Journal ArticleDOI
Sign problem in the numerical simulation of many-electron systems
E.Y. Loh,James Gubernatis,Richard T. Scalettar,Steven R. White,Douglas J. Scalapino,Robert L. Sugar +5 more
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TLDR
A recent proposal for dealing with the sign problem due to Sorella leads to an uncontrolled approximation for the ground-state energy, and a method for calculating the correction needed to make it exact is presented.Abstract:
We discuss the problems that arise in the numerical simulation of many-electron systems when the measure of the functional integrals is not positive definite. We present theoretical arguments and numerical data which indicate that the expectation value of the sign of the measure decreases exponentially as the inverse temperature \ensuremath{\beta} increases, unless the measure is forced to be positive by an explicit symmetry. We therefore conclude that a recent proposal for dealing with the sign problem due to Sorella et al. Leads to an uncontrolled approximation. In the cases we have studied it is a good approximation for the ground-state energy, and we present a method for calculating the correction needed to make it exact. However, for some physical quantities, such as the d-wave pair field susceptibility, the neglect of signs can yield misleading results.read more
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Journal ArticleDOI
One dimensional bosons: From condensed matter systems to ultracold gases
TL;DR: The physics of one-dimensional interacting bosonic systems is reviewed in this paper, where the effects of various perturbations on the Tomonaga-Luttinger liquid state are discussed as well as extensions to multicomponent and out of equilibrium situations.
Journal ArticleDOI
Continuous-Time Solver for Quantum Impurity Models
Philipp Werner,Armin Comanac,Luca de' Medici,Luca de' Medici,Matthias Troyer,Andrew J. Millis +5 more
TL;DR: A new continuous-time solver for quantum impurity models such as those relevant to dynamical mean field theory, based on a stochastic sampling of a perturbation expansion in the impurity-bath hybridization parameter is presented, which allows very efficient simulations even at low temperatures and for strong interactions.
Journal ArticleDOI
Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
James P.F. LeBlanc,Andrey E. Antipov,Federico Becca,Ireneusz W. Bulik,Garnet Kin-Lic Chan,Chia-Min Chung,Youjin Deng,Michel Ferrero,Michel Ferrero,Thomas M. Henderson,Carlos A. Jiménez-Hoyos,Evgeny Kozik,X. Liu,Andrew J. Millis,Nikolay Prokof'ev,Nikolay Prokof'ev,Mingpu Qin,Gustavo E. Scuseria,Hao Shi,Boris Svistunov,Luca F. Tocchio,Igor S. Tupitsyn,Steven R. White,Shiwei Zhang,Bo-Xiao Zheng,Zhenyue Zhu,Emanuel Gull +26 more
TL;DR: In this article, numerical results for ground state and excited state properties (energies, double occupancies, and Matsubara-axis self energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit.
Journal ArticleDOI
Semi-Metal-Insulator Transition of the Hubbard Model in the Honeycomb Lattice
TL;DR: Using quantum Monte Carlo and finite-size scaling for the Hubbard model, this paper found evidence of a zero-temperature transition between the nonmagnetic semi-metal and an antiferromagnetic insulator in the 2D honeycomb lattice for a nontrivial value of U/t?=?4.5???0.5.
Journal ArticleDOI
Machine learning quantum phases of matter beyond the fermion sign problem
TL;DR: In this article, a convolutional neural network (CNN) was used to identify and locate quantum phase transitions in quantum many-fermion systems using auxiliary-field quantum Monte Carlo simulations.
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