418 citations · 2.2k across the 78 of their papers we have counts for
6 papers · 1 filter
On the flux phase conjecture at half-filling: an improved proof
Nicolas Macris, Bruno Nachtergaele
We present a simplification of Lieb's proof of the flux phase conjecture for interacting fermion systems -- such as the Hubbard model --, at half filling on a general class of grap…
The spectral gap of the ferromagnetic XXZ chain
Tohru Koma, Bruno Nachtergaele
We prove that the spectral gap of the spin-1/2 ferromagnetic XXZ chain with Hamiltonian , is given…
Bounds on the mass gap of the ferromagnetic XXZ chain
Bruno Nachtergaele
We prove rigorous lower and upper bounds for the mass gap of the ferromagnetic spin 1/2 XXZ chain. The two bounds coincide asymptotically in the Ising limit . Near the…
The spectral gap for some spin chains with discrete symmetry breaking
Bruno Nachtergaele
We prove that for any finite set of generalized valence bond solid (GVBS) states of a quantum spin chain there exists a translation invariant finite-range Hamiltonian for which thi…
Quasi-state decompositions for quantum spin systems
Bruno Nachtergaele
I discuss the concept of quasi-state decompositions for ground states and equilibrium states of quantum spin systems. Some recent results on the ground states of a class of one-dim…
Geometric Aspects of Quantum Spin States
Michael Aizenman, Bruno Nachtergaele
A number of interesting features of the ground states of quantum spin chains are analized with the help of a functional integral representation of the system's equilibrium states.…