Publications

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Krylov complexity in a natural basis for the Schrödinger algebra

Dimitrios Patramanis, Watse Sybesma

SciPost Phys. Core 7, 037 (2024) · published 20 June 2024 | · 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.
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 | · 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.
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 | · 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 | · 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.
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 | · 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.
Efficient qudit based scheme for photonic quantum computing

Márton Karácsony, László Oroszlány, Zoltan Zimboras

SciPost Phys. Core 7, 032 (2024) · published 3 June 2024 | · 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.
Incorporating non-local anyonic statistics into a graph decomposition

Matthias Mühlhauser, Viktor Kott, Kai Phillip Schmidt

SciPost Phys. Core 7, 031 (2024) · published 30 May 2024 | · pdf

In this work we describe how to systematically implement a full graph decomposition to set up a linked-cluster expansion for the topological phase of Kitaev's toric code in a field. This demands to include the non-local effects mediated by the mutual anyonic statistics of elementary charge and flux excitations. Technically, we describe how to consistently integrate such non-local effects into a hypergraph decomposition for single excitations. The approach is demonstrated for the ground-state energy and the elementary excitation energies of charges and fluxes in the perturbed topological phase.
Ground state of the staggered Heisenberg-Γ honeycomb model in a magnetic field

Mojtaba Ahmadi-Yazdi, Mohammad-Hossein Zare, Hamid Mosadeq, Farhad Fazileh

SciPost Phys. Core 7, 030 (2024) · published 15 May 2024 | · pdf

We study the ground state properties of the S=1/2 staggered Heisenberg-$\Gamma$ honeycomb model under a magnetic field based on analytical and numerical methods. Our calculations show that the conventional zigzag and stripy phases are favored because of the staggered Heisenberg interaction away from the pure $\Gamma$ limit. In our classical analysis, we find that the field induces a series of competing magnetic phases with relatively large unit cells in the region sandwiched between the two magnetic phases with long-range ordering. In the quantum treatment, these large magnetic unit cells are destabilized by strong quantum fluctuations that result in the stabilization of a gapless quantum spin liquid behavior. In a honeycomb $\Gamma$ magnet, we disclose an intermediate-field gapless quantum spin liquid phase driven by a tilted field away from the out-of-plane direction only for a narrow region between the low-field zigzag and high-field fully polarized phases.
Quantum revivals in HgTe/CdTe quantum wells and topological phase transitions

Alberto Mayorgas, Manuel Calixto, Nicolás A. Cordero, Elvira Romera, Octavio Héctor Castaños Garza

SciPost Phys. Core 7, 029 (2024) · published 13 May 2024 | · pdf

The time evolution of a wave packet is a tool to detect topological phase transitions in two-dimensional Dirac materials, such as graphene and silicene. Here we extend the analysis to HgTe/CdTe quantum wells and study the evolution of their electron current wave packet, using 2D effective Dirac Hamiltonians and different layer thicknesses. We show that the two different periodicities that appear in this temporal evolution reach a minimum near the critical thickness, where the system goes from normal to inverted regime. Moreover, the maximum of the electron current amplitude changes with the layer thickness, identifying that current maxima reach their higher value at the critical thickness. Thus, we can characterize the topological phase transitions in terms of the periodicity and amplitude of the electron currents.
Quantum Monte Carlo simulation of the 3D Ising transition on the fuzzy sphere

Johannes Stephan Hofmann, Florian Goth, Wei Zhu, Yin-Chen He, Emilie Huffman

SciPost Phys. Core 7, 028 (2024) · published 9 May 2024 | · pdf

We present a numerical quantum Monte Carlo (QMC) method for simulating the 3D phase transition on the recently proposed fuzzy sphere [Phys. Rev. X 13, 021009 (2023)]. By introducing an additional SU(2) layer degree of freedom, we reformulate the model into a form suitable for sign-problem-free QMC simulation. From the finite-size-scaling, we show that this QMC-friendly model undergoes a quantum phase transition belonging to the 3D Ising universality class, and at the critical point we compute the scaling dimensions from the state-operator correspondence, which largely agrees with the prediction from the conformal field theory. These results pave the way to construct sign-problem-free models for QMC simulations on the fuzzy sphere, which could advance the future study on more sophisticated criticalities.

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