Publications

Order by: publication date number of 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.

  2 citations

• Greedy optimization of the geometry of Majorana Josephson junctions

  André Melo, Tanko Tanev, Anton R. Akhmerov

  SciPost Phys. 14, 047 (2023) · published 23 March 2023 | Toggle abstract · pdf

  Josephson junctions in a two-dimensional electron gas with spin-orbit coupling are a promising candidate to realize topological superconductivity. While it is known that the geometry of the junction strongly influences the size of the topological gap, the question of how to construct optimal geometries remains unexplored. We introduce a greedy numerical algorithm to optimize the shape of Majorana junctions. The core of the algorithm relies on perturbation theory and is embarrassingly parallel, which allows it to explore the design space efficiently. By introducing stochastic variations in the junction Hamiltonian, we avoid overfitting geometries to specific system parameters. Furthermore, we constrain the optimizer to produce smooth geometries by applying image filtering and fabrication resolution constraints. We run the algorithm in various setups and find that it reliably produces geometries with increased topological gaps over large parameter ranges. The results are robust to variations in the optimization starting point and the presence of disorder, which suggests the optimizer is capable of finding global maxima.

  2 citations

• Catalogue of phonon modes in several cuprate high-temperature superconductors from density functional theory

  Noah J. Jabusch, Pavan Dayal, Alexander F. Kemper

  SciPost Phys. Core 6, 018 (2023) · published 23 March 2023 | Toggle abstract · pdf

  Cuprates are promising candidates for study in developing higher temperature superconductors. A thorough understanding of a material's phonon modes enables further investigation of its emergent properties, however, no complete reference of the phonon modes exists. Here, using density functional theory, we evaluate the phonon frequencies and atomic displacements for $\text{La}_2\text{CuO}_4$, $\text{Bi}_2\text{Sr}_2\text{CuO}_6$, and $\text{Bi}_2\text{Sr}_2\text{CaCu}_2\text{O}_8$, in their tetragonal structures. The phonon modes for all materials agree with those expected from space group symmetry and display instabilities corresponding to known low-temperature structural phase transitions.

• Non-coplanar magnetism, topological density wave order and emergent symmetry at half-integer filling of moiré Chern bands

  Patrick H. Wilhelm, Thomas C. Lang, Mathias S. Scheurer, Andreas M. Läuchli

  SciPost Phys. 14, 040 (2023) · published 20 March 2023 | Toggle abstract · pdf

  Twisted double- and mono-bilayer graphene are graphene-based moiré materials hosting strongly correlated fermions in a gate-tunable conduction band with a topologically non-trivial character. Using unbiased exact diagonalization complemented by unrestricted Hartree-Fock calculations, we find that the strong electron-electron interactions lead to a non-coplanar magnetic state, which has the same symmetries as the tetrahedral antiferromagnet on the triangular lattice and can be thought of as a skyrmion lattice commensurate with the moiré scale, competing with a set of ferromagnetic, topological charge density waves featuring an approximate emergent O(3) symmetry, "rotating" the different charge density wave states into each other. Direct comparison with exact diagonalization reveals that the ordered phases are accurately described within the unrestricted Hartree-Fock approximation. Exhibiting a finite charge gap and Chern number $|C|=1$, the formation of charge density wave order which is intimately connected to a skyrmion lattice phase is consistent with recent experiments on these systems.

  6 citations

• Quantum tricriticality of incommensurate phase induced by quantum strings in frustrated Ising magnetism

  Zheng Zhou (周正), Changle Liu (刘长乐), Dong-Xu Liu (刘东旭), Zheng Yan (严正), Yan Chen (陈焱), Xue-Feng Zhang (张学锋)

