Cálculo de la concurrencia para el modelo de Heisenberg

Abstract

La concurrencia es una cantidad que nos permite medir el grado de entreveramiento que presenta un sistema cuántico y se puede calcular a partir de la matriz densidad reducida. En este artículo mostramos explicitamente como calcular la concurrencia para una cadena finita de espines s = 1/2 descrita por el modelo de Heisenberg anistrópico. Nosotros mostramos que para cadenas finitas la concurrencia tiene un máximo en el punto crítico ∆ = 1, la cual es una de las principales características en el límite termodinámico. Se mostró que es posible obtener información sobre las transiciones de fase del modelo calculando la concurrencia para cadenas de por lo menos 12 sitios. Palavras-chave: concurrencia, entreveramiento cuántico, modelo de Heisenberg.The concurrence is a quantity that allows us to measure the entanglement of a quantum system and can be calculated from the reduced density matrix. In this paper we show explicitly how to calculate the concurrence for a finite chain of spins s = 1/2 described by the anisotropic Heisenberg model. We show that for finite chains the concurrence has a maximum at the critical point ∆ = 1, which is the main feature in the thermodynamic limit. We observe that it is possible to obtain information about quantum phase transitions of the model by calculating the concurrence for chains of at least 12 sites.

Entanglement and the ticking of the clock

“…In a few decades, entanglement evolved from being a puzzling manifestation of the weirdness of quantum mechanics to become a useful resource in promising quantum technologies, and a central phenomenon for the understanding of many aspects of the workings of Nature [1][2][3]. As a result, entanglement has gained a more prominent role in classrooms, and efforts have been devoted to incorporate the diverse facets of the concept of entanglement to the teaching of quantum mechanics [4][5][6][7][8][9][10][11][12][13]. However, there is an interesting aspect of quantum theory -known as the timeless picture of quantum mechanics-in which entanglement is crucial for solving the so-called time problem, that has received little or no attention from a pedagogical point of view.…”