Publications

Order by: publication date number of citations

• Spectral solutions for the Schrödinger equation with a regular singularity

  Pushkar Mohile, Ayaz Ahmed, T. R. Vishnu, Pichai Ramadevi

  SciPost Phys. Core 7, 041 (2024) · published 5 July 2024 | Toggle abstract · pdf

  We propose a modification in the Bethe-like ansatz to reproduce the hydrogen atom spectrum and the wave functions. Such a proposal provided a clue to attempt the exact quantization condition (EQC) for the quantum periods associated with potentials $V(x)$ which are of the form $(V(x) = |x| + a/|x| + b/|x|^2 )$. We validate the EQC proposal by showing that our computed Voros spectrum in the limit $a,b → 0$ is matching well with the true spectrum of the familiar $|x|$ potential. Thus we have given a route to obtain the spectral solution for the one dimensional Schrödinger equation involving potentials with regular singularity at the origin.

• Exact Mazur bounds in the pair-flip model and beyond

  Oliver Hart

  SciPost Phys. Core 7, 040 (2024) · published 4 July 2024 | Toggle abstract · pdf

  By mapping the calculation of Mazur bounds to the enumeration of walks on fractal structures, we present exact bounds on the late-time behavior of spin autocorrelation functions in models exhibiting pair-flip dynamics and more general $p$-flip dynamics. While the pair-flip model is known to exhibit strong Hilbert space fragmentation, the effect of its nontrivial conservation laws on autocorrelation functions has, thus far, only been calculated numerically, which has led to incorrect conclusions about their thermodynamic behavior. Here, using exact results, we prove that infinite-temperature autocorrelation functions exhibit infinite coherence times at the boundary, and that bulk Mazur bounds decay asymptotically as $1/\sqrt{L}$, rather than $1/L$, as had previously been thought. This result implies that the nontrivial conserved operators implied by $p$-flip dynamics have an important qualitative impact on bulk thermalization properties beyond the constraints imposed by the simple global symmetries of the models.

  3 citations

• THz higher-order topological photonics in Ge-on-Si heterostructures

  Ian Colombo, Pietro Minazzi, Emiliano Bonera, Fabio Pezzoli, Jacopo Pedrini

  SciPost Phys. Core 7, 039 (2024) · published 4 July 2024 | Toggle abstract · pdf

  We design germanium-based higher-order topological cavities for terahertz applications by breaking the symmetry of a two-dimensional photonic crystal following the Su-Schrieffer-Heeger model. Calculations demonstrate the parity inversion of the electric field in differently deformed unit cells. The interface between domains of opposite topology presents edge and corner modes. The former are chiral, locking light propagation to its helicity. The latter prove that Ge-based structures can be used as high-order topological photonic crystals. These findings can accelerate the development of Si-photonic components working in a spectral range of high technological interest.

• (Almost) everything is a Dicke model - Mapping non-superradiant correlated light-matter systems to the exactly solvable Dicke model

  Andreas Schellenberger, Kai Phillip Schmidt

  SciPost Phys. Core 7, 038 (2024) · published 2 July 2024 | Toggle abstract · pdf

  We investigate classes of interacting quantum spin systems in a single-mode cavity with a Dicke coupling, as a paradigmatic example of strongly correlated light-matter systems. Coming from the limit of weak light-matter couplings and large number of matter entities, we map the relevant low-energy sector of a broad class of models in the non-superradiant phases onto the exactly solvable Dicke model. We apply the outcomes to the Dicke-Ising model as a paradigmatic example [Phys. Rev. Res. 2, 023131 (2020), Sci. Rep. 4, 4083 (2014)], in agreement with results obtained by mean-field theory [Sci. Rep. 4, 4083 (2014)]. We further accompany and verify our findings with finite-size calculations, using exact diagonalization and the series expansion method pcst$^{++}$ [Phys. Rev. A 108, 013323 (2023)]

  7 citations

• Krylov complexity in a natural basis for the Schrödinger algebra

  Dimitrios Patramanis, Watse Sybesma

  SciPost Phys. Core 7, 037 (2024) · published 20 June 2024 | Toggle abstract · pdf

  We investigate operator growth in quantum systems with two-dimensional Schrödinger group symmetry by studying the Krylov complexity. While feasible for semisimple Lie algebras, cases such as the Schrödinger algebra which is characterized by a semi-direct sum structure are complicated. We propose to compute Krylov complexity for this algebra in a natural orthonormal basis, which produces a pentadiagonal structure of the time evolution operator, contrasting the usual tridiagonal Lanczos algorithm outcome. The resulting complexity behaves as expected. We advocate that this approach can provide insights to other non-semisimple algebras.