  SciPost Phys. 14, 037 (2023) · published 16 March 2023 | Toggle abstract · pdf

  Incommensurability plays a critical role in many strongly correlated systems. In some cases, the origin of such exotic order can be theoretically understood in the framework of 1d line-like topological excitations known as "quantum strings". Here we study an extended transverse field Ising model on a triangular lattice. Using large-scale quantum Monte Carlo simulations, we find that the spatial anisotropy can stabilize an incommensurate phase out of the commensurate clock order. Our results for the structure factor and the string density exhibit a linear relationship between incommensurate ordering wave vector and the density of quantum strings, which is reminiscent of hole density in under-doped cuprate superconductors. When introducing the next-nearest-neighbor interaction, we observe a quantum tricritical point out of the incommensurate phase. After carefully analyzing the ground state energies within different string topological sectors, we conclude that this tricriticality is non-trivially caused by effective long-range inter-string interactions with two competing terms following different decaying behaviors.

  2 citations

• Learning a restricted Boltzmann machine using biased Monte Carlo sampling

  Nicolas Béreux, Aurélien Decelle, Cyril Furtlehner, Beatriz Seoane

  SciPost Phys. 14, 032 (2023) · published 14 March 2023 | Toggle abstract · pdf

  Restricted Boltzmann Machines are simple and powerful generative models that can encode any complex dataset. Despite all their advantages, in practice the trainings are often unstable and it is difficult to assess their quality because the dynamics are affected by extremely slow time dependencies. This situation becomes critical when dealing with low-dimensional clustered datasets, where the time required to sample ergodically the trained models becomes computationally prohibitive. In this work, we show that this divergence of Monte Carlo mixing times is related to a phenomenon of phase coexistence, similar to that which occurs in physics near a first-order phase transition. We show that sampling the equilibrium distribution using the Markov chain Monte Carlo method can be dramatically accelerated when using biased sampling techniques, in particular the Tethered Monte Carlo (TMC) method. This sampling technique efficiently solves the problem of evaluating the quality of a given trained model and generating new samples in a reasonable amount of time. Moreover, we show that this sampling technique can also be used to improve the computation of the log-likelihood gradient during training, leading to dramatic improvements in training RBMs with artificial clustered datasets. On real low-dimensional datasets, this new training method fits RBM models with significantly faster relaxation dynamics than those obtained with standard PCD recipes. We also show that TMC sampling can be used to recover the free-energy profile of the RBM. This proves to be extremely useful to compute the probability distribution of a given model and to improve the generation of new decorrelated samples in slow PCD-trained models. The main limitations of this method are, first, the restriction to effective low-dimensional datasets and, second, the fact that the Tethered MC method breaks the possibility of performing parallel alternative Monte Carlo updates, which limits the size of the systems we can consider in practice.

  4 citations

• Automatic transformation of irreducible representations for efficient contraction of tensors with cyclic group symmetry

  Yang Gao, Phillip Helms, Garnet Kin-Lic Chan, Edgar Solomonik

  SciPost Phys. Codebases 10 (2023) · published 24 February 2023 | Toggle abstract · pdf

  Tensor contractions are ubiquitous in computational chemistry and physics, where tensors generally represent states or operators and contractions express the algebra of these quantities. In this context, the states and operators often preserve physical conservation laws, which are manifested as group symmetries in the tensors. These group symmetries imply that each tensor has block sparsity and can be stored in a reduced form. For nontrivial contractions, the memory footprint and cost are lowered, respectively, by a linear and a quadratic factor in the number of symmetry sectors. State-of-the-art tensor contraction software libraries exploit this opportunity by iterating over blocks or using general block-sparse tensor representations. Both approaches entail overhead in performance and code complexity. With intuition aided by tensor diagrams, we present a technique, irreducible representation alignment, which enables efficient handling of Abelian group symmetries via only dense tensors, by using contraction-specific reduced forms. This technique yields a general algorithm for arbitrary group symmetric contractions, which we implement in Python and apply to a variety of representative contractions from quantum chemistry and tensor network methods. As a consequence of relying on only dense tensor contractions, we can easily make use of efficient batched matrix multiplication via Intel's MKL and distributed tensor contraction via the Cyclops library, achieving good efficiency and parallel scalability on up to 4096 Knights Landing cores of a supercomputer.

