Abstract
We prove that translationally invariant Hamiltonians of a chain of n qubits with nearestneighbour interactions have two seemingly contradictory features. Firstly in the limit $${n \rightarrow \infty}$$n→∞ we show that any translationally invariant Hamiltonian of a chain of n qubits has an eigenbasis such that almost all eigenstates have maximal entanglement between fixedsize subblocks of qubits and the rest of the system; in this sense these eigenstates are like those of completely general Hamiltonians (i.e., Hamiltonians with interactions of all orders between arbitrary groups of qubits). Secondly, in the limit $${n \rightarrow \infty}$$n→∞ we show that any nearestneighbour Hamiltonian of a chain of n qubits has a Gaussian density of states; thus as far as the eigenvalues are concerned the system is like a noninteracting one. The comparison applies to chains of qubits with translationally invariant nearestneighbour interactions, but we show that it is extendible to much more general systems (both in terms of the local dimension and the geometry of interaction). Numerical evidence is also presented that suggests that the translational invariance condition may be dropped in the case of nearestneighbour chains.
Original language  English 

Pages (fromto)  81102 
Number of pages  22 
Journal  Communications in Mathematical Physics 
Volume  338 
Issue number  1 
Early online date  1 May 2015 
DOIs  
Publication status  Published  1 Aug 2015 
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Professor Noah Linden
 Fundamental Bioscience
 School of Mathematics  Professor of Theoretical Physics
 The Bristol Centre for Nanoscience and Quantum Information
 Applied Mathematics
 Quantum Information Theory
 Mathematical Physics
Person: Academic , Member