Entanglement phase transitions in random stabilizer tensor networks

Journal Article · Thu Mar 10 00:00:00 EST 2022 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.105.104306· OSTI ID:1979728

Yang, Zhi-Cheng  ^[1]; Li, Yaodong  ^[2]; Fisher, Matthew A.  ^[2]; Chen, Xiao ^[3]

---

1. University of Maryland, College Park, MD (United States)
2. University of California, Santa Barbara, CA (United States)
3. Boston College, Chestnut Hill, MA (United States)

Here we explore a class of random tensor network models with “stabilizer” local tensors which we name random stabilizer tensor networks (RSTNs). For RSTNs defined on a two-dimensional square lattice, we perform extensive numerical studies of entanglement phase transitions between volume-law and area-law entangled phases of the one-dimensional boundary states. These transitions occur when either (a) the bond dimension D of the constituent tensors is varied or (b) the tensor network is subject to random breaking of bulk bonds, implemented by forced measurements. In the absence of broken bonds, we find that the RSTN supports a volume-law entangled boundary state with bond dimension D ≥ 3 where D is a prime number, and an area-law entangled boundary state for D = 2. Upon breaking bonds at random in the bulk with probability p, there exists a critical measurement rate p_c for each D ≥ 3 above which the boundary state becomes area-law entangled. To explore the conformal invariance at these entanglement transitions for different prime D, we consider tensor networks on a finite rectangular geometry with a variety of boundary conditions, and extract universal operator scaling dimensions via extensive numerical calculations of the entanglement entropy, mutual information, and mutual negativity at their respective critical points. Our results at large D approach known universal data of percolation conformal field theory, while showing clear discrepancies at smaller D, suggesting a distinct entanglement transition universality class for each prime D. We further study universal entanglement properties in the volume-law phase and demonstrate quantitative agreement with the recently proposed description in terms of a directed polymer in a random environment.

• Research Organization: Univ. of Maryland, College Park, MD (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF); Heising-Simons Foundation; Simons Foundation
• Grant/Contract Number: SC0020312; 651440; PHY- 1607611
• OSTI ID: 1979728
• Journal Information: Physical Review. B, Vol. 105, Issue 10; ISSN 2469-9950
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
dynamical phase transitions
hybrid quantum systems
nonequilibrium statistical mechanics
quantum entanglement
quantum measurements
conformal field theory
tensor network methods