  4 citations

• State diagrams to determine tree tensor network operators

  Richard M. Milbradt, Qunsheng Huang, Christian B. Mendl

  SciPost Phys. Core 7, 036 (2024) · published 19 June 2024 | Toggle abstract · pdf

  This work is concerned with tree tensor network operators (TTNOs) for representing quantum Hamiltonians. We first establish a mathematical framework connecting tree topologies with state diagrams. Based on these, we devise an algorithm for constructing a TTNO given a Hamiltonian. The algorithm exploits the tensor product structure of the Hamiltonian to add paths to a state diagram, while combining local operators if possible. We test the capabilities of our algorithm on random Hamiltonians for a given tree structure. Additionally, we construct explicit TTNOs for nearest neighbour interactions on a tree topology. Furthermore, we derive a bound on the bond dimension of tensor operators representing arbitrary interactions on trees. Finally, we consider an open quantum system in the form of a Heisenberg spin chain coupled to bosonic bath sites as a concrete example. We find that tree structures allow for lower bond dimensions of the Hamiltonian tensor network representation compared to a matrix product operator structure. This reduction is large enough to reduce the number of total tensor elements required as soon as the number of baths per spin reaches 3.

  6 citations

• Rapid measurements and phase transition detections made simple by AC-GANs

  Jiewei Ding, Ho-Kin Tang, Wing Chi Yu

  SciPost Phys. Core 7, 035 (2024) · published 11 June 2024 | Toggle abstract · pdf

  In recent years, significant attention has been paid to using end-to-end neural networks for analyzing Monte Carlo data. However, the exploration of non-end-to-end generative adversarial neural networks remains limited. Here, we investigate classical many-body systems using generative adversarial neural networks. We employ the conditional generative adversarial network with an auxiliary classifier (AC-GAN) and integrate self-attention layers into the generator. This modification enables the network learn the distribution of the two-dimensional (2D) XY model's spin configurations and the physical quantities of interest. Utilizing the symmetry of the systems, we discover that AC-GAN can be trained with a very small raw dataset. This approach allows us to obtain reliable measurements for models typically demanding large samples, such as the large-sized 2D XY and the 3D constrained Heisenberg models. Moreover, we demonstrate the capability of AC-GAN to identify the phase transition points by quantifying the distribution changes in the spin configurations of the systems.

• Matrix method and the suppression of Runge's phenomenon

  Shui-Fa Shen, Wei-Liang Qian, Jie Zhang, Yu Pan, Yu-Peng Yan, Cheng-Gang Shao

  SciPost Phys. Core 7, 034 (2024) · published 5 June 2024 | Toggle abstract · pdf

  Higher-degree polynomial interpolations carried out on uniformly distributed nodes are often plagued by overfitting, known as Runge's phenomenon. This work investigates Runge's phenomenon and its suppression in various versions of the matrix method for black hole quasinormal modes. It is shown that an appropriate choice of boundary conditions gives rise to desirable suppression of oscillations associated with the increasing Lebesgue constant. For the case of discontinuous effective potentials, where the application of the above boundary condition is not feasible, the recently proposed scheme with delimited expansion domain also leads to satisfactory results. The onset of Runge's phenomenon and its effective suppression are demonstrated by evaluating the relevant waveforms. Furthermore, we argue that both scenarios are either closely related to or practical imitations of the Chebyshev grid. The implications of the present study are also addressed.

  4 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

• Efficient qudit based scheme for photonic quantum computing

  Márton Karácsony, László Oroszlány, Zoltan Zimboras

  SciPost Phys. Core 7, 032 (2024) · published 3 June 2024 | Toggle abstract · pdf

  Linear optics is a promising alternative for the realization of quantum computation protocols due to the recent advancements in integrated photonic technology. In this context, usually qubit based quantum circuits are considered, however, photonic systems naturally allow also for d-ary, i.e., qudit based, algorithms. This work investigates qudits defined by the possible photon number states of a single photon in d > 2 optical modes. We demonstrate how to construct locally optimal non-deterministic many-qudit gates using linear optics and photon number resolving detectors, and explore the use of qudit cluster states in the context of a d-ary optimization problem. We find that the qudit cluster states require less optical modes and are encoded by a fewer number of entangled photons than the qubit cluster states with similar computational capabilities. We illustrate the benefit of our qudit scheme by applying it to the k-coloring problem.

  10 citations