# Entanglement spectrum of a random partition: Connection with the localization transition

## Abstract

We study the entanglement spectrum of a translationally invariant lattice system under a random partition, implemented by choosing each site to be in one subsystem with probability *p*ϵ[0,1]. We apply this random partitioning to a translationally invariant (i.e., clean) topological state, and argue on general grounds that the corresponding entanglement spectrum captures the universal behavior about its *disorder-driven* transition to a trivial localized phase. Specifically, as a function of the partitioning probability *p*, the entanglement Hamiltonian *H _{A}* must go through a topological phase transition driven by the percolation of a random network of edge states. For example, we analytically derive the entanglement Hamiltonian for a one-dimensional topological superconductor under a random partition, and demonstrate that its phase diagram includes transitions between Griffiths phases. We discuss potential advantages of studying disorder-driven topological phase transitions via the entanglement spectra of random partitions.

- Authors:

- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

- Publication Date:

- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE

- OSTI Identifier:
- 1505793

- Alternate Identifier(s):
- OSTI ID: 1184683

- Grant/Contract Number:
- SC0010526

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review. B, Condensed Matter and Materials Physics

- Additional Journal Information:
- Journal Volume: 91; Journal Issue: 22; Journal ID: ISSN 1098-0121

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Vijay, Sagar, and Fu, Liang. Entanglement spectrum of a random partition: Connection with the localization transition. United States: N. p., 2015.
Web. doi:10.1103/physrevb.91.220101.
```

```
Vijay, Sagar, & Fu, Liang. Entanglement spectrum of a random partition: Connection with the localization transition. United States. doi:10.1103/physrevb.91.220101.
```

```
Vijay, Sagar, and Fu, Liang. Mon .
"Entanglement spectrum of a random partition: Connection with the localization transition". United States. doi:10.1103/physrevb.91.220101. https://www.osti.gov/servlets/purl/1505793.
```

```
@article{osti_1505793,
```

title = {Entanglement spectrum of a random partition: Connection with the localization transition},

author = {Vijay, Sagar and Fu, Liang},

abstractNote = {We study the entanglement spectrum of a translationally invariant lattice system under a random partition, implemented by choosing each site to be in one subsystem with probability pϵ[0,1]. We apply this random partitioning to a translationally invariant (i.e., clean) topological state, and argue on general grounds that the corresponding entanglement spectrum captures the universal behavior about its disorder-driven transition to a trivial localized phase. Specifically, as a function of the partitioning probability p, the entanglement Hamiltonian HA must go through a topological phase transition driven by the percolation of a random network of edge states. For example, we analytically derive the entanglement Hamiltonian for a one-dimensional topological superconductor under a random partition, and demonstrate that its phase diagram includes transitions between Griffiths phases. We discuss potential advantages of studying disorder-driven topological phase transitions via the entanglement spectra of random partitions.},

doi = {10.1103/physrevb.91.220101},

journal = {Physical Review. B, Condensed Matter and Materials Physics},

number = 22,

volume = 91,

place = {United States},

year = {2015},

month = {6}

}

*Citation information provided by*

Web of Science

Web of Science

#### Figures / Tables:

*p-*wave superconductor with dimerization of Majorana fermions

*across*(top) and

*within*(bottom) lattice sites, corresponding to a TSC and a trivial

*p-*wave superconductor, respectively.

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*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*