Publications

Order by: publication date number of citations

• Quantum phases of hardcore bosons with repulsive dipolar density-density interactions on two-dimensional lattices

  J. A. Koziol, G. Morigi, K. P. Schmidt

  SciPost Phys. 17, 111 (2024) · published 10 October 2024 | Toggle abstract · pdf

  We analyse the ground-state quantum phase diagram of hardcore Bosons interacting with repulsive dipolar potentials. The bosons dynamics is described by the extended-Bose-Hubbard Hamiltonian on a two-dimensional lattice. The ground state results from the interplay between the lattice geometry and the long-range interactions, which we account for by means of a classical spin mean-field approach limited by the size of the considered unit cells. This extended classical spin mean-field theory accounts for the long-range density-density interaction without truncation. We consider three different lattice geometries: square, honeycomb, and triangular. In the limit of zero hopping the ground state is always a devil's staircase of solid (gapped) phases. Such crystalline phases with broken translational symmetry are robust with respect to finite hopping amplitudes. At intermediate hopping amplitudes, these gapped phases melt, giving rise to various lattice supersolid phases, which can have exotic features with multiple sublattice densities. At sufficiently large hoppings the ground state is a superfluid. The stability of phases predicted by our approach is gauged by comparison to the known quantum phase diagrams of the Bose-Hubbard model with nearest-neighbour interactions as well as quantum Monte Carlo simulations for the dipolar case on the square and triangular lattice. Our results are of immediate relevance for experimental realisations of self-organised crystalline ordering patterns in analogue quantum simulators, e.g., with ultracold dipolar atoms in an optical lattice.

  5 citations

• High temperature series expansions of S = 1/2 Heisenberg spin models: Algorithm to include the magnetic field with optimized complexity

  Laurent Pierre, Bernard Bernu, Laura Messio

  SciPost Phys. 17, 105 (2024) · published 7 October 2024 | Toggle abstract · pdf

  This work presents an algorithm for calculating high temperature series expansions (HTSE) of Heisenberg spin models with spin $S=1/2$ in the thermodynamic limit. This algorithm accounts for the presence of a magnetic field. The paper begins with a comprehensive introduction to HTSE and then focuses on identifying the bottlenecks that limit the computation of higher order coefficients. HTSE calculations involve two key steps: graph enumeration on the lattice and trace calculations for each graph. The introduction of a non-zero magnetic field adds complexity to the expansion because previously irrelevant graphs must now be considered: bridged graphs. We present an efficient method to deduce the contribution of these graphs from the contribution of sub-graphs, that drastically reduces the time of calculation for the last order coefficient (in practice increasing by one the order of the series at almost no cost). Previous articles of the authors have utilized HTSE calculations based on this algorithm, but without providing detailed explanations. The complete algorithm is publicly available, as well as the series on many lattice and for various interactions.

  5 citations

• Supersymmetry and multicriticality in a ladder of constrained fermions

  Natalia Chepiga, Jiří Minář, Kareljan Schoutens

  SciPost Phys. 11, 059 (2021) · published 16 September 2021 | Toggle abstract · pdf

  Supersymmetric lattice models of constrained fermions are known to feature exotic phenomena such as superfrustration, with an extensive degeneracy of ground states, the nature of which is however generally unknown. Here we address this issue by considering a superfrustrated model, which we deform from the supersymetric point. By numerically studying its two-parameter phase diagram, we reveal a rich phenomenology. The vicinity of the supersymmetric point features period-4 and period-5 density waves which are connected by a floating phase (incommensurate Luttinger liquid) with smoothly varying density. The supersymmetric point emerges as a multicritical point between these three phases. Inside the period-4 phase we report a valence-bond solid type ground state that persists up to the supersymmetric point. Our numerical data for transitions out of density-wave phases are consistent with the Pokrovsky-Talapov universality class. Furthermore, our analysis unveiled a period-3 phase with a boundary determined by a competition between single and two-particle instabilities accompanied by a doubling of the wavevector of the density profiles along a line in the phase diagram.

