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Finite size behavior of collective quantum spin systems

LIBERTI G, Franco Piperno, Francesco Plastina

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

In a ferromagnetic spin chain, the control of the local effective magnetic field allows us to manipulate the static and dynamical properties of entanglement. In particular, the propagation of quantum correlations can be driven to a great extent so as to achieve an entanglement transfer on demand toward a selected site.

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The coherent transport of quantum states between distant qubits is one of the key milestones towards the realisation of large-scale quantum computers [1]. For static qubits, this state transfer is often envisioned to be carried out only by the internal dynamics of the system, which has the great advantage that detrimental influences of the environment are minimised. A chain of spin-1/2-qubits with ferromagnetic coupling has been suggested as an implementation of a coherent transport which is perfect in theory [2]. In this scheme, a precise engineering of the coupling strengths between adjacent spins is crucial. To date, such a quantum state transfer has only been achieved for the modest system size of three qubits, employing nuclear magnetic resonance [3]. However, this concept is by no means restricted to spin chains; it is therefore possible to resort to another physical platform, such as optics, to investigate the capabilities of the transferring Hamiltonian.
This paper considers a finite-sized two-leg ladder of spin-1/2 particles with local inter-chain Ising interaction. We include the effects of an external magnetic field by incorporating a Zeeman-type coupling between the magnetic field and the spins localized on the lattice sites. To analyze the system, we utilize the transfer-matrix formalism to calculate the partition function. We compute the magnetization for different configurations by varying the system's parameters. We observe the presence 3of spontaneous magnetization within the system. As the inter-chain Ising interaction changes its sign, the magnetization value changes from negative to positive values. Furthermore, we identify a phase transition from diamagnetic to ferromagnetic states when examining the temperature dependence of the magnetization at zero magnetic fields. We observe a step-like behavior in the magnetization curve in the low temperature limit.
We present exact analytical results for a critical field and correlations functions for N site ring and arbitrary size two dimensional coupled chains in a two component Hubbard model with a strong magnetic field and exactly at half-filling. The critical field near the Nagaoka instability with one spin and two spin flips is driven by Coulomb interaction, lattice geometry, dimensionality and crucially depends on the number of atomic sites N. Unsaturated ferromagnetism, reminiscent of Nagaoka-like behavior, and spin liquid state are examined in the structure of off-diagonal spin correlation at large U.