DOI: 10.1103/PhysRevX.8.021013

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DOI: 10.1103/PhysRevX.8.021013 #27

Open refraction-ray opened 5 years ago

refraction-ray commented 5 years ago

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Title: Operator Hydrodynamics, OTOCs, and Entanglement Growth in Systems without Conservation Laws
Reason (optional): Operator dynamics and entanglement spread in random circuit systems.

Relevant paper

Link
Title: Operator Spreading in Random Unitary Circuits

Summary: The two papers both talked about the diffusive of the front of operators in random circuits (Heisenberg picture). The front of OTOC shows diffusive behavior beyond light cone which could described by hydrodynamics. eg. Fig 2 in PhysRevX.8.021013. Random circuit setup is two in two out gates with spin half chain.

Important tools: Operator expansion on operator string basis, and $$\rho_r$$ characterizing the front of operator. Understanding and picture, see page 5&6 eq 12&13 in PhysRevX.8.031057.

refraction-ray commented 5 years ago

Two more relevant work on PRX

Random circuit with some conservations

Operator Spreading and the Emergence of Dissipative Hydrodynamics under Unitary Evolution with Conservation Laws, Vedika Khemani, Ashvin Vishwanath, and David A. Huse, Phys. Rev. X 8, 031057 (2018).
Diffusive Hydrodynamics of Out-of-Time-Ordered Correlators with Charge Conservation, Tibor Rakovszky, Frank Pollmann, and C. W. von Keyserlingk, Phys. Rev. X 8, 031058 (2018).

Summary: See Fig3 in PhysRevX.8.031057 for operator spreading in comparison to unconstrained random circuits.

refraction-ray commented 5 years ago

Comments: It is somehow like three steps from random circuit dynamics to fracton circuits. 1 random circuits; 2 random circuits with conserved U(1) charge; 3 random circuits with conserved U(1) charge and dipole of charges. The third step is nothing else but fracton circuits. For the third step, see the reference in https://github.com/quclub/Paper-reading/issues/20#issue-462414652. Accordingly, the system dynamics goes from thermal to somewhat "MBL" or with quantum scars noticed recently in such fracton circuits as in https://github.com/quclub/Paper-reading/issues/8#issue-461424346 and https://github.com/quclub/Paper-reading/issues/2#issue-461350320