Reduced density operators of finite-sized Heisenberg XXZ chains

Francisco Castilho Alcaraz, Michael Baake, Uwe Grimm +1 more

The finite-size scaling spectra of the XXZ Heisenberg chain are presented for even and odd numbers of sites, respectively. The operator content is given for free as well as for toroidal boundary conditions.

J. Ginibre

和樹 山本, Kazuki YAMAMOTO

Eric Ashendorf, Joe Weiner, Jay D. Mancini +2 more

Mario Salerno, Vladislav Popkov

In this paper we investigate the spin currents and the von Neumann entropy (vNE) of a Heisenberg XXZ chain in contact with twisted XY-boundary magnetic reservoirs by means of the Lindblad master equation. Exact solutions for the stationary reduced density matrix are explicitly constructed for chains of small sizes by using a quantum symmetry operation of the system. These solutions are then used to investigate the optimal transport in the chain in terms of the vNE. As a result we show that the maximal spin current always occurs in the proximity of minima of the vNE and for particular choices of parameters (coupling with reservoirs and anisotropy) it can exactly coincide with them. As the coupling is increased, current reversals may occur and in the limit of strong coupling we show that minima of the vNE tend to zero, meaning that the maximal transport is achieved in this case with states that are very close to pure states.

Chris J. Hamer

The methods of de Vega and Woynarovitch (1985) are used to calculate finite-size corrections to the ground state energy in different sectors for the XXZ Heisenberg chain, in the critical region -1< Delta <1. The finite-size scaling amplitude for the mass gap between the lowest lying sectors is derived. Using conformal invariance, the scaling dimension is extracted for an associated operator, corresponding to the electric field operator in the 8-vertex model. The conjecture of Baxter and Kelland (1974) for the electric field exponent is confirmed.