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arXiv · 2005.01758

Prime Suspects in a Quantum Ladder

Giuseppe Mussardo·Andrea Trombettoni·Zhao Zhang
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Abstract

In this Letter we set up a suggestive number theory interpretation of a quantum ladder system made of N coupled chains of spin 1/2. Using the hard-core boson representation and a leg-Hamiltonian made of a magnetic field and a hopping term, we can associate to the spins $s_a$ the prime numbers $p_a$ so that the chains become quantum registers for square-free integers. The rung Hamiltonian involves permutation terms between next neighborhood chains and a coprime repulsive interaction. The system has various phases; in particular there is one whose ground state is a coherent superposition of the first N prime numbers. We also discuss the realization of such a model in terms of an open quantum system with a dissipative Lindblad dynamics.

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Giuseppe Mussardo, Andrea Trombettoni, Zhao Zhang. 2020-05-04. Prime Suspects in a Quantum Ladder. https://doi.org/10.1103/physrevlett.125.240603

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