Publications

Order by: publication date number of citations

• Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function

  Hiroshi Shinaoka, Naoya Chikano, Emanuel Gull, Jia Li, Takuya Nomoto, Junya Otsuki, Markus Wallerberger, Tianchun Wang, Kazuyoshi Yoshimi

  SciPost Phys. Lect. Notes 63 (2022) · published 22 September 2022 | Toggle abstract · pdf

  This lecture note reviews recently proposed sparse-modeling approaches for efficient ab initio many-body calculations based on the data compression of Green's functions. The sparse-modeling techniques are based on a compact orthogonal basis, an intermediate representation (IR) basis, for imaginary-time and Matsubara Green's functions. A sparse sampling method based on the IR basis enables solving diagrammatic equations efficiently. We describe the basic properties of the IR basis, the sparse sampling method and its applications to ab initio calculations based on the GW approximation and the Migdal-Eliashberg theory. We also describe a numerical library for the IR basis and the sparse sampling method, sparse-ir, and provide its sample codes. This lecture note follows the Japanese review article with major revisions [H. Shinaoka et al., Solid State Physics 56(6), 301 (2021)].

  12 citations

• Topological to magnetically ordered quantum phase transition in antiferromagnetic spin ladders with long-range interactions

  Luhang Yang, Phillip Weinberg, Adrian E. Feiguin

  SciPost Phys. 13, 060 (2022) · published 21 September 2022 | Toggle abstract · pdf

  We study a generalized quantum spin ladder with staggered long range interactions that decay as a power-law with exponent $\alpha$. Using large scale quantum Monte Carlo (QMC) and density matrix renormalization group (DMRG) simulations, we show that this model undergoes a transition from a rung-dimer phase characterized by a non-local string order parameter, to a symmetry broken N\'eel phase. We find evidence that the transition is second order. In the magnetically ordered phase, the spectrum exhibits gapless modes, while excitations in the gapped phase are well described in terms of triplons -- bound states of spinons across the legs. We obtain the momentum resolved spin dynamic structure factor numerically and find a well defined triplon band that evolves into a gapless magnon dispersion across the transition. We further discuss the possibility of deconfined criticality in this model.

  4 citations

• Rapid detection of phase transitions from Monte Carlo samples before equilibrium

  Jiewei Ding, Ho-Kin Tang, Wing Chi Yu

  SciPost Phys. 13, 057 (2022) · published 9 September 2022 | Toggle abstract · pdf

  We found that Bidirectional LSTM and Transformer can classify different phases of condensed matter models and determine the phase transition points by learning features in the Monte Carlo raw data before equilibrium. Our method can significantly reduce the time and computational resources required for probing phase transitions as compared to the conventional Monte Carlo simulation. We also provide evidence that the method is robust and the performance of the deep learning model is insensitive to the type of input data (we tested spin configurations of classical models and green functions of a quantum model), and it also performs well in detecting Kosterlitz–Thouless phase transitions.

• Topological multiferroic order in twisted transition metal dichalcogenide bilayers

  Mikael Haavisto, J. L. Lado, Adolfo Otero Fumega

  SciPost Phys. 13, 052 (2022) · published 5 September 2022 | Toggle abstract · pdf

  Layered van der Waals materials have risen as powerful platforms to artificially engineer correlated states of matter. Here we show the emergence of a multiferroic order in a twisted dichalcogenide bilayer superlattice at quarter-filling. We show that the competition between Coulomb interactions leads to the simultaneous emergence of ferrimagnetic and ferroelectric orders. We derive the magnetoelectric coupling for this system, which leads to a direct strong coupling between the charge and spin orders. We show that, due to intrinsic spin-orbit coupling effects, the electronic structure shows a non-zero Chern number, thus displaying a topological multiferroic order. We show that this topological state gives rise to interface modes at the different magnetic and ferroelectric domains of the multiferroic. We demonstrate that these topological modes can be tuned with external electric fields as well as triggered by supermoire effects generated by a substrate. Our results put forward twisted van der Waals materials as a potential platform to explore multiferroic symmetry breaking orders and, ultimately, controllable topological excitations in magnetoelectric domains.

  10 citations

• Noncoplanar magnetic orders and gapless chiral spin liquid on the kagome lattice with staggered scalar spin chirality

  Fabrizio Oliviero, João Augusto Sobral, Eric C. Andrade, Rodrigo G. Pereira

  SciPost Phys. 13, 050 (2022) · published 5 September 2022 | Toggle abstract · pdf

  Chiral three-spin interactions can suppress long-range magnetic order and stabilize quantum spin liquid states in frustrated lattices. We study a spin-1/2 model on the kagome lattice involving a staggered three-spin interaction $J_\chi$ in addition to Heisenberg exchange couplings $J_1$ on nearest-neighbor bonds and $J_d$ across the diagonals of the hexagons. We explore the phase diagram using a combination of a classical approach, parton mean-field theory, and variational Monte Carlo methods. We obtain a variety of noncoplanar magnetic orders, including a phase that interpolates between cuboc-1 and cuboc-2 states. In the regime of dominant $J_{\chi}$, we find a classically disordered region and argue that it may harbor a gapless chiral spin liquid with a spinon Fermi surface. Our results show that the competition between the staggered three-spin interaction and Heisenberg exchange interactions gives rise to unusual ground states of spin systems.

