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Complex Langevin and other approaches to the sign problem in quantum many-body physics

Florian Ehmann, C.E. Berger, Lukas Rammelmüller +3 more

Jan 23, 20230 citations

Complex Langevin simulations of quantum systems with the sign problem

Mitsuaki Hirasawa

Mar 24, 20210 citations

Complex Langevin equation and the many-fermion problem

Christoph Adami, S. E. Koonin

We study the utility of a complex Langevin (CL) equation as an alternative for the Monte Carlo (MC) procedure in the evaluation of expectation values occurring in fermionic many-body problems. We find that a CL approach is natural in cases where nonpositive definite probability measures occur, and remains accurate even when the corresponding MC calculation develops a severe ``sign problem.'' While the convergence of CL averages cannot be guaranteed in principle, we show how convergent results can be obtained in two simple quantum mechanical models, as well as a nontrivial schematic shell model path integral with multiple particles and a noncommuting interaction (the Lipkin model).We study the utility of a complex Langevin (CL) equation as an alternative for the Monte Carlo (MC) procedure in the evaluation of expectation values occurring in fermionic many-body problems. We find that a CL approach is natural in cases where nonpositive definite probability measures occur, and remains accurate even when the corresponding MC calculation develops a severe ``sign problem.'' While the convergence of CL averages cannot be guaranteed in principle, we show how convergent results can be obtained in two simple quantum mechanical models, as well as a nontrivial schematic shell model path integral with multiple particles and a noncommuting interaction (the Lipkin model).

arXiv:nucl-th/0009021Physical Review CFeb 20, 200114 citations

Sign problem, complex wave function and the Hubbard model

昌弘井町, 博志米山

物性研究Mar 20, 19940 citations

Few-body physics on a spacetime lattice in the worldline approach

Hersh Singh, Shailesh Chandrasekharan A

We formulate the physics of two species of nonrelativistic hard-core bosons with attractive or repulsive delta function interactions on a spacetime lattice in the worldline approach. We show that worm algorithms can efficiently sample the worldline configurations in any fixed particle-number sector if the chemical potential is tuned carefully. Since fermions can be treated as hard-core bosons up to a permutation sign, we apply this approach to study nonrelativistic fermions. The fermion permutation sign is an observable in this approach and can be used to extract energies in each particle-number sector. In one dimension, nonrelativistic fermions can only permute across boundaries, and so our approach does not suffer from sign problems in many cases, unlike the auxiliary field method. Using our approach, we discover limitations of the recently proposed complex Langevin calculations in one spatial dimension for some parameter regimes. In higher dimensions, our method suffers from the usual fermion sign problem. Here we provide evidence that it may be possible to alleviate this problem for few-body physics.We formulate the physics of two species of nonrelativistic hard-core bosons with attractive or repulsive delta function interactions on a spacetime lattice in the worldline approach. We show that worm algorithms can efficiently sample the worldline configurations in any fixed particle-number sector if the chemical potential is tuned carefully. Since fermions can be treated as hard-core bosons up to a permutation sign, we apply this approach to study nonrelativistic fermions. The fermion permutation sign is an observable in this approach and can be used to extract energies in each particle-number sector. In one dimension, nonrelativistic fermions can only permute across boundaries, and so our approach does not suffer from sign problems in many cases, unlike the auxiliary field method. Using our approach, we discover limitations of the recently proposed complex Langevin calculations in one spatial dimension for some parameter regimes. In higher dimensions, our method suffers from the usual fermion sign problem. Here we provide evidence that it may be possible to alleviate this problem for few-body physics.

arXiv:1812.05080Physical review. D/Physical review. D.Apr 24, 201910 citations

Advances in non-relativistic matter via complex Langevin approaches

Joaquín E. Drut

The recent progress in understanding the mathematics of complex stochastic quantization, as well as its application to quantum chromodynamics in situations that have a complex phase problem (e.g. finite quark density, real time), has opened up an intriguing possibility for non-relativistic many-body physics which has so far remained largely unexplored. In this brief contribution, I review a few specific examples of advances in the characterization of the thermodynamics of non-relativistic matter in a variety of one-dimensional cases affected by the sign problem: repulsive interactions, finite polarization, finite mass imbalance, and projection to finite systems to obtain virial coefficients.The recent progress in understanding the mathematics of complex stochastic quantization, as well as its application to quantum chromodynamics in situations that have a complex phase problem (e.g. finite quark density, real time), has opened up an intriguing possibility for non-relativistic many-body physics which has so far remained largely unexplored. In this brief contribution, I review a few specific examples of advances in the characterization of the thermodynamics of non-relativistic matter in a variety of one-dimensional cases affected by the sign problem: repulsive interactions, finite polarization, finite mass imbalance, and projection to finite systems to obtain virial coefficients.

arXiv:1710.10176Journal of Physics Conference SeriesJun 1, 20183 citations

Complex Langevin and other approaches to the sign problem in quantum many-body physics

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