skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Entanglement spectra of stabilizer codes: A window into gapped quantum phases of matter

Journal Article · · Physical Review. B
 [1];  [1];  [2]
  1. Univ. of Colorado, Boulder, CO (United States)
  2. Princeton Univ., NJ (United States)
+ Show Author Affiliations

The entanglement spectrum (ES) provides a barometer of quantum entanglement and encodes physical information beyond that contained in the entanglement entropy. In this paper, we explore the ES of stabilizer codes, which furnish exactly solvable models for a plethora of gapped quantum phases of matter. Studying the ES for stabilizer Hamiltonians in the presence of arbitrary weak local perturbations thus allows us to develop a general framework within which the entanglement features of gapped topological phases can be computed and contrasted. In particular, we study models harboring fracton order, both type-I and type-II, and compare the resulting ES with that of both conventional topological order and of (strong) subsystem symmetry protected topological (SSPT) states. We find that nonlocal surface stabilizers (NLSS), a set of symmetries of the Hamiltonian which form on the boundary of the entanglement cut, act as purveyors of universal nonlocal features appearing in the entanglement spectrum. While in conventional topological orders and fracton orders, the NLSS retain a form of topological invariance with respect to the entanglement cut, subsystem symmetric systems—fracton and SSPT phases—additionally show a nontrivial geometric dependence on the entanglement cut, corresponding to the subsystem symmetry. This sheds further light on the interplay between geometric and topological effects in fracton phases of matter and demonstrates that strong SSPT phases harbour a measure of quasilocal entanglement beyond that encountered in conventional SPT phases. Here, we further show that a version of the edge-entanglement correspondence, established earlier for gapped two-dimensional topological phases, also holds for gapped three-dimensional fracton models.

Research Organization:
Univ. of Colorado, Boulder, CO (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
SC0014415
OSTI ID:
1612178
Alternate ID(s):
OSTI ID: 1511510
Journal Information:
Physical Review. B, Vol. 99, Issue 20; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 14 works
Citation information provided by
Web of Science

References (109)