  1 citation

• Codebase release 1.3 for SymTensor

  Yang Gao, Phillip Helms, Garnet Kin-Lic Chan, Edgar Solomonik

  SciPost Phys. Codebases 10-r1.3 (2023) · published 24 February 2023 | Toggle abstract · src

  Tensor contractions are ubiquitous in computational chemistry and physics, where tensors generally represent states or operators and contractions express the algebra of these quantities. In this context, the states and operators often preserve physical conservation laws, which are manifested as group symmetries in the tensors. These group symmetries imply that each tensor has block sparsity and can be stored in a reduced form. For nontrivial contractions, the memory footprint and cost are lowered, respectively, by a linear and a quadratic factor in the number of symmetry sectors. State-of-the-art tensor contraction software libraries exploit this opportunity by iterating over blocks or using general block-sparse tensor representations. Both approaches entail overhead in performance and code complexity. With intuition aided by tensor diagrams, we present a technique, irreducible representation alignment, which enables efficient handling of Abelian group symmetries via only dense tensors, by using contraction-specific reduced forms. This technique yields a general algorithm for arbitrary group symmetric contractions, which we implement in Python and apply to a variety of representative contractions from quantum chemistry and tensor network methods. As a consequence of relying on only dense tensor contractions, we can easily make use of efficient batched matrix multiplication via Intel's MKL and distributed tensor contraction via the Cyclops library, achieving good efficiency and parallel scalability on up to 4096 Knights Landing cores of a supercomputer.

  1 citation

• Floquet engineering of non-equilibrium superradiance

  Lukas Broers, Ludwig Mathey

  SciPost Phys. 14, 018 (2023) · published 13 February 2023 | Toggle abstract · pdf

  We demonstrate the emergence of a non-equilibrium superradiant phase in the dissipative Rabi-Dicke model. This phase is characterized by a photonic steady state that oscillates with a frequency close to the cavity frequency, in contrast to the constant photonic steady state of the equilibrium superradiant phase in the Dicke model. We relate this superradiant phase to the population inversion of Floquet states by introducing a Schwinger representation of the driven two-level systems in the cavity. This inversion is depleted near Floquet energies that are resonant with the cavity frequency to sustain a coherent light-field. In particular, our model applies to solids within a two-band approximation, in which the electrons act as Schwinger fermions. We propose to use this Floquet-assisted superradiant phase to obtain controllable optical gain for a laser-like operation.

  1 citation

• Building models of topological quantum criticality from pivot Hamiltonians

  Nathanan Tantivasadakarn, Ryan Thorngren, Ashvin Vishwanath, Ruben Verresen

  SciPost Phys. 14, 013 (2023) · published 2 February 2023 | Toggle abstract · pdf

  Progress in understanding symmetry-protected topological (SPT) phases has been greatly aided by our ability to construct lattice models realizing these states. In contrast, a systematic approach to constructing models that realize quantum critical points between SPT phases is lacking, particularly in dimension $d>1$. Here, we show how the recently introduced notion of the pivot Hamiltonian—generating rotations between SPT phases—facilitates such a construction. We demonstrate this approach by constructing a spin model on the triangular lattice, which is midway between a trivial and SPT phase. The pivot Hamiltonian generates a $U(1)$ pivot symmetry which helps to stabilize a direct SPT transition. The sign-problem free nature of the model—with an additional Ising interaction preserving the pivot symmetry—allows us to obtain the phase diagram using quantum Monte Carlo simulations. We find evidence for a direct transition between trivial and SPT phases that is consistent with a deconfined quantum critical point with emergent $SO(5)$ symmetry. The known anomaly of the latter is made possible by the non-local nature of the $U(1)$ pivot symmetry. Interestingly, the pivot Hamiltonian generating this symmetry is nothing other than the staggered Baxter-Wu three-spin interaction. This work illustrates the importance of $U(1)$ pivot symmetries and proposes how to generally construct sign-problem-free lattice models of SPT transitions with such anomalous symmetry groups for other lattices and dimensions.

  4 citations