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The zero-temperature XX chain is studied with emphasis on the properties of ablock of $L$ spins inside the chain. We investigate the quantum fluctuationsresulting from the entanglement of the block with the rest of the chain usinganalytical as well as numerical (density matrix renormalization group) methods.It is found that the rest of the chain acts as a thermal environment and aneffective temperature can be introduced to describe the fluctuations. We showthat the effective temperature description is robust in the sense that severalindependent definitions (through fluctuation dissipation theorem, comparingwith a finite temperature system) yield the same functional form in the limitof large block size ($L\to\infty$). The effective temperature can also be shownto satisfy the basic requirements on how it changes when two bodies of equal orunequal temperatures are brought into contact.Comment: 19 pages, 7 figure

Fluctuations in subsystems of the zero-temperatureXXchain: emergence of an effective temperature