2010/09/03 by Peter N. Meisinger, Meisinger, Peter N., Michael C. Ogilvie +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #FOS: Physical sciences #Fractal and DNA sequence analysis #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #Quantum Physics (quant-ph) #hep-lat #hep-th #quant-ph
paper · pdf · doi:10.48550/arxiv.1009.0745
11 pages, 3 figures
arxiv created 2010/09/03 · openalex publication_date 2010/09/03 · arxiv updated 2010/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Generalized PT symmetry provides crucial insight into the sign problem for two classes of models. In the case of quantum statistical models at non-zero chemical potential, the free energy density is directly related to the ground state energy of a non-Hermitian, but generalized PT-symmetric Hamiltonian. There is a corresponding class of PT-symmetric classical statistical mechanics models with non-Hermitian transfer matrices. For both quantum and classical models, the class of models with generalized PT symmetry is precisely the class where the complex weight problem can be reduced to real weights, i.e., a sign problem. The spatial two-point functions of such models can exhibit three different behaviors: exponential decay, oscillatory decay, and periodic behavior. The latter two regions are associated with PT symmetry breaking, where a Hamiltonian or transfer matrix has complex conjugate pairs of eigenvalues. The transition to a spatially modulated phase is associated with PT symmetry breaking of the ground state, and is generically a first-order transition. In the region where PT symmetry is unbroken, the sign problem can always be solved in principle. Moreover, there are models with PT symmetry which can be simulated for all parameter values, including cases where PT symmetry is broken.