The tensor-network renormalization group (TNRG) is used to study phase transitions in quantum and classical systems. This paper incorporates lattice symmetries and PT symmetry in TNRG for the hard-square lattice gas model, comparing mean-field theory, exact diagonalization, and TNRG results to validate the approach and understand critical behavior.
Key findings
TNRG accurately incorporates lattice symmetries and PT symmetry in two dimensions.
Mean-field theory fails to capture checkerboard ordering due to local correlations neglect.
Exact diagonalization confirms checkerboard order at intermediate chemical potentials.
Symmetry enforcement in TNRG maintains physical properties and reveals spontaneous symmetry breaking.
Limitations & open questions
Future work needed to extend TNRG to larger bond dimensions.
Critical exponents extraction is an open question for future research.