Symmetry-projected wave function methods capture static correlation by breaking and restoring the symmetries of a system. In this article, we present the symmetry-projected spin antisymmetrized geminal power (spin-AGP) state projected onto space group symmetry as well as complex conjugation, spin-flip, and time-reversal symmetries. The method is benchmarked on the 1D XXZ model and the 2D J1 - J2 model with square and triangular lattices. Our results indicate that symmetry projection methods provide a powerful tool for frustrated spin systems.Symmetry-projected wave function methods capture static correlation by breaking and restoring the symmetries of a system. In this article, we present the symmetry-projected spin antisymmetrized geminal power (spin-AGP) state projected onto space group symmetry as well as complex conjugation, spin-flip, and time-reversal symmetries. The method is benchmarked on the 1D XXZ model and the 2D J1 - J2 model with square and triangular lattices. Our results indicate that symmetry projection methods provide a powerful tool for frustrated spin systems.

arXiv:2504.08130The Journal of Chemical PhysicsJul 10, 20250 citations

Symmetry and quantum systems

Anthony Brinton Wolbarst

Jan 1, 19776 citations

Ground state degeneracy in quantum spin systems protected by crystal symmetries

Yang Qi, Chen Fang, Liang Fu

We develop a no-go theorem for two-dimensional bosonic systems with crystal symmetries: if there is a half-integer spin at a rotation center, where the point-group symmetry is $\mathbb D_{2,4,6}$ , such a system must have a ground-state degeneracy protected by the crystal symmetry. Such a degeneracy indicates either a broken-symmetry state or a unconventional state of matter. Comparing to the Lieb-Schultz-Mattis Theorem, our result counts the spin at each rotation center, instead of the total spin per unit cell, and therefore also applies to certain systems with an even number of half-integer spins per unit cell.We develop a no-go theorem for two-dimensional bosonic systems with crystal symmetries: if there is a half-integer spin at a rotation center, where the point-group symmetry is $\mathbb D_{2,4,6}$, such a system must have a ground-state degeneracy protected by the crystal symmetry. Such a degeneracy indicates either a broken-symmetry state or a unconventional state of matter. Comparing to the Lieb-Schultz-Mattis Theorem, our result counts the spin at each rotation center, instead of the total spin per unit cell, and therefore also applies to certain systems with an even number of half-integer spins per unit cell.

arXiv:1705.09190May 25, 20178 citations

Quantum Spin Systems

Ola Bratteli, Derek W. Robinson

Springer eBooksJan 1, 19970 citations

Symmetry Studies of Antiferromagnetic Heisenberg Model

Takashi Ishino, Riichiro Saito, Hiroshi Kamimura

A general treatment of the symmetry for quantum spin systems is presented with the use of permutational operators. Symmetry operations which are commutable with a Hamiltonian form the symmetry group. Complete sets of spin functions which are specified by the total spin ( S tot ) are projected onto the irreducible representations of the symmetry group, using the character table. We show from symmetry consideration that a minimum dimension exists for the ground state of the Heisenberg Hamiltonian with finite N spins. The diagonalization of the Hamiltonian with the use of symmetry consideration can be effectively performed for the complete sets of S tot =0 by the method proposed in this paper. Numerical results of the ground state and all the excited states of S tot =0 are presented for spin systems up to N =20.A general treatment of the symmetry for quantum spin systems is presented with the use of permutational operators. Symmetry operations which are commutable with a Hamiltonian form the symmetry group. Complete sets of spin functions which are specified by the total spin ( S tot ) are projected onto the irreducible representations of the symmetry group, using the character table. We show from symmetry consideration that a minimum dimension exists for the ground state of the Heisenberg Hamiltonian with finite N spins. The diagonalization of the Hamiltonian with the use of symmetry consideration can be effectively performed for the complete sets of S tot =0 by the method proposed in this paper. Numerical results of the ground state and all the excited states of S tot =0 are presented for spin systems up to N =20.

Journal of the Physical Society of JapanNov 15, 199016 citations

We develop a no-go theorem for two-dimensional bosonic systems with crystal symmetries: if there is a half-integer spin at a rotation center, where the point-group symmetry is

\mathbb D_{2,4,6}

, such a system must have a ground-state degeneracy protected by the crystal symmetry. Such a degeneracy indicates either a broken-symmetry state or a unconventional state of matter. Comparing to the Lieb-Schultz-Mattis Theorem, our result counts the spin at each rotation center, instead of the total spin per unit cell, and therefore also applies to certain systems with an even number of half-integer spins per unit cell.