Ground State Degeneracy of Interacting Spinless Fermions

Abstract

We propose an eigen-operator scheme to study the lattice model of interacting spinless fermions at half filling and show that this model possesses a hidden form of reflection positivity in its Majorana fermion representation. Based on this observation, we prove rigourously that the ground state of this model is either unique or doubly degenerate if the lattice size $N$ is even, and is always doubly degenerate if $N$ is odd. This proof holds in all dimensions with arbitrary lattice structures.

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Cited by in corpus (12)

• Majorana Positivity and the Fermion sign problem of Quantum Monte Carlo Simulations
• Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications
• Split orthogonal group: A guiding principle for sign-problem-free fermionic simulations
• Spontaneous particle-hole symmetry breaking of correlated fermions on the Lieb lattice
• Rigorous results on the ground state of the attractive SU($N$) Hubbard model
• Semigroup approach to the sign problem in quantum Monte Carlo simulations
• Interacting spinless fermions on the square lattice: Charge order, phase separation, and superconductivity
• Projective symmetry group classification of $Z_3$ parafermion spin liquids on a honeycomb lattice
• Parity-dependent phase diagrams in spin-cluster two-leg ladders
• Lowest energy states of an $O(N)$ fermionic chain
• An algebraic approach to revealing magnetic structures of ground states in many-electron systems
• Ground state of one-dimensional fermion-phonon systems