Exact Bethe Ansatz Spectrum of a Tight-Binding Chain with Dephasing Noise

Abstract

We construct an exact map between a tight-binding model on any bipartite lattice in the presence of dephasing noise and a Hubbard model with imaginary interaction strength. In one dimension, the exact many-body Liouvillian spectrum can be obtained by application of the Bethe ansatz method. We find that both the nonequilibrium steady state and the leading decay modes describing the relaxation at late times are related to the η-pairing symmetry of the Hubbard model. We show that there is a remarkable relation between the time evolution of an arbitrary k-point correlation function in the dissipative system and k-particle states of the corresponding Hubbard model.

Exact Nonequilibrium Steady State of Open XXZ/XYZ Spin- 1/2 Chain with Dirichlet Boundar

“…It has, however, remained an open question of how these exact steady state solutions fit into the general framework of integrability. For example, except in the special case of dissipatively driven noninteracting models [12], the solvable dissipatively driven boundaries cannot be generated using the solutions of the ubiquitous reflection equations [13], which constitute the standard framework for generating integrable boundaries in the coherent (nondissipative, Hamiltonian) setting.In the present letter we make a step forward in the understanding of integrability of open XYZ spin-1/2 chain, dissipatively driven at the boundaries. We present an exact solution for the nonequilibrium steady state of the model with arbitrary boundary processes, as long as the edge spins are described by pure states in the large dissipation limit.…”

“…It has, however, remained an open question of how these exact steady state solutions fit into the general framework of integrability. For example, except in the special case of dissipatively driven noninteracting models [12], the solvable dissipatively driven boundaries cannot be generated using the solutions of the ubiquitous reflection equations [13], which constitute the standard framework for generating integrable boundaries in the coherent (nondissipative, Hamiltonian) setting.…”

“…that can be interpreted as an extended version of the U q (sl 2 ) algebra, where 1 2 (q + q −1 ) = ∆. Unlike the usual U q (sl 2 ) algebra with three generators, the extension (12) has infinite number of generators and is equivalent to the recurrence relations (10). Vector |0 is the highestweight element of the representation given in (11).…”

“…Vector |0 is the highestweight element of the representation given in (11). For L ± n ≡ L ± n+1 ≡ S ± , and after substitution K ± = q ±S z , algebra (12) reduces to the usual U q (sl 2 ), which governs the exact solution of the dissipatively driven XXZ chain for boundary driving along the z-axis, i.e. for φ l = φ r = FIG.…”

Yang-Baxter integrable Lindblad equations

“…The first example of a Lindblad equation that is related to an interacting Yang-Baxter integrable model was presented in Ref. [27], where it was shown that the Lindblad equation for a tight-binding chain with dephasing noise can be mapped onto a fermionic Hubbard model with purely imaginary interactions. We now briefly review some results obtained in that work.…”