  5 citations

• Charge order and antiferromagnetism in twisted bilayer graphene from the variational cluster approximation

  B. Pahlevanzadeh, P. Sahebsara, D. Sénéchal

  SciPost Phys. 13, 040 (2022) · published 30 August 2022 | Toggle abstract · pdf

  We study the possibility of charge order at quarter filling and antiferromagnetism at half-filling in a tight-binding model of magic angle twisted bilayer graphene. We build on the model proposed by Kang and Vafek, relevant to a twist angle of $1.30^\circ$, and add on-site and extended density-density interactions. Applying the variational cluster approximation with an exact-diagonalization impurity solver, we find that the system is indeed a correlated (Mott) insulator at fillings $\frac14$, $\frac12$ and $\frac34$. At quarter filling, we check that the most probable charge orders do not arise, for all values of the interaction tested. At half-filling, antiferromagnetism only arises if the local repulsion $U$ is sufficiently large compared to the extended interactions, beyond what is expected from the simplest model of extended interactions.

  2 citations

• Quantum dynamics in 1D lattice models with synthetic horizons

  Corentin Morice, Dmitry Chernyavsky, Jasper van Wezel, Jeroen van den Brink, Ali G. Moghaddam

  SciPost Phys. Core 5, 042 (2022) · published 29 August 2022 | Toggle abstract · pdf

  We investigate the wave packet dynamics and eigenstate localization in recently proposed generalized lattice models whose low-energy dynamics mimic a quantum field theory in (1+1)D curved spacetime with the aim of creating systems analogous to black holes. We identify a critical slowdown of zero-energy wave packets in a family of 1D tight-binding models with power-law variation of the hopping parameter, indicating the presence of a horizon. Remarkably, wave packets with non-zero energies bounce back and reverse direction before reaching the horizon. We additionally observe a power-law localization of all eigenstates, each bordering a region of exponential suppression. These forbidden regions dictate the closest possible approach to the horizon of states with any given energy. These numerical findings are supported by a semiclassical description of the wave packet trajectories, which are shown to coincide with the geodesics expected for the effective metric emerging from the considered lattice models in the continuum limit.

  4 citations

• Multi-band D-TRILEX approach to materials with strong electronic correlations

  Matteo Vandelli, Josef Kaufmann, Mohammed El-Nabulsi, Viktor Harkov, Alexander I. Lichtenstein, Evgeny A. Stepanov

  SciPost Phys. 13, 036 (2022) · published 26 August 2022 | Toggle abstract · pdf

  We present the multi-band dual triply irreducible local expansion (D-TRILEX) approach to interacting electronic systems and discuss its numerical implementation. This method is designed for a self-consistent description of multi-orbital systems that can also have several atoms in the unit cell. The current implementation of the D-TRILEX approach is able to account for the frequency- and channel-dependent long-ranged electronic interactions. We show that our method is accurate when applied to small multi-band systems such as the Hubbard-Kanamori dimer. Calculations for the extended Hubbard, the two-orbital Hubbard-Kanamori, and the bilayer Hubbard models are also discussed.

  11 citations

• Codebase release 3.4 for NetKet

  Filippo Vicentini, Damian Hofmann, Attila Szabó, Dian Wu, Christopher Roth, Clemens Giuliani, Gabriel Pescia, Jannes Nys, Vladimir Vargas-Calderón, Nikita Astrakhantsev, Giuseppe Carleo

  SciPost Phys. Codebases 7-r3.4 (2022) · published 24 August 2022 | Toggle abstract · src

  We introduce version 3 of NetKet, the machine learning toolbox for many-body quantum physics. NetKet is built around neural-network quantum states and provides efficient algorithms for their evaluation and optimization. This new version is built on top of JAX, a differentiable programming and accelerated linear algebra framework for the Python programming language. The most significant new feature is the possibility to define arbitrary neural network ansätze in pure Python code using the concise notation of machine-learning frameworks, which allows for just-in-time compilation as well as the implicit generation of gradients thanks to automatic differentiation. NetKet 3 also comes with support for GPU and TPU accelerators, advanced support for discrete symmetry groups, chunking to scale up to thousands of degrees of freedom, drivers for quantum dynamics applications, and improved modularity, allowing users to use only parts of the toolbox as a foundation for their own code.

  2 citations

• NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems

  Filippo Vicentini, Damian Hofmann, Attila Szabó, Dian Wu, Christopher Roth, Clemens Giuliani, Gabriel Pescia, Jannes Nys, Vladimir Vargas-Calderón, Nikita Astrakhantsev, Giuseppe Carleo

  SciPost Phys. Codebases 7 (2022) · published 24 August 2022 | Toggle abstract · pdf

  We introduce version 3 of NetKet, the machine learning toolbox for many-body quantum physics. NetKet is built around neural-network quantum states and provides efficient algorithms for their evaluation and optimization. This new version is built on top of JAX, a differentiable programming and accelerated linear algebra framework for the Python programming language. The most significant new feature is the possibility to define arbitrary neural network ansätze in pure Python code using the concise notation of machine-learning frameworks, which allows for just-in-time compilation as well as the implicit generation of gradients thanks to automatic differentiation. NetKet 3 also comes with support for GPU and TPU accelerators, advanced support for discrete symmetry groups, chunking to scale up to thousands of degrees of freedom, drivers for quantum dynamics applications, and improved modularity, allowing users to use only parts of the toolbox as a foundation for their own code.

  44 citations