A tensor network representation of PT-symmetric φ^4 lattices on complex contours yields exact parity-decomposed local tensors and a finite-volume identity between wedge-contour and continued Hermitian partition functions in any dimension.
Investigation of complex $\phi^{4}$ theory at finite density in two dimensions using TRG
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We study the two-dimensional complex $\phi^{4}$ theory at finite chemical potential using the tensor renormalization group. This model exhibits the Silver Blaze phenomenon in which bulk observables are independent of the chemical potential below the critical point. Since it is expected to be a direct outcome of an imaginary part of the action, an approach free from the sign problem is needed. We study this model systematically changing the chemical potential in order to check the applicability of the tensor renormalization group to the model in which scalar fields are discretized by the Gaussian quadrature. The Silver Blaze phenomenon is successfully confirmed on the extremely large volume $V=1024^2$ and the results are also ensured by another tensor network representation with a character expansion.
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Tensor Network Formulation of $\mathcal{PT}$-Symmetric Quantum Field Theory
A tensor network representation of PT-symmetric φ^4 lattices on complex contours yields exact parity-decomposed local tensors and a finite-volume identity between wedge-contour and continued Hermitian partition functions in any dimension.