Efficient Continuous-time Quantum Monte Carlo Method for the Ground State of Correlated Fermions

TL;DR

This paper introduces a new continuous-time quantum Monte Carlo algorithm for calculating the ground state of correlated fermions, which is more efficient, flexible, and scalable than traditional methods, enabling precise studies of quantum critical points.

Contribution

The paper extends an existing quantum Monte Carlo algorithm to the ground state, offering a systematic-error-free, linearly scalable approach that integrates well with advanced simulation techniques.

Findings

Algorithm accurately reproduces known results for the $t-V$ model.

Successfully studies the fermionic quantum critical point on a honeycomb lattice.

Confirms previous critical exponent measurements with improved efficiency.

Abstract

We present the ground state extension of the efficient quantum Monte Carlo algorithm for lattice fermions of arXiv:1411.0683. Based on continuous-time expansion of imaginary-time projection operator, the algorithm is free of systematic error and scales \emph{linearly} with projection time and interaction strength. Compared to the conventional quantum Monte Carlo methods for lattice fermions, this approach has greater flexibility and is easier to combine with powerful machinery such as histogram reweighting and extended ensemble simulation techniques. We discuss the implementation of the continuous-time projection in detail using the spinless $t-V$ model as an example and compare the numerical results with exact diagonalization, density-matrix-renormalization-group and infinite projected entangled-pair states calculations. Finally we use the method to study the fermionic quantum critical point of spinless fermions on a honeycomb lattice and confirm previous results concerning its critical exponents.