We investigate the phase diagram of hard-core bosons on a square lattice with competing interactions. The hard-core bosons can also be represented by spin- $1/2$ operators and the model can therefore be mapped onto an anisotropic ${J}_{1}$ - ${J}_{2}$ Heisenberg model. We find the N\'eel state and a collinear antiferromagnetic state as classical ordered phases to be suppressed by the introduction of ferromagnetic exchange terms in the $x$ - $y$ plane that result in a ferromagnetic phase for large interactions. For an intermediate regime, the emergence of new quantum states like valence bond crystals or supersolids is predicted for similar models. We do not observe any signal for long-range order in terms of conventional order or dimer correlations in our model and find an exponential decay in the spin correlations. Hence, all evidence is pointing toward a quantum-disordered ground state for a small region in the phase diagram.We investigate the phase diagram of hard-core bosons on a square lattice with competing interactions. The hard-core bosons can also be represented by spin-$1/2$ operators and the model can therefore be mapped onto an anisotropic ${J}_{1}$-${J}_{2}$ Heisenberg model. We find the N\'eel state and a collinear antiferromagnetic state as classical ordered phases to be suppressed by the introduction of ferromagnetic exchange terms in the $x$-$y$ plane that result in a ferromagnetic phase for large interactions. For an intermediate regime, the emergence of new quantum states like valence bond crystals or supersolids is predicted for similar models. We do not observe any signal for long-range order in terms of conventional order or dimer correlations in our model and find an exponential decay in the spin correlations. Hence, all evidence is pointing toward a quantum-disordered ground state for a small region in the phase diagram.

arXiv:1101.5115Physical Review BMay 31, 201112 citations

Ferromagnetism in the Hubbard model

Andreas Mielke, Hal Tasaki

Communications in Mathematical PhysicsNov 1, 1993369 citations

Spin-flip-induced superfluidity in a ring of spinful hard-core bosons

Kaushal Kumar Kesharpu, E. A. Kochetov

The $t\ensuremath{-}J$ Hamiltonian of the spinful hard-core bosonic ring in the Nagaoka limit is solved. The energy spectrum becomes quantized due to presence of spin, where each energy level corresponds to a cyclic permutation state of the spin chains. The ground state is true ferromagnetic when the ring contains $N=2$ and 3 spinful hard-core bosons; for all other $N$ it is a mixture of the ferromagnetic and nonferromagnetic states. This behavior is different from the fermionic ring, where ground state is true ferromagnetic only for $N=3$ . It is shown that the intrinsic spin-generated gauge fields are analogous to the synthetic gauge fields generated by rotation of either the condensate or the confining potential. It is argued that the low-lying excited levels of the spin-flipped states intrinsically support the superfluidity. Possible ways to experimentally verify these results are also discussed.The $t\ensuremath{-}J$ Hamiltonian of the spinful hard-core bosonic ring in the Nagaoka limit is solved. The energy spectrum becomes quantized due to presence of spin, where each energy level corresponds to a cyclic permutation state of the spin chains. The ground state is true ferromagnetic when the ring contains $N=2$ and 3 spinful hard-core bosons; for all other $N$ it is a mixture of the ferromagnetic and nonferromagnetic states. This behavior is different from the fermionic ring, where ground state is true ferromagnetic only for $N=3$. It is shown that the intrinsic spin-generated gauge fields are analogous to the synthetic gauge fields generated by rotation of either the condensate or the confining potential. It is argued that the low-lying excited levels of the spin-flipped states intrinsically support the superfluidity. Possible ways to experimentally verify these results are also discussed.

arXiv:2209.06149Physical Review ASep 29, 20222 citations

Ferromagnetism in the Hubbard Model

Wolfgang Nolting, Michael Potthoff, T. Herrmann +1 more

arXiv:cond-mat/0107255Lecture notes in physicsJan 1, 20015 citations

We investigate the phase diagram of hard-core bosons on a square lattice with competing interactions. The hard-core bosons can also be represented by spin-

1/2

operators and the model can therefore be mapped onto an anisotropic

{J}_{1}

{J}_{2}

Heisenberg model. We find the N\'eel state and a collinear antiferromagnetic state as classical ordered phases to be suppressed by the introduction of ferromagnetic exchange terms in the

x

y

plane that result in a ferromagnetic phase for large interactions. For an intermediate regime, the emergence of new quantum states like valence bond crystals or supersolids is predicted for similar models. We do not observe any signal for long-range order in terms of conventional order or dimer correlations in our model and find an exponential decay in the spin correlations. Hence, all evidence is pointing toward a quantum-disordered ground state for a small region in the phase diagram.

N=2

and 3 spinful hard-core bosons; for all other

N

it is a mixture of the ferromagnetic and nonferromagnetic states. This behavior is different from the fermionic ring, where ground state is true ferromagnetic only for

N=3

. It is shown that the intrinsic spin-generated gauge fields are analogous to the synthetic gauge fields generated by rotation of either the condensate or the confining potential. It is argued that the low-lying excited levels of the spin-flipped states intrinsically support the superfluidity. Possible ways to experimentally verify these results are also discussed.