The complex Langevin analysis of spontaneous symmetry breaking induced by complex fermion determinant

Abstract

In many interesting physical systems, the determinant which appears from integrating out fermions becomes complex, and its phase plays a crucial role in the determination of the vacuum. An example of this is QCD at low temperature and high density, where various exotic fermion condensates are conjectured to form. Another example is the Euclidean version of the type IIB matrix model for 10d superstring theory, where spontaneous breaking of the SO(10) rotational symmetry down to SO(4) is expected to occur. When one applies the complex Langevin method to these systems, one encounters the singular-drift problem associated with the appearance of nearly zero eigenvalues of the Dirac operator. Here we propose to avoid this problem by deforming the action with a fermion bilinear term. The results for the original system are obtained by extrapolations with respect to the deformation parameter. We demonstrate the power of this approach by applying it to a simple matrix model, in which spontaneous symmetry breaking from SO(4) to SO(2) is expected to occur due to the phase of the complex fermion determinant. Unlike previous work based on a reweighting-type method, we are able to determine the true vacuum by calculating the order parameters, which agree with the prediction by the Gaussian expansion method.

arXiv comment23 pages, 26 figures. The version accepted for publication in JHEP

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• Review on novel methods for lattice gauge theories
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• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Complex Langevin analysis of the space-time structure in the Lorentzian type IIB matrix model
• Control the model sign problem via path optimization method: Monte-Carlo approach to QCD effective model with Polyakov loop
• Complex Langevin analysis of the spontaneous symmetry breaking in dimensionally reduced super Yang-Mills models
• Combining the complex Langevin method and the generalized Lefschetz-thimble method
• Progress in the numerical studies of the type IIB matrix model
• Complex Langevin calculations in finite density QCD at large $\mu /T$ with the deformation technique
• Application of the path optimization method to the sign problem in an effective model of QCD with a repulsive vector-type interaction
• Testing the criterion for correct convergence in the complex Langevin method
• Complex Langevin calculations in QCD at finite density
• Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
• On the gauge invariant path-integral measure for the overlap Weyl fermions in $\underline{16}$ of SO(10)
• Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
• Complex Langevin Simulations of Zero-dimensional Supersymmetric Quantum Field Theories
• Complex Langevin Dynamics in Large $N$ Unitary Matrix Models
• On the structure of the emergent 3d expanding space in the Lorentzian type IIB matrix model
• Complex Langevin simulation of QCD at finite density and low temperature using the deformation technique
• Complex Langevin Dynamics and Supersymmetric Quantum Mechanics
• Comparative studies of the deformation techniques for the singular-drift problem in the complex Langevin method
• Lefschetz Thimbles and Quantum Phases in Zero-Dimensional Bosonic Models