Rejection-free quantum Monte Carlo in continuous time from transition path sampling

Causer, Luke; Sfairopoulos, Konstantinos; Mair, Jamie F.; Garrahan, Juan P.

Abstract

Continuous-time quantum Monte Carlo refers to a class of algorithms designed to sample the thermal distribution of a quantum Hamiltonian through exact expansions of the Boltzmann exponential in terms of stochastic trajectories which are periodic in imaginary time. Here, we show that for (sign-problem-free) quantum many-body systems with discrete degrees of freedom—such as spins on a lattice—this sampling can be done in a rejection-free manner using transition path sampling (TPS). The key idea is to converge the trajectory ensemble through updates where one individual degree of freedom is modified across all time while the remaining unaltered ones provide a time-dependent background. The ensuing single-body dynamics provides a way to generate trajectory updates exactly, allowing one to obtain the target ensemble efficiently via rejection-free TPS. We demonstrate our method on the transverse field Ising model in one and two dimensions, and on the quantum triangular plaquette (or Newman-Moore) model. We show that despite large autocorrelation times, our method is able to efficiently recover the respective quantum phase transition of each model. We also discuss the connection to rare event sampling in continuous-time Markov dynamics.

Citation

Causer, L., Sfairopoulos, K., Mair, J. F., & Garrahan, J. P. (2024). Rejection-free quantum Monte Carlo in continuous time from transition path sampling. Physical Review B, 109(2), Article 024307. https://doi.org/10.1103/physrevb.109.024307

• Journal Article Type: Article
• Acceptance Date: Jan 2, 2024
• Online Publication Date: Jan 16, 2024
• Publication Date: Jan 1, 2024
• Deposit Date: Mar 7, 2024
• Publicly Available Date: Mar 7, 2024
• Journal: Physical Review B
• Print ISSN: 2469-9950
• Electronic ISSN: 2469-9969
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 109
• Issue: 2
• Article Number: 024307
• DOI: https://doi.org/10.1103/physrevb.109.024307
• Keywords: Continuous phase transition; First order phase transitions; 1-dimensional spin chains; Triangular lattice; Ising model; Large deviation & rare event statistics; Quantum Monte Carlo
• Public URL: https://nottingham-repository.worktribe.com/output/30412092
• Publisher URL: https://journals.aps.org/prb/pdf/10.1103/PhysRevB.109.024307