量子阶梯中的头号嫌疑犯
Prime Suspects in a Quantum Ladder
摘要：
在这封信中，我们建立了一个暗示性的数论解释的量子阶梯系统的N个耦合链的自旋1/2。使用硬核玻色子表示和由磁场和跳跃项组成的腿哈密顿量，我们可以将素数$p_a$与自旋$s_a$联系起来，这样链就成为无平方整数的量子寄存器。梯级哈密顿量涉及相邻链之间的置换项和互质排斥相互作用。该系统有各种相位;特别是有一个其基态是前N个素数的相干叠加。我们还讨论了在具有耗散Lindblad动力学的开放量子系统中该模型的实现。
英文摘要：
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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