  5 citations

• Quantum spin spiral ground state of the ferrimagnetic sawtooth chain

  Roman Rausch, Matthias Peschke, Cassian Plorin, Jürgen Schnack, Christoph Karrasch

  SciPost Phys. 14, 052 (2023) · published 28 March 2023 | Toggle abstract · pdf

  The ferrimagnetic phase of the sawtooth chain with mixed ferromagnetic nearest-neighbour interactions $J$ and antiferromagnetic next-nearest-neighbour interactions $J'$ (within the isotropic Heisenberg model) was previously characterized as a phase with commensurate order. In this paper, we demonstrate that the system in fact exhibits an incommensurate quantum spin spiral. Even though the ground state is translationally invariant in terms of the local spin expectations $\left<{\vec{S}_i}\right>$, the spiral can be detected via the connected spin-spin correlations $\left<{\vec{S}_i\cdot\vec{S}_j}\right>-\left<{\vec{S}_i}\right>\cdot\left<{\vec{S}_j}\right>$ between the apical spins. It has a long wavelength that grows with $J'$ and that soon exceeds finite-system sizes typically employed in numerical simulations. A faithful treatment thus requires the use of state-of-the-art simulations for large, periodic systems. In this work, we are able to accurately treat up to $L=400$ sites (200 unit cells) with periodic boundary conditions using the density-matrix renormaliztion group (DMRG). Exploiting the SU(2) symmetry allows us to directly compute the lowest-energy state for a given total spin. Our results are corroborated by variational uniform matrix product state (VUMPS) calculations, which work directly in the thermodynamic limit at the cost of a lower accuracy.

  4 citations

• QArray: A GPU-accelerated constant capacitance model simulator for large quantum dot arrays

  Barnaby van Straaten, Joseph Hickie, Lucas Schorling, Jonas Schuff, Federico Fedele, Natalia Ares

  SciPost Phys. Codebases 35 (2024) · published 21 October 2024 | Toggle abstract · pdf

  Semiconductor quantum dot arrays are a leading architecture for the development of quantum technologies. Over the years, the constant capacitance model has served as a fundamental framework for simulating, understanding, and navigating the charge stability diagrams of small quantum dot arrays. However, while the size of the arrays keeps growing, solving the constant capacitance model becomes computationally prohibitive. This paper presents an open-source software package able to compute a $100 × 100$ pixels charge stability diagram of a 16-dot array in less than a second. Smaller arrays can be simulated in milliseconds - faster than they could be measured experimentally, enabling the creation of diverse datasets for training machine learning models and the creation of digital twins that can interface with quantum dot devices in real-time. Our software package implements its core functionalities in the systems programming language Rust and the high-performance numerical computing library JAX. The Rust implementation benefits from advanced optimisations and parallelisation, enabling the users to take full advantage of multi-core processors. The JAX implementation allows for GPU acceleration.

  4 citations

• Quantifying uncertainties in crystal electric field Hamiltonian fits to neutron data

  Allen Scheie

  SciPost Phys. Core 5, 018 (2022) · published 31 March 2022 | Toggle abstract · pdf

  We systematically examine uncertainties from fitting rare earth single-ion crystal electric field (CEF) Hamiltonians to inelastic neutron scattering data. Using pyrochlore and delafossite structures as test cases, we find that uncertainty in CEF parameters can be large despite visually excellent fits. These results show Yb$^{3+}$ compounds have particularly large $g$-tensor uncertainty because of the few available peaks. In such cases, additional constraints are necessary for meaningful fits.

  4 citations

• Tensor network variational optimizations for real-time dynamics: Application to the time-evolution of spin liquids

