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Title: From tunnels to towers: Quantum scars from Lie algebras and q -deformed Lie algebras

Abstract

We present a general symmetry-based framework for obtaining many-body Hamiltonians with scarred eigenstates that do not obey the eigenstate thermalization hypothesis. Our models are derived from