3$, and $4$, where $\hat A$ and $\hat B$ are time-independent matrices.

  1 citation

• Universal Chern number statistics in random matrix fields

  Or Swartzberg, Michael Wilkinson, Omri Gat

  SciPost Phys. 15, 015 (2023) · published 19 July 2023 | Toggle abstract · pdf

  We investigate the probability distribution of Chern numbers (quantum Hall conductance integers) for a parametric version of the GUE random matrix ensemble, which is a model for a chaotic or disordered system. The numerically-calculated single-band Chern number statistics agree well with predictions based on an earlier study [O. Gat and M. Wilkinson, SciPost Phys., 10, 149, (2021)] of the statistics of the quantum adiabatic curvature, when the parametric correlation length is small. However, contrary to an earlier conjecture, we find that the gap Chern numbers are correlated, and that the correlation is weak but slowly-decaying. Also, the statistics of weighted sums of Chern numbers differs markedly from predictions based upon the hypothesis that gap Chern numbers are uncorrelated. All our results are consistent with the universality hypothesis described in the earlier paper, including in the previously unstudied regime of large correlation length, where the Chern statistics is highly non-Gaussian.

  1 citation

• Bloch-Lorentz magnetoresistance oscillations in delafossites

  Kostas Vilkelis, Lin Wang, Anton Akhmerov

  SciPost Phys. 15, 019 (2023) · published 20 July 2023 | Toggle abstract · pdf

  Recent measurements of the out-of-plane magnetoresistance of delafossites (PdCoO$_2$ and PtCoO$_2$) observed oscillations closely resembling the Aharonov-Bohm effect. Here, we show that the magnetoresistance oscillations are explained by the Bloch-like oscillations of the out-of-plane electron trajectories. We develop a semiclassical theory of these Bloch-Lorentz oscillations and show that they are a consequence of the ballistic motion and quasi-2D dispersion of delafossites. Our model identifies the sample wall scattering to be the most likely factor limiting the visibility of these Bloch-Lorentz oscillations in existing experiments.

  1 citation

• Quenched random mass disorder in the large N theory of vector bosons

  Han Ma

  SciPost Phys. 14, 039 (2023) · published 17 March 2023 | Toggle abstract · pdf

  We study the critical bosonic O(N) vector model with quenched random mass disorder in the large N limit. Due to the replicated action which is sometimes not bounded from below, we avoid the replica trick and adopt a traditional approach to directly compute the disorder averaged physical observables. At $N=\infty$, we can exactly solve the disordered model. The resulting low energy behavior can be described by two scale invariant theories, one of which has an intrinsic scale. At finite $N$, we find that the previously proposed attractive disordered fixed point at $d=2$ continues to exist at $d=2+\epsilon$ spatial dimensions. We also studied the system in the $3<d<4$ spatial dimensions where the disorder is relevant at the Gaussian fixed point. However, no physical attractive fixed point is found right below four spatial dimensions. Nevertheless, the stable fixed point at $2+\epsilon$ dimensions can still survive at $d=3$ where the system has experimental realizations. Some critical exponents are predicted in order to be checked by future numerics and experiments.

  1 citation

• Random circuits in the black hole interior

  Javier M. Magan, Martin Sasieta, Brian Swingle

  SciPost Phys. 19, 007 (2025) · published 3 July 2025 | Toggle abstract · pdf

  We present a quantitative holographic relation between a microscopic measure of randomness and the geometric length of the wormhole in the black hole interior. To this end, we perturb an AdS black hole with Brownian semiclassical sources, implementing the continuous version of a random quantum circuit for the black hole. We use the random circuit to prepare ensembles of states of the black hole whose semiclassical duals contain Einstein-Rosen (ER) caterpillars: Long cylindrical wormholes with large numbers of matter inhomogeneities, of linearly growing length with the circuit time. In this setup, we show semiclassically that the ensemble of ER caterpillars of average length $k\ell_{\Delta}$ and matter correlation scale $\ell_{\Delta}$ forms an approximate quantum state $k$-design of the black hole. At exponentially long circuit times, the ensemble of ER caterpillars becomes polynomial-copy indistinguishable from a collection of random states of the black hole. We comment on the implications of these results for holographic circuit complexity and for the holographic description of the black hole interior.

