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Computational Field Theory : From Polymers to Superfluids
I will discuss a new approximation-free, finite-temperature method for simulating the equilibrium properties of many-boson systems. The technique involves a direct numerical attack on quantum field theories formulated in an imaginary time path integral representation using coherent states. We address the ’sign problem’ inherent to such theories by importance sampling in the complex plane of (d+1)-dimensional fields using a complex Langevin (CL) scheme.
We have recently shown that CL algorithms adapted from simulation methods for classical polymers are equally effective on Bose quantum field theories [1]. As a first demonstration, we numerically reproduced the equation of state of an ideal Bose gas and mapped the normal fluid to superfluid critical transition (lambda line) of a Bose fluid with pairwise contact interactions by field-theoretic simulations coupled with finite-size scaling. The method enjoys near-linear scaling with system size and the computational effort is remarkably independent of the number of bosons. A second application to atomic gases subject to magnetic and optical field-induced spin-orbit coupling led to the discovery of the first quantum “spin microemulsion” phase [2], emerging from the melting of a previously known “smectic-like” supersolid. We expect that our technique will enable a wide range of studies, including Bose systems subject to artificial gauge fields, models of quantum magnetism, and real-time quantum dynamics, all practically inaccessible with existing simulation methods.
[1] K. T. Delaney, H. Orland, and G. H. Fredrickson, Phys. Rev. Lett. 124, 070601 (2020).
[2] E. McGarrigle, K. T. Delaney, L. Balents, and G. H. Fredrickson, ’Emergence of a spin microemulsion in spin-orbit coupled Bose-Einstein condensates,’ https://arxiv.org/abs/2305.10390