Qsymm: Algorithmic symmetry finding and symmetric Hamiltonian generation

Abstract

Symmetry is a guiding principle in physics that allows to generalize conclusions between many physical systems. In the ongoing search for new topological phases of matter, symmetry plays a crucial role because it protects topological phases. We address two converse questions relevant to the symmetry classification of systems: Is it possible to generate all possible single-body Hamiltonians compatible with a given symmetry group? Is it possible to find all the symmetries of a given family of Hamiltonians? We present numerically stable, deterministic polynomial time algorithms to solve both of these problems. Our treatment extends to all continuous or discrete symmetries of non-interacting lattice or continuum Hamiltonians. We implement the algorithms in the Qsymm Python package, and demonstrate their usefulness with examples from active research areas in condensed matter physics, including Majorana wires and Kekule graphene.

arXiv comment16 pages, 4 figures

References in corpus (40)

• Topological Insulators
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides
• Topological Photonics
• Classification of topological insulators and superconductors in three spatial dimensions
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological Crystalline Insulators
• Periodic table for topological insulators and superconductors
• Topological quantum chemistry
• Topological superconductors: a review
• Topological Crystalline Insulators in the SnTe Material Class
• Kwant: a software package for quantum transport
• Topological characterization of periodically-driven quantum systems
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides
• Realization of Quantum Spin Hall State in Monolayer 1T'-WTe2
• Introduction to topological superconductivity and Majorana fermions
• Observation of the Quantum Spin Hall Effect up to 100 Kelvin in a Monolayer Crystal
• Topological Boundary Modes in Isostatic Lattices
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Hexagonal Warping Effects in the Surface States of Topological Insulator Bi${}_2$Te${}_3$
• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
• The space group classification of topological band insulators
• Topological classification of crystalline insulators through band structure combinatorics
• Edge conduction in monolayer WTe2
• Electron fractionalization in two-dimensional graphenelike structures
• Tight-binding model and direct-gap/indirect-gap transition in single-layer and multi-layer MoS${}_2$
• Time Reversal Invariant Topologically Insulating Circuits
• Structure and Topology of Band Structures in the 1651 Magnetic Space Groups
• \textit{Ab-initio} Tight-Binding Hamiltonian for Transition Metal Dichalcogenides
• On the quantum spin Hall gap of monolayer 1T'-WTe2
• Topological Superconductivity induced by Ferromagnetic Metal Chains
• Direct Visualization of 2D Topological Insulator in Single-layer 1T'-WTe2
• Statistical Topological Insulators
• Quantum Spin Hall Effect in 2D Transition Metal Dichalcogenide Haeckelites
• Emergence of topological semimetals in gap closing in semiconductors without inversion symmetry
• Orbital effect of magnetic field on the Majorana phase diagram
• Valley-momentum locking in a graphene superlattice with Y-shaped Kekulé bond texture
• Band Connectivity for Topological Quantum Chemistry: Band Structures As A Graph Theory Problem
• Bulk invariants and topological response in insulators and superconductors with nonsymmorphic symmetries

Cited by in corpus (41)

• Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure
• Topological phases without crystalline counterparts
• MagneticTB: A package for tight-binding model of magnetic and non-magnetic materials
• Strain-engineering the topological type-II Dirac semimetal NiTe${}_2$
• Topological semimetals in the SnTe material class: Nodal lines and Weyl points
• The influence of lattice termination on the edge states of the quantum spin Hall insulator monolayer $1T^{\prime }$-WTe${}_2$
• Spin-orbit coupling in wurtzite quantum wells
• From triple-point materials to multiband nodal links
• Amorphous topological phases protected by continuous rotation symmetry
• MagneticKP: A package for quickly constructing $\mathbf{k}\cdot \mathbf{p}$ models of magnetic and non-magnetic crystals
• Correlation-induced valley topology in buckled graphene superlattices
• Universal higher-order bulk-boundary correspondence of triple nodal points
• Interplay between boundary conditions and Wilson's mass in Dirac-like Hamiltonians
• Platform for nodal topological superconductors in monolayer molybdenum dichalcogenides
• Magnetic warping in topological insulators
• DFT2kp: effective kp models from ab-initio data
• Identification of strongly interacting organic semimetals
• Engineering Topological Models with a General-Purpose Symmetry-to-Hamiltonian Approach
• Multiplicative Majorana zero-modes
• Multiplicative topological semimetals
• Pfaffian invariant identifies magnetic obstructed atomic insulators
• Nonreciprocal Ballistic Transport in Asymmetric Bands
• Topological quantum criticality from multiplicative topological phases
• Dual topological insulator with mirror symmetry protected helical edge states
• A programmable $k\cdot p$ Hamiltonian method and application to magnetic topological insulator MnBi${}_2$Te${}_4$
• Interplay between inversion and translation symmetries in trigonal PtBi${}_2$
• Charge-Spin Conversion in Two-Subband Quantum Wells with Conventional and Unconventional Rashba Spin-Orbit Coupling
• Scattering theory of higher order topological phases
• Stability of Weyl node merging processes under symmetry constraints
• Controlling topology through targeted composite symmetry manipulation in magnetic systems
• (110) Facet of MgTe Zinc Blende Semiconductor: A Holy Grail for Modern Spintronics
• Topological Classification of One-Dimensional Chiral Symmetric Interfaces
• Isotropic 3D topological phases with broken time reversal symmetry
• Investigating Quantum Spin-Textures Using Universal MJ Hamiltonians
• Light-induced pseudo-magnetic fields in three-dimensional topological semimetals
• Reentrant topological phase in half-Heusler compounds
• Nodal higher-order topological superconductivity from C6-symmetric Dirac semimetals
• Nonreciprocal ballistic transport in multi-layer Weyl semimetal films with surface engineering
• Observable-enriched entanglement
• Physical Pictures for Quasisymmetry in Crystals
• An Unusual Dresselhaus Spin-Orbit Contribution of Even Order in Momentum