  1 citation

• Low-temperature electron mobility in doped semiconductors with high dielectric constant

  Khachatur G. Nazaryan, Mikhail Feigel'man

  SciPost Phys. 14, 046 (2023) · published 23 March 2023 | Toggle abstract · pdf

  We propose and study theoretically a new mechanism of electron-impurity scattering in doped seminconductors with large dielectric constant. It is based upon the idea of vector character of deformations caused in the crystalline lattice by any point defects siting asymmetrically in the unit cell. In result, local lattice compression due to the elastic deformations decay as $1/r^2$ with distance from impurity. Electron scattering (due to standard deformation potential) on such defects leads to low-temperature mobility $\mu(n)$ scaling with electron density $n$ of the form $\mu(n) \propto n^{-2/3}$ that is close to experimental observations on a number of relevant materials.

  1 citation

• Generating long-distance magnetic couplings with flat bands

  Georges Bouzerar, Maxime Thumin

  SciPost Phys. 19, 011 (2025) · published 8 July 2025 | Toggle abstract · pdf

  One of the great challenges for the large-scale development of quantum technologies is to generate and control the entanglement of quantum bits through interactions of sufficiently long range. Two decades ago, spin chains have been proposed for quantum communication. Unfortunately, couplings are of very short range in general which drastically limits the communication to very short distances. Here, we demonstrate that the presence of flat bands (FBs) can trigger very long-distance magnetic couplings in spin chains. Furthermore, we show that the typical decaying lengthscale is directly related to the quantum metric of the flat band eigenstates. We have validated the robustness of our results in the case where flat bands become weakly dispersive. We believe that our unexpected findings could open up an alternative route to enable long-distance quantum communication.

  1 citation

• Classifying irreducible fixed points of five scalar fields in perturbation theory

  Junchen Rong, Slava Rychkov

  SciPost Phys. 16, 040 (2024) · published 1 February 2024 | Toggle abstract · pdf

  Classifying perturbative fixed points near upper critical dimensions plays an important role in understanding the space of conformal field theories and critical phases of matter. In this work, we consider perturbative fixed points of N=5 scalar bosons coupled with quartic interactions preserving an arbitrary subgroup $G\subset O(5)$. We perform an exhaustive algorithmic search over the symmetry groups G which are irreducible and satisfy the Landau condition, so that the fixed point can be reached by fine-tuning a single mass term and there is no need to tune the cubic couplings. We also impose stability of the RG flow in the space of quartic couplings, and reality. We thus prove that there exist no new stable fixed points in d=4-$\epsilon$ dimensions beyond the two known ones: namely the O(5) nvariant fixed point and the Cubic(5) fixed point. This work is a continuation of the classification of such fixed points with N=4 scalars by Toledano, Michel, Toledano and Brézin in 1985 [Phys. Rev. B 31, 7171 (1985)].

  1 citation

• Quasi-particle functional renormalisation group calculations in the two-dimensional t-t'-Hubbard model

  Daniel Rohe

  SciPost Phys. 15, 192 (2023) · published 13 November 2023 | Toggle abstract · pdf

  We extend and apply a recently introduced quasi-particle functional renormalisation group scheme to the two-dimensional Hubbard model with next-nearest-neighbour hopping and away from half filling. We confirm the generation of superconducting correlations in some regions of the phase diagram, but also find that the inclusion of self-energy feedback by means of a decreasing quasi-particle weight can suppress superconducting tendencies more than anti-ferromagnetic correlations by which they are generated. As a supplement, we provide sample results for the self-energy in second-order perturbation theory and address some conceptual matters.

  1 citation

• Particle dynamics on torsional galilean spacetimes

  José Figueroa-O'Farrill, Can Görmez, Dieter Van den Bleeken

  SciPost Phys. 14, 059 (2023) · published 4 April 2023 | Toggle abstract · pdf

  We study free particle motion on homogeneous kinematical spacetimes of galilean type. The three well-known cases of Galilei and (A)dS-Galilei spacetimes are included in our analysis, but our focus will be on the previously unexplored torsional galilean spacetimes. We show how in well-chosen coordinates free particle motion becomes equivalent to the dynamics of a damped harmonic oscillator, with the damping set by the torsion. The realization of the kinematical symmetry algebra in terms of conserved charges is subtle and comes with some interesting surprises, such as a homothetic version of hamiltonian vector fields and a corresponding generalization of the Poisson bracket. We show that the Bargmann extension is universal to all galilean kinematical symmetries, but also that it is no longer central for nonzero torsion. We also present a geometric interpretation of this fact through the Eisenhart lift of the dynamics.

  1 citation