Entanglement growth in diffusive systems with large spin
Entanglement growth in diffusive systems with large spin
复制标题
大自旋扩散系统中的纠缠增长
DOI：
10.1038/s42005-021-00594-4
复制
发表时间：
2021
影响因子：
5.5
通讯作者：
Rakovszky T
中科院分区：
文献类型：
--
作者：
Rakovszky T
最近的工作1，2认为，指数α> 1的雷尼熵Sα在扩散输运的系统中表现出亚弹道增长。随后的一项工作，由Annidarian 3声称，这种亚弹道增长只发生在某些情况下（特别是，d= 1维系统与q= 2个国家的每一个网站），一般被取代的弹道增长，在没有进一步的微调。下面，我们试图使扩散（而不是弹道）雷尼增长所需的条件精确化，并认为它们适用于比Annidarian [3]所建议的更广泛的一类系统。特别是，由Nididarian提出的避免扩散增长的例子是因为额外的非保守自由度的存在，而不仅仅是它们更大的局部希尔伯特空间。第3章考虑了U（1）对称Floquet系统，并声称要使Sα> 1 ffi t p需要所有的在位对角算子（在某些优选的基础上）对应于守恒量，其输运行为是扩散的（或较慢的）。这在具有单个U（1）对称性的每个位置q= 2个状态的系统（例如自旋为1/2的系统）中自动满足（例如，∑ jSz j是守恒的），但对于q> 2，通常不是这种情况，导致在这样的系统中，Sα> 1~ t，除非存在额外的守恒密度（例如，如果∑ jm Sz j <$2也是单独守恒的）。我们现在提出的证据表明，这种说法是不正确的，一般来说，仅Sz的守恒就足以诱导任意有限q的ffffi t p增长。我们还强调了Nidarian所做的假设，我们预计这些假设是造成这种分歧的原因。通过在q= 3的系统中计算S2，可以直接反驳上述主张。这在随机电路模型中很容易实现，扩展了早期的结果，其中对q= 2链1进行了相同的操作。具体地说，我们考虑一个链，其中的在位希尔伯特空间类似于无限相互作用极限下的哈伯德模型（即，双占据投影）：三个在位态对应于一个空的位置（0 j i），或者一个被自旋向上/自旋向下的粒子占据的位置（“，#分别）。我们发展的系统与砖墙电路的2站点随机幺正守恒的粒子总数，但不是自旋。
Recent works 1, 2 argued that Rényi entropies Sα with indices α> 1 exhibit a sub-ballistic,/ffiffi t p, growth in systems with diffusive transport. A subsequent work by Žnidarič 3 claims that such sub-ballistic growth occurs only in certain cases (in particular, d= 1 dimensional systems with q= 2 states per site) and is generically replaced by ballistic growth in the absence of further fine-tuning. Below, we try to make precise the conditions needed for diffusive (rather than ballistic) Rényi growth and argue that they apply to a much wider class of systems than what is suggested by Žnidarič 3. In particular, the examples presented by Žnidarič that avoid diffusive growth do so because of the presence of additional non-conserved degrees of freedom, not merely their larger local Hilbert space. Žnidarič 3 considers U (1)-symmetric Floquet systems and claims that to have Sα> 1 ffiffi t p requires that all on-site diagonal operators (in some preferred basis) correspond to conserved quantities, with transport behavior that is diffusive (or slower). This is automatically satisfied in a system with q= 2 states per site (eg, a spin-1/2 system) with a single U (1) symmetry (eg,∑ jSz j being conserved), but it is not generally the case for q> 2, leading to the claim that in such systems, Sα> 1~ t, unless additional conserved densities are present (eg, if∑ jðSz j Þ2 is also separately conserved). We now present evidence that this claim is incorrect and that generically the conservation of Sz alone is sufficient to induce ffiffi t p growth for arbitrary finite q. We also highlight the assumptions Žnidarič makes that we expect are responsible for this disagreement. A direct refutation of the above claim is obtained by evaluating S2 in a system with q= 3. This is readily achieved in a random circuit model, extending earlier results where the same was done for a q= 2 chain 1. To be concrete, we consider a chain where the on-site Hilbert space resembles a Hubbard model in the infinite interaction limit (ie, with double occupancies projected out): the three on-site states correspond to an empty site (0j i), or a site occupied by a spin-up/spin-down particle (",# respectively). We evolve the system with a brick-wall circuit of 2-site random unitaries which conserve the total number of particles but not the spin.
影响因子：
12.5
作者：
Nahum, Adam;Vijay, Sagar;Haah, Jeongwan
通讯作者：
Haah, Jeongwan