  Ravi Teja Ponnaganti, Matthieu Mambrini, Didier Poilblanc

  SciPost Phys. 15, 158 (2023) · published 12 October 2023 | Toggle abstract · pdf

  Within the Projected Entangled Pair State (PEPS) tensor network formalism, a simple update (SU) method has been used to investigate the time evolution of a two-dimensional U(1) critical spin-1/2 spin liquid under Hamiltonian quench [Phys. Rev. B 106, 195132 (2022)]. Here we introduce two different variational frameworks to describe the time dynamics of SU(2)-symmetric translationally-invariant PEPS, aiming to improve the accuracy. In one approach, after using a Trotter-Suzuki decomposition of the time evolution operator in term of two-site elementary gates, one considers a single bond embedded in an environment approximated by a Corner Transfer Matrix Renormalization Group (CTMRG). A variational update of the two tensors on the bond is performed under the application of the elementary gate and then, after symmetrization of the site tensors, the environment is updated. In the second approach, a cluster optimization is performed on a finite (periodic) cluster, maximizing the overlap of the exact time-evolved state with a symmetric finite-size PEPS ansatz. Observables are then computed on the infinite lattice contracting the infinite-PEPS (iPEPS) by CTMRG. We show that the variational schemes outperform the SU method and remain accurate over a significant time interval before hitting the entanglement barrier. Studying the spectrum of the transfer matrix, we find that the asymptotic correlations are very well preserved under time evolution, including the critical nature of the singlet correlations, as expected from the Lieb-Robinson (LR) bound theorem. Consistently, the system (asymptotic) boundary is found to be described by the same Conformal Field Theory of central charge $c = 1$ during time evolution. We also compute the time-evolution of the short distance spin-spin correlations and estimate the LR velocity.

  4 citations

• Detection of Berezinskii-Kosterlitz-Thouless transition via Generative Adversarial Networks

  Daniele Contessi, Elisa Ricci, Alessio Recati, Matteo Rizzi

  SciPost Phys. 12, 107 (2022) · published 25 March 2022 | Toggle abstract · pdf

  The detection of phase transitions in quantum many-body systems with lowest possible prior knowledge of their details is among the most rousing goals of the flourishing application of machine-learning techniques to physical questions. Here, we train a Generative Adversarial Network (GAN) with the Entanglement Spectrum of a system bipartition, as extracted by means of Matrix Product States ans\"atze. We are able to identify gapless-to-gapped phase transitions in different one-dimensional models by looking at the machine inability to reconstruct outsider data with respect to the training set. We foresee that GAN-based methods will become instrumental in anomaly detection schemes applied to the determination of phase-diagrams.

  4 citations

• Pressure-dependent structural and electronic instabilities in LaSb$_2$

  Theodore I. Weinberger, Christian K. de Podesta, Jiasheng Chen, Stephen A. Hodgson, F. Malte Grosche

  SciPost Phys. Proc. 11, 018 (2023) · published 6 June 2023 | Toggle abstract · pdf

  LaSb$_2$ exhibits a large, non-saturating, linear magnetoresistance at low temperatures, defying the expectations of Fermi liquid theory. This is thought to be caused by charge density wave order emerging below an abrupt, hysteretic anomaly in the resistivity at $\sim$ 355 K. We find that, under hydrostatic pressure, this anomaly becomes much more pronounced, develops strong hysteresis, and shifts rapidly towards lower temperatures. The anomaly is fully suppressed by only 6 kbar. Moreover, we observe a second transition anomaly at lower temperature, which likewise disappears under pressure. These findings are discussed in the context of a structural transition recently discovered in the sister material CeSb$_2$ and of density functional theory calculations, which indicate that the SmSb$_2$-type structure adopted by LaSb$_2$ at ambient conditions is unstable at moderate applied pressures.

  4 citations

• A time-dependent momentum-resolved scattering approach to core-level spectroscopies

  Krissia Zawadzki, Alberto Nocera, Adrian E. Feiguin

  SciPost Phys. 15, 166 (2023) · published 17 October 2023 | Toggle abstract · pdf

  While new light sources allow for unprecedented resolution in experiments with X-rays, a theoretical understanding of the scattering cross-section is lacking. In the particular case of strongly correlated electron systems, numerical techniques are quite limited, since conventional approaches rely on calculating a response function (Kramers-Heisenberg formula) that is obtained from a perturbative analysis of scattering processes in the frequency domain. This requires a knowledge of a full set of eigenstates in order to account for all intermediate processes away from equilibrium, limiting the applicability to small tractable systems. In this work, we present an alternative paradigm, recasting the problem in the time domain and explicitly solving the time-dependent Schrödinger equation without the limitations of perturbation theory: a faithful simulation of the scattering processes taking place in actual experiments, including photons and core electrons. We show how this approach can yield the full time and momentum resolved Resonant Inelastic X-Ray Scattering (RIXS) spectrum of strongly interacting many-body systems. We demonstrate the formalism with an application to Mott insulating Hubbard chains using the time-dependent density matrix renormalization group method, which does not require a priory knowledge of the eigenstates and can solve very large systems with dozens of orbitals. This approach can readily be applied to systems out of equilibrium without modification and generalized to other spectroscopies.

  4 citations