Fermion sign bounds theory in quantum Monte Carlo simulation
arXiv:2112.06139 · doi:10.1103/PhysRevB.106.035121
Abstract
Sign problem in fermion quantum Monte Carlo (QMC) simulation appears to be an extremely hard problem. Traditional lore passing around for years tells people that when there is a sign problem, the average sign in QMC simulation approaches zero exponentially fast with the space-time volume of the configurational space. We, however, analytically show this is not always the case and manage to find physical bounds for the average sign. Our understanding is based on a direct connection between the sign bounds and a well-defined partition function of reference system and could distinguish when the bounds have the usual exponential scaling, and when they are bestowed on an algebraic scaling at low temperature limit. We analytically explain such algebraic sign problems found in flat band moiré lattice models at low temperature limit. At finite temperature, a domain size argument based on sign bounds also explains the connection between sign behavior and finite temperature phase transition. Sign bounds, as a well-defined observable, may have ability to ease or even make use of the sign problem.
arXiv comment11 pages, 3 figures
References in corpus (57)
- The density-matrix renormalization group
- Moire bands in twisted double-layer graphene
- Graphene bilayer with a twist: electronic structure
- Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
- Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
- Quantum Monte Carlo methods for nuclear physics
- Localization of Dirac electrons by Moire patterns in graphene bilayers
- Continuous Time Quantum Monte Carlo method for fermions
- Continuum Model of the Twisted Bilayer
- Computational Studies of Quantum Spin Systems
- Electronic properties of graphene-based bilayer systems
- Machine learning quantum phases of matter beyond the fermion sign problem
- Strong coupling phases of partially filled twisted bilayer graphene narrow bands
- Numerical studies of confined states in rotated bilayers of graphene
- Absence of superconductivity in the pure two-dimensional Hubbard model
- Monte Carlo evaluation of path integrals for the nuclear shell model
- Twisted Bilayer Graphene IV. Exact Insulator Ground States and Phase Diagram
- A sufficient condition for the absence of the sign problem in the fermionic quantum Monte-Carlo algorithm
- A Constrained Path Quantum Monte Carlo Method for Fermion Ground States
- Meron-Cluster Solution of Fermion Sign Problems
- Twisted bilayer graphene III. Interacting Hamiltonian and exact symmetries
- Solving fermion sign problem in quantum Monte Carlo by Majorana representation
- Numerical Study of Dense Adjoint Matter in Two Color QCD
- Majorana-time-reversal symmetries: a fundamental principle for sign-problem-free quantum Monte Carlo simulations
- Majorana Positivity and the Fermion sign problem of Quantum Monte Carlo Simulations
- Determinant Diagrammatic Monte Carlo in the Thermodynamic Limit
- Valence bond solids for SU(n) spin chains: exact models, spinon confinement, and the Haldane gap
- Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications
- Geometry Dependence of the Sign Problem
- Correlation-induced insulating topological phases at charge neutrality in twisted bilayer graphene
- Quantum Critical Points and the Sign Problem
- Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: the Parent State of Quantum Phases
- Easing the Monte Carlo sign problem
- Solution to sign problems in half-filled spin-polarized electronic systems
- Split orthogonal group: A guiding principle for sign-problem-free fermionic simulations
- Momentum space quantum Monte Carlo on twisted bilayer Graphene
- On the Computational Complexity of Curing the Sign Problem
- Lefschetz thimbles decomposition for the Hubbard model on the hexagonal lattice
- Thermodynamic properties of the Shastry-Sutherland model from quantum Monte Carlo simulations
- Polynomial complexity despite the fermionic sign
- How Quantum Are Non-Negative Wavefunctions?
- Negative sign problem in continuous-time quantum Monte Carlo: optimal choice of single-particle basis for impurity problems
- Dynamical properties of collective excitations in twisted bilayer Graphene
- Correlated Insulating Phases in the Twisted Bilayer Graphene
- Leveraging Machine Learning to Alleviate Hubbard Model Sign Problems
- Wavefunction positivization via automatic differentiation
- Mitigating the Sign Problem Through Basis Rotations
- Quantum Many-Body Simulations of the 2D Fermi-Hubbard Model in Ultracold Optical Lattices
- 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
- Topological Origin of the Fermion Sign Problem
- Intrinsic sign problems in topological quantum field theories
- An Amelioration for the Sign Problem: Adiabatic Quantum Monte Carlo
- Projection of Infinite- Hubbard Model and Algebraic Sign Structure
- Deconvolving the components of the sign problem
- Taming the sign problem of the finite density Hubbard model via Lefschetz thimbles
- Reduction of the sign problem near in quantum Monte Carlo simulations
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