Exact eigenstates of extended SU($N$) Hubbard models: Generalizations of $η$-pairing states with $N$-particle off-diagonal long-range order

Abstract

We consider N -particle generalizations of η-pairing states in a chain of N -component fermions and show that these states are exact (high-energy) eigenstates of an extended SU(N ) Hubbard model. We compute the singlet correlation function of the states and find that its behavior is qualitatively different for even and odd N . When N is even, these states exhibit off-diagonal long-range order in N -particle reduced density matrix. On the other hand, when N is odd, the singlet correlation function decays exponentially toward the other end of the chain but shows a revival at the other end. Finally, we prove that these states are the unique ground states of suitably tailored Hamiltonians.

Spatial, spin, and charge symmetry projections for a Fermi-Hubbard model on a quantum computer

“…The η symmetry also exists in other systems such as Kondo-lattice systems [116,117] and spin-orbit-coupled systems [80,114] under certain constraints of the Hamiltonian. Moreover, N-particle generalizations of the η-pairing states as eigenstates of an extended SU(N) Fermi-Hubbard model have been reported [118]. Therefore, the η symmetry and in particular its symmetry projection can also help to prepare the ground states of these quantum many-body systems on a quantum computer.…”

“…(C16) is identical with the Givens-rotation gate in Eqs. (117) and (118). Since the Jordan-Wigner string ẐJW,i j can be implemented as the sequences of CZ or fermionic SWAP gates, as shown in Fig.…”

Cooper quartet correlations in infinite symmetric nuclear matter

“…q,Sz /µ = 1.16 [53] as a typical value of Fermi superfluids, the solutions to Eqs. (42b) and (49) are plotted in Fig. 1.…”

“…Moreover, the theoretical framework of quartet correlations in infinite matter can be applied to other systems such as biexciton condensation [34,35], SU(4) Fermi atomic gases [36][37][38], and charge 4e superconductors [39,40]. In the context of interdisciplinary studies of multicomponent fermions, more than two-body cluster states induced by the Cooper instability [41][42][43][44][45][46][47] and groundstate properties and N -particle off-diagonal long-range order of η pairing in the attractive SU(N ) Hubbard model [48,49] have been studied theoretically. Also, the recent experiment indicates the existence of quartet correlations with broken time-reversal symmetry above the superconducting critical temperature in a condensedmatter system [50].…”