Reaching the continuum limit in finite-temperature ab initio field-theory computations in many-fermion systems

Abstract

Finite-temperature, grand-canonical computations based on field theory are widely applied in areas including condensed matter physics, ultracold atomic gas systems, and lattice gauge theory. However, these calculations have computational costs scaling as $N_s^3$ with the size of the lattice or basis set, $N_s$. We report a new approach based on systematically controllable low-rank factorization which reduces the scaling of such computations to $N_s{N}_e^2$, where $N_e$ is the average number of fermions in the system. In any realistic calculations aiming to describe the continuum limit, $N_s/N_e$ is large and needs to be extrapolated effectively to infinity for convergence. The method thus fundamentally changes the prospect for finite-temperature many-body computations in correlated fermion systems. Its application, in combination with frameworks to control the sign or phase problem as needed, will provide a powerful tool in {\it ab initio} quantum chemistry and correlated electron materials. We demonstrate the method by computing exact properties of the two-dimensional Fermi gas with zero-range attractive interaction, as a function of temperature in both the normal and superfluid states.

arXiv comment6 pages, 4 figures

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• Quantitative functional renormalization-group description of the two-dimensional Hubbard model
• A Phaseless Auxiliary-Field Quantum Monte Carlo Perspective on the Uniform Electron Gas at Finite Temperatures: Issues, Observations, and Benchmark Study
• Finite Temperature Auxiliary Field Quantum Monte Carlo in the Canonical Ensemble
• Magnetic, thermodynamic, and dynamical properties of the three-dimensional fermionic Hubbard model: A comprehensive Monte Carlo study
• Extended Metal-Insulator Crossover with Strong Antiferromagnetic Spin Correlation in Half-Filled 3D Hubbard Model
• Non-Hertz-Millis scaling of the antiferromagnetic quantum critical metal via scalable Hybrid Monte Carlo
• Precision Many-Body Study of the Berezinskii-Kosterlitz-Thouless Transition and Temperature-Dependent Properties in the Two-Dimensional Fermi Gas
• Effective theory for ultracold strongly interacting fermionic atoms in two dimensions
• Pseudogap regime of a strongly interacting two-dimensional Fermi gas with and without confinement-induced effect range of interactions
• Boosting quantum Monte Carlo and alleviating sign problem by Gutzwiller projection
• Ising phase transitions and thermodynamics of correlated fermions in a two-dimensional spin-dependent lattice potential
• Boosting Determinant Quantum Monte Carlo with Submatrix Updates: Unveiling the Phase Diagram of the 3D Hubbard Model
• Observing Spatial Charge and Spin Correlations in a Strongly-Interacting Fermi Gas
• Accelerating ground-state auxiliary-field quantum Monte Carlo simulations by delayed update and block force-bias update
• Quantum Monte Carlo study of the metal-insulator crossover in the square-lattice Hubbard model
• Spin-triplet pairing instability in a two-dimensional repulsive Hubbard model