Mitigating the fermion sign problem by automatic differentiation

Abstract

As an intrinsically unbiased method, the quantum Monte Carlo (QMC) method is of unique importance in simulating interacting quantum systems. Although the QMC method often suffers from the notorious sign problem, the sign problem of quantum models may be mitigated by finding better choices of the simulation scheme. However, a general framework for identifying optimal QMC schemes has been lacking. Here, we propose a general framework using automatic differentiation to automatically search for the best QMC scheme within a given ansatz of the Hubbard-Stratonovich transformation, which we call "automatic differentiable sign optimization" (ADSO). We apply the ADSO framework to the honeycomb lattice Hubbard model with Rashba spin-orbit coupling and demonstrate that ADSO is remarkably effective in mitigating and even solving its sign problem. Specifically, ADSO finds a sign-free point in the model which was previously thought to be sign-problematic. For the sign-free model discovered by ADSO, its ground state is shown by sign-free QMC simulations to possess spiral magnetic ordering; we also obtained the critical exponents characterizing the magnetic quantum phase transition.

arXiv comment4.5 pages + supplemental materials, 8 figures

References in corpus (75)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Interactions and phase transitions on graphene's honeycomb lattice
• Rashba effect in the graphene/Ni(111) system
• Graphene for spintronics: giant Rashba splitting due to hybridization with Au
• Machine learning quantum phases of matter beyond the fermion sign problem
• A Review of automatic differentiation and its efficient implementation
• Correlation Effects in Quantum Spin-Hall Insulators: A Quantum Monte Carlo Study
• Differentiable Programming Tensor Networks
• A sufficient condition for the absence of the sign problem in the fermionic quantum Monte-Carlo algorithm
• Numerical evidence of fluctuating stripes in the normal state of high-Tc cuprate superconductors
• Single and two-particle energy gaps across the disorder-driven superconductor-insulator transition
• Universal quantum criticality in the metal-insulator transition of two-dimensional interacting Dirac electrons
• Solving fermion sign problem in quantum Monte Carlo by Majorana representation
• Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
• Quantum phase transitions in the Kane-Mele-Hubbard model
• Persistent spin excitations in doped antiferromagnets revealed by resonant inelastic light scattering
• Phase diagram of the half-filled two-dimensional SU(N) Hubbard-Heisenberg model: a quantum Monte Carlo study
• Low-temperature behavior of two-dimensional Gaussian Ising spin glasses
• Duality between the deconfined quantum-critical point and the bosonic topological transition
• Ising nematic quantum critical point in a metal: a Monte Carlo study
• Majorana-time-reversal symmetries: a fundamental principle for sign-problem-free quantum Monte Carlo simulations
• Breakdown of Migdal-Eliashberg theory; a determinant quantum Monte Carlo study
• Spin and charge dynamics of the ferromagnetic and antiferromagnetic two-dimensional half-filled Kondo lattice model
• Fermion-induced quantum critical points
• Majorana Positivity and the Fermion sign problem of Quantum Monte Carlo Simulations
• Charged fermions coupled to ${\mathbb{Z}}_2$ gauge fields: Superfluidity, confinement and emergent Dirac fermions
• Algorithmic differentiation and the calculation of forces by quantum Monte Carlo
• Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications
• Geometry Dependence of the Sign Problem
• What makes the Tc of monolayer FeSe on SrTiO3 so high: a sign-problem-free quantum Monte Carlo study
• Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions
• Confinement transition of ${\mathbb{Z}}_2$ gauge theories coupled to massless fermions: emergent QCD${}_3$ and $SO(5)$ symmetry
• Monte Carlo Studies of Quantum Critical Metals
• Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: the Parent State of Quantum Phases
• Easing the Monte Carlo sign problem
• Self-Learning Monte Carlo Method in Fermion Systems
• Competing Orders in a Nearly Antiferromagnetic Metal
• Split orthogonal group: A guiding principle for sign-problem-free fermionic simulations
• A simple fermionic model of deconfined phases and phase transitions
• Revisiting the Hybrid Quantum Monte Carlo Method for Hubbard and Electron-Phonon Models
• Quantum Monte Carlo simulation of the chiral Heisenberg Gross-Neveu-Yukawa phase transition with a single Dirac cone
• Characterizing the three-orbital Hubbard model with determinant quantum Monte Carlo
• Competing orders in the 2D half-filled SU(2N) Hubbard model through the pinning field quantum Monte-Carlo simulations
• Charge Order in the Holstein Model on a Honeycomb Lattice
• Investigation of the Néel phase of the frustrated Heisenberg antiferromagnet by differentiable symmetric tensor networks
• Bona fide interaction-driven topological phase transition in correlated SPT states
• On the Computational Complexity of Curing the Sign Problem
• Lefschetz thimbles decomposition for the Hubbard model on the hexagonal lattice
• Tropical Tensor Network for Ground States of Spin Glasses
• Pseudogap crossover in the electron-phonon system
• Quantum magnetic properties of the SU(2N) Hubbard model in the square lattice: a quantum Monte Carlo study
• Observation of Emergent Spacetime Supersymmetry at Superconducting Quantum Criticality
• Edge quantum criticality and emergent supersymmetry in topological phases
• Itinerant Quantum Critical Point with Fermion Pockets and Hot Spots
• How Quantum Are Non-Negative Wavefunctions?
• The nature of effective interaction in cuprate superconductors: a sign-problem-free quantum Monte-Carlo study
• Negative sign problem in continuous-time quantum Monte Carlo: optimal choice of single-particle basis for impurity problems
• Automatic Differentiation for Second Renormalization of Tensor Networks
• Automatic differentiation of dominant eigensolver and its applications in quantum physics
• Competing nodal d-wave superconductivity and antiferromagnetism
• Leveraging Machine Learning to Alleviate Hubbard Model Sign Problems
• The fermion sign problem: A new decoupling transformation, and a new simulation algorithm
• Wavefunction positivization via automatic differentiation
• Mitigating the Sign Problem Through Basis Rotations
• Protocol Discovery for the Quantum Control of Majoranas by Differentiable Programming and Natural Evolution Strategies
• Intrinsic sign problem in fermionic and bosonic chiral topological matter
• Alleviating the Sign Problem in Quantum Monte Carlo Simulations of Spin-Orbit-Coupled Multi-Orbital Hubbard Models
• Intrinsic sign problems in topological quantum field theories
• Superconductivity in the presence of strong electron-phonon interactions and frustrated charge order
• Spontaneous particle-hole symmetry breaking of correlated fermions on the Lieb lattice
• Hierarchy of energy scales in an O(3) symmetric antiferromagnetic quantum critical metal: a Monte Carlo study
• Entanglement and the fermion sign problem in auxiliary field quantum Monte Carlo simulations
• The dynamical exponent of a quantum critical itinerant ferromagnet: a Monte Carlo study
• Automatic design of Hamiltonians
• Topological terms on topological defects: a quantum Monte Carlo study

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