Charge ordering induced by strong short-range repulsion in itinerant fermion systems typically follows a two-site alternation pattern. However, the covariance matrix spectrum of the one-dimensional, half-filled, spinless $t\ensuremath{-}V$ model reveals a post-Hartree-Fock picture at strong repulsion, with emergent four-site disruptions of the underlying staggered mean-field state. These disruptions are captured in a thermodynamically extensive manner by a compact four-fermion coupled cluster (doubles) state (CCS). Remarkably, all properties of this state may be computed analytically by combinatorial means, and also derived from an exactly solvable correlated hopping Hamiltonian. Furthermore, this coupled cluster state can be reexpressed as a low-rank matrix product state (MPS) with bond dimension exactly four. In addition, we unveil a hidden connection between this coupled cluster ansatz and a Rokhsar-Kivelson state (RKS), which is the ground state of a solvable parent quantum tetramer model. The broad picture that we uncover here thus provides deep connections between several core concepts of correlated fermions and quantum chemistry that have previously enjoyed limited synergy. In contrast to a recent perturbative treatment on top of Hartree-Fock theory, our approach asymptotically captures the correct correlations in the $t\ensuremath{-}V$ model at small $t/V$ , and remains a qualitatively accurate approximation even outside the perturbative regime. Our results make the case for further studies of the covariance matrix for correlated electron systems in which ground states have nontrivial unit-cell structure.Charge ordering induced by strong short-range repulsion in itinerant fermion systems typically follows a two-site alternation pattern. However, the covariance matrix spectrum of the one-dimensional, half-filled, spinless $t\ensuremath{-}V$ model reveals a post-Hartree-Fock picture at strong repulsion, with emergent four-site disruptions of the underlying staggered mean-field state. These disruptions are captured in a thermodynamically extensive manner by a compact four-fermion coupled cluster (doubles) state (CCS). Remarkably, all properties of this state may be computed analytically by combinatorial means, and also derived from an exactly solvable correlated hopping Hamiltonian. Furthermore, this coupled cluster state can be reexpressed as a low-rank matrix product state (MPS) with bond dimension exactly four. In addition, we unveil a hidden connection between this coupled cluster ansatz and a Rokhsar-Kivelson state (RKS), which is the ground state of a solvable parent quantum tetramer model. The broad picture that we uncover here thus provides deep connections between several core concepts of correlated fermions and quantum chemistry that have previously enjoyed limited synergy. In contrast to a recent perturbative treatment on top of Hartree-Fock theory, our approach asymptotically captures the correct correlations in the $t\ensuremath{-}V$ model at small $t/V$, and remains a qualitatively accurate approximation even outside the perturbative regime. Our results make the case for further studies of the covariance matrix for correlated electron systems in which ground states have nontrivial unit-cell structure.

arXiv:2507.02625Physical review. B./Physical review. BSep 8, 20250 citations

Conserved charges of series of solvable lattice models

Kazuhiko Minami

An infinite number of solvable Hamiltonians, including the transverse Ising chain, the XY chain with an external field, the cluster model with next-nearest-neighbor x - x interactions, or with next-nearest-neighbor z - z interactions, and other solvable models that can be mapped to the free fermion system are considered. All the conserved charges of these models written by the string-type products of the interactions are obtained. In the case of the transverse Ising chain, all the known charges are rederived, and in the case of the other models, new conserved charges are obtained.An infinite number of solvable Hamiltonians, including the transverse Ising chain, the XY chain with an external field, the cluster model with next-nearest-neighbor x - x interactions, or with next-nearest-neighbor z - z interactions, and other solvable models that can be mapped to the free fermion system are considered. All the conserved charges of these models written by the string-type products of the interactions are obtained. In the case of the transverse Ising chain, all the known charges are rederived, and in the case of the other models, new conserved charges are obtained.

arXiv:2410.20798Nuclear Physics BFeb 14, 20251 citation

Few-cluster solutions of many-fermion problem

I. A. Gnilozub, Sergei Kurgalin, Yu. M. Tchuvil’sky

Nuclear Physics AJun 1, 20075 citations

t/V

, and remains a qualitatively accurate approximation even outside the perturbative regime. Our results make the case for further studies of the covariance matrix for correlated electron systems in which ground states have nontrivial unit-cell structure.