Abstract
We study in this paper the properties of a two-body random matrix ensemble for distinguishable spins. We require the ensemble to be invariant under the group of local transformations and analyze a parametrization in terms of the group parameters and the remaining parameters associated with the ‘entangling’ part of the interaction. We then specialize to a spin chain with nearest-neighbour interactions and numerically find a new type of quantum-phase transition related to the strength of a random external field, i.e. the time-reversal-breaking one-body interaction term.
Highlights
Eugene Wigner introduced random matrix models about fifty years ago into nuclear physics [1]
There the concept of individual qubits and their interactions becomes important. This implies that we enter the field of two-body random ensembles (TBRE) [10, 11], i.e. ensembles of Hamiltonians of n-body systems interacting by two-body forces
In order to show the relevance of the new ensemble we address the simplest possible topology, namely the chain with nearest neighbour interactions. For this system we focus on the ensemble averaged structure of the ground state and demonstrate the existence of an unusual quantum phase transition [16], which is triggered by breaking of time-reversal invariance (TRI)
Summary
Eugene Wigner introduced random matrix models about fifty years ago into nuclear physics [1]. In order to show the relevance of the new ensemble we address the simplest possible topology, namely the chain with nearest neighbour interactions For this system we focus on the ensemble averaged structure of the ground state and demonstrate the existence of an unusual quantum phase transition [16], which is triggered by breaking of time-reversal invariance (TRI). When the strength of external field goes to zero, and time-reversal invariance is restored, we find long range order, logarithmically divergent entanglement entropy, and exponential decay of the spectral gap, while the level repulsion disappears We argue that this quantum phase transition is non-conventional from the point of view of established models, since in what we shall call non-critical case we still find slow power law closing of the spectral gap
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