Physical systems have some degree of disorder present in them. We discuss how to treat natural, thermal entanglement in any random macroscopic system from which a thermodynamic witness bounded by a constant can be found. We propose that functional many-body perturbation theory be applied to allow either a quenched or an annealed average over the disorder to be taken. We find, when considering the example of an XX Heisenberg spin chain with a random coupling strength, that the region of natural entanglement detected by both witnesses can be enhanced by the disorder.
We investigate macroscopic entanglement in an infinite XX spin-1 2 chain with staggered magnetic field, B l = B + e −iπl b. Using single-site entropy and by constructing an entanglement witness, we search for the existence of entanglement when the system is at absolute zero, as well as in thermal equilibrium. Although the role of the alternating magnetic field b is, in general, to suppress entanglement as do B and T , we find that when T = 0, introducing b allows the existence of entanglement even when the uniform magnetic field B is arbitrarily large. We find that the region and the amount of entanglement in the spin chain can be enhanced by a staggered magnetic field.PACS numbers: 03.65. Ud, 75.10.Jm Quantum entanglement is a fundamental aspect of quantum physics. It demonstrates the non-local nature of the theory in that an entangled system contains correlations that cannot be described by its subsystems alone. Instead these quantum correlations are attributed to the overall system [1]. Further, entanglement is an important resource in quantum information and computation. In particular, solid state quantum computation has become a topic of much research and several proposals for physical implementation have been investigated. The Heisenberg interaction is the model used in many physical applications of quantum computation, for example, quantum dots [2] and cavity QED [3]. It has also been shown that the Heisenberg interaction can be used to implement any circuit required by a quantum computer [4]. Therefore, entanglement in one-dimensional spin chains has been the subject of much interest. This entanglement has been studied both in the case of a finite spin chain [5,6] and in the thermodynamic limit [7] where the length of the spin chain becomes infinite.Macroscopic entanglement is a more recent concept. It demonstrates that non-local correlations persist even in the thermodynamic limit. This type of entanglement can be detected by measuring macroscopic quantities such as internal energy and magnetic susceptibility [13] as it has been proven that such quantities can be used as entanglement witnesses. It has been shown experimentally [14,15], that the behaviour of observable macroscopic quantities such as magnetic susceptibility depends, most significantly at low temperatures, on entanglement. This demonstrates that entanglement is vital in the explanation of how macroscopic materials behave. Macroscopic entanglement in a Heisenberg spin chain has been studied previously [7] only for a uniform magnetic field. The Hamiltonian of this chain is used to construct an entanglement witness [8, 9, 10] which shows that entanglement disappears for high uniform magnetic field just as it does for high temperature.In real systems, the magnetic field need not be the same at each site in the chain. In solid state systems, there exists a possibility that an inhomogeneous Zeeman coupling could induce a non-uniform magnetic field. Moreover, an experimental system is likely to contain magnetic impurities. Copper Benzoate [11]...
We present a method for detecting the entanglement of a state using non-equilibrium processes. A comparison of relative entropies allows us to construct an entanglement witness. The relative entropy can further be related to the quantum Jarzynski equality, allowing non-equilibrium work to be used in entanglement detection. To exemplify our results, we consider two different spin chains.
We investigate how the interplay between a staggered magnetic field and staggered coupling strength affects both ground state and thermal entanglement. Upon analytically calculating thermodynamic quantities and the correlation functions for such a system, we consider both the global Meyer-Wallach measure of entanglement and the concurrence between pairs of spins. We discover two quantum phase transitions present in the model and show that the quantum phase transitions are reflected in the behaviour of the entanglement at zero temperature. We discover that increasing the alternating field and alternating coupling strength can actually increase the amount of entanglement present at both zero temperature and for thermal states of the system.
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