@article{cf2c9182565041efa7aef844bf70f1b8,

title = "Mitigating the Sign Problem through Basis Rotations",

abstract = "Quantum Monte Carlo simulations of quantum many-body systems are plagued by the Fermion sign problem. The computational complexity of simulating Fermions scales exponentially in the projection time β and system size. The sign problem is basis dependent and an improved basis, for fixed errors, leads to exponentially quicker simulations. We show how to use sign-free quantum Monte Carlo simulations to optimize over the choice of basis on large two-dimensional systems. We numerically illustrate these techniques decreasing the {"}badness{"}of the sign problem by optimizing over single-particle basis rotations on one- and two-dimensional Hubbard systems. We find a generic rotation which improves the average sign of the Hubbard model for a wide range of U and densities for L×4 systems. In one example improvement, the average sign (and hence simulation cost at fixed accuracy) for the 16×4 Hubbard model at U/t=4 and n=0.75 increases by exp[8.64(6)β]. For typical projection times of β⪆100, this accelerates such simulation by many orders of magnitude.",

author = "Ryan Levy and Clark, {Bryan K.}",

note = "Funding Information: We acknowledge Luiz Santos for helping to initiate this work, trying to find a sign-problem mitigating unitary, early collaboration on this project, and useful discussions and insights related to this work. B. K. C. thanks David Ceperley, as well as Shiwei Zhang, Miles Stoudenmire, and Giuseppe Carleo for conversations. R. L. thanks Shivesh Pathak for useful conversations and Yubo Yang for visualization assistance. We acknowledge support from the Department of Energy (DOE) Award No. DE-SC0020165. This project is part of the Blue Waters sustained-petascale computing project, which is supported by the National Science Foundation (Grants No. OCI-0725070 and No. ACI-1238993) and the State of Illinois. Blue Waters is a joint effort of the University of Illinois at Urbana-Champaign and its National Center for Supercomputing Applications. This work also made use of the Illinois Campus Cluster, a computing resource that is operated by the Illinois Campus Cluster Program (ICCP) in conjunction with the National Center for Supercomputing Applications (NCSA) and which is supported by funds from the University of Illinois at Urbana-Champaign. Publisher Copyright: {\textcopyright} 2021 American Physical Society.",

year = "2021",

month = may,

day = "24",

doi = "10.1103/PhysRevLett.126.216401",

language = "English (US)",

volume = "126",

journal = "Physical Review Letters",

issn = "0031-9007",

publisher = "American Physical Society",

number = "21",

}