A new kind of topological quantum order: A dimensional hierarchy of quasiparticles built from stationary excitations journal December 2015
General Relationship between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States journal May 2012
Fracton topological order from nearest-neighbor two-spin interactions and dualities journal October 2017
Fractons from partons journal October 2017
Commuting Pauli Hamiltonians as Maps between Free Modules journal October 2013
On Many-Body Localization for Quantum Spin Chains journal April 2016
Quantum Glassiness in Strongly Correlated Clean Systems: An Example of Topological Overprotection journal January 2005
X-cube model on generic lattices: Fracton phases and geometric order journal April 2018
Glassy quantum dynamics in translation invariant fracton models journal April 2017
Braiding and gapped boundaries in fracton topological phases journal March 2019
Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States journal July 2008
Edge-state inner products and real-space entanglement spectrum of trial quantum Hall states journal December 2012
Quantum Orders in an Exact Soluble Model journal January 2003
Topological Entanglement and Clustering of Jain Hierarchy States journal June 2009
Bulk-edge correspondence in entanglement spectra journal November 2011
Emergent phases of fractonic matter journal February 2018
A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes journal April 2009
Detecting Topological Order in a Ground State Wave Function journal March 2006
Boundary-Locality and Perturbative Structure of Entanglement Spectra in Gapped Systems journal May 2012
Cage-Net Fracton Models journal April 2019
Topological Entanglement Entropy journal March 2006
Subsystem symmetry protected topological order journal July 2018
Fracton topological order from the Higgs and partial-confinement mechanisms of rank-two gauge theory journal July 2018
Edge-entanglement spectrum correspondence in a nonchiral topological phase and Kramers-Wannier duality journal March 2015
Generalized electromagnetism of subdimensional particles: A spin liquid story journal July 2017
Glassy dynamics and aging in an exactly solvable spin model journal November 1999
Recoverable information and emergent conservation laws in fracton stabilizer codes journal April 2018
Quantum memories at finite temperature journal November 2016
Interactions along an entanglement cut in 2 + 1 D Abelian topological phases journal August 2015
Exotic topological order in fractal spin liquids journal September 2013
Topological phases of fermions in one dimension journal February 2011
Fracton topological order via coupled layers journal June 2017
Fractal symmetries: Ungauging the cubic code journal October 2016
Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order journal October 2010
Localization in Fractonic Random Circuits journal April 2019
Fractal Symmetric Phases of Matter journal January 2019
Deciphering the nonlocal entanglement entropy of fracton topological orders journal April 2018
Anyons in an exactly solved model and beyond journal January 2006
Fracton topological order, generalized lattice gauge theory, and duality journal December 2016
Algebraic Methods for Quantum Codes on Lattices journal January 2017
Duality in Generalized Ising Models and Phase Transitions without Local Order Parameters journal October 1971
Universal edge information from wave-function deformation journal June 2017
Topological entanglement entropy of fracton stabilizer codes journal March 2018
Higgs mechanism in higher-rank symmetric U(1) gauge theories journal June 2018
Classification of subsystem symmetry-protected topological phases journal December 2018
Entanglement entropy from tensor network states for stabilizer codes journal March 2018
Twisted fracton models in three dimensions journal April 2019
Universal quantum computation using fractal symmetry-protected cluster phases journal August 2018
Fracton Models on General Three-Dimensional Manifolds journal August 2018
Spurious Topological Entanglement Entropy from Subsystem Symmetries journal April 2019
Measurement of the Entanglement Spectrum of a Symmetry-Protected Topological State Using the IBM Quantum Computer journal August 2018
Higher-spin Witten effect and two-dimensional fracton phases journal September 2017
Topological Entanglement in Abelian and Non-Abelian Excitation Eigenstates journal February 2011
Subdimensional particle structure of higher rank U ( 1 ) spin liquids journal March 2017
Fixed Points of Wegner-Wilson Flows and Many-Body Localization journal August 2017
Entanglement entropy as a portal to the physics of quantum spin liquids journal February 2013
Edge-entanglement correspondence for a gapped topological phase with symmetry journal May 2017
Universal entanglement signatures of foliated fracton phases journal January 2019
Symmetry-Enriched Fracton Phases from Supersolid Duality journal December 2018
Geometric proof of the equality between entanglement and edge spectra journal July 2012
Relation between the Anderson and Kondo Hamiltonians journal September 1966
Fault-tolerant quantum computation by anyons journal January 2003
Entanglement Spectrum of Topological Insulators and Superconductors journal April 2010
Fractons journal March 2019
Entanglement spectrum of a topological phase in one dimension journal February 2010
Foliated fracton order from gauging subsystem symmetries journal January 2019
Symmetry protection of measurement-based quantum computation in ground states journal November 2012
Entanglement Spectrum of a Disordered Topological Chern Insulator journal September 2010
Foliated field theory and string-membrane-net condensation picture of fracton order journal January 2019
Schrieffer–Wolff transformation for quantum many-body systems journal October 2011
Pinch point singularities of tensor spin liquids journal October 2018
Entanglement and inversion symmetry in topological insulators journal December 2010
Chiral Topological Elasticity and Fracton Order journal February 2019
Hyperbolic fracton model, subsystem symmetry, and holography journal April 2019
A symmetry principle for topological quantum order journal May 2009
Measurement of the Entanglement Spectrum of a Symmetry-Protected Topological State Using the IBM Quantum Computer text January 2018
A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes text January 2008
Entanglement Spectrum of a Disordered Topological Chern Insulator text January 2010
Topological Entanglement in Abelian and non-Abelian Excitation Eigenstates text January 2010
Schrieffer-Wolff transformation for quantum many-body systems text January 2011
Boundary-locality and perturbative structure of entanglement spectra in gapped systems text January 2011
Commuting Pauli Hamiltonians as maps between free modules text January 2012
Edge state inner products and real-space entanglement spectrum of trial quantum Hall states text January 2012
Entanglement Entropy as a Portal to the Physics of Quantum Spin Liquids text January 2013
Exotic topological order in fractal spin liquids text January 2013
A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations text January 2015
Algebraic Methods for Quantum Codes on Lattices text January 2016
Fixed points of Wegner-Wilson flows and many-body localization text January 2016
Edge--Entanglement correspondence for gapped topological phases with symmetry text January 2016
Fractons from Partons text January 2017
Deciphering the nonlocal entanglement entropy of fracton topological orders text January 2017
Higher-Spin Witten Effect and Two-Dimensional Fracton Phases text January 2017
Emergent Phases of Fractonic Matter text January 2017
Correlation function diagnostics for type-I fracton phases text January 2017
Recoverable Information and Emergent Conservation Laws in Fracton Stabilizer Codes text January 2017
Fracton Models on General Three-Dimensional Manifolds text January 2017
Fracton topological order from Higgs and partial confinement mechanisms of rank-two gauge theory text January 2018
Measurement of the entanglement spectrum of a symmetry-protected topological state using the IBM quantum computer text January 2018
Twisted Fracton Models in Three Dimensions text January 2018
Universal quantum computation using fractal symmetry-protected cluster phases text January 2018
Cage-Net Fracton Models text January 2018
Foliated fracton order from gauging subsystem symmetries text January 2018
Localization in fractonic random circuits text January 2018
Spurious topological entanglement entropy from subsystem symmetries text January 2018
Symmetry Enriched Fracton Phases from Supersolid Duality text January 2018
Anyons in an exactly solved model and beyond text January 2005
A symmetry principle for Topological Quantum Order text January 2007
Fault-tolerant quantum computation by anyons text January 1997
Simplex solids in SU(N) Heisenberg models on the kagome and checkerboard lattices text January 2012

Cited By (7)

Detecting subsystem symmetry protected topological order via entanglement entropy journal September 2019
Crystal-to-fracton tensor gauge theory dualities journal October 2019
Sorting topological stabilizer models in three dimensions journal October 2019
Hyperbolic fracton model, subsystem symmetry, and holography. II. The dual eight-vertex model journal December 2019
Gauging permutation symmetries as a route to non-Abelian fractons journal January 2019
Hyperbolic Fracton Model, Subsystem Symmetry, and Holography II: The Dual Eight-Vertex Model text January 2019
Crystal-to-Fracton Tensor Gauge Theory Dualities text January 2019

Similar Records

Comments on foliated gauge theories and dualities in 3+1d
Journal Article · Tue Aug 17 00:00:00 EDT 2021 · SciPost Physics · OSTI ID:1612178
Odd fracton theories, proximate orders, and parton constructions
Journal Article · Fri Nov 06 00:00:00 EST 2020 · Physical Review. B · OSTI ID:1612178
Cage-Net Fracton Models
Journal Article · Wed Apr 17 00:00:00 EDT 2019 · Physical Review. X · OSTI ID:1612178
+1 more

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Materials Science
Physics
Entanglement measures
Geometric & topological phases
Quantum entanglement
Quantum error correction
Symmetry protected topological states
Topological phases of matter