Phase diagram of the non-Hermitian asymmetricXXZspin chain

Breakdown of the Mott insulator: Exact solution of an asymmetric Hubbard model

“…The difference among them is the mechanism to realize the insulating phases when Ψ = 0: The Mott insulator is stabilized by the Hubbard interaction for the present model, whereas the Anderson insulator is realized by random potentials for disordered tight-binding models, and the spin-gapped state appears by the Ising-anisotropy for the asymmetric XXZ model. Therefore, the present insulator-metal transition may have essentially the same origin as for the Hatano-Nelson model [14] and also the asymmetric XXZ model [22,28].…”

“…The Bethe ansatz method still works even for such unconventional Hamiltonian, because asymmetric hoppings in the model are incorporated as twisted boundary conditions with imaginary twist angle [31,32], as mentioned above. In fact, the asymmetric XXZ model have been extensively investigated by the Bethe ansatz method [21][22][23][24][25][26][27][28][29]. It has been shown that the gap due to Ising-anisotropy closes when the imaginary twist is increased [22,28].…”

“…In fact, the asymmetric XXZ model have been extensively investigated by the Bethe ansatz method [21][22][23][24][25][26][27][28][29]. It has been shown that the gap due to Ising-anisotropy closes when the imaginary twist is increased [22,28]. Now, applying the Bethe-ansatz technique to our model, we diagonalize the Hamiltonian (1) to obtain the Bethe-ansatz equations [10,[33][34][35],…”

The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics

“…In particular, combinatorial expansions for the energy such as (85) valid for finite values of L and N are not known. However, a very thorough study has been carried out, in the limit L → ∞, by Doochul Kim and his collaborators in a series of papers (Noh and Kim 1994, Kim 1995, Kim 1997, Lee and Kim 1999; see also related works on the non-Hermitian XXZ chain by Albertini et al 1996Albertini et al , 1997. They developed a perturbative scheme that enabled them to calculate the finite size corrections of the gap and the low lying excitations of the asymmetric XXZ chain.…”

Direction-Dependent Free Energy Singularity of the Antiferroelectric Asymmetric Six-Vertex Model

“…If one treats the problem with the transfer matrix method, an exact solution is provided by the Bethe-ansatz [1,2,3]. The phase diagram was outlined in the original paper [1], while further developments came more recently [2,5,6,7,8] (the list is not exhaustive. Papers dealing with the ferroelectric regime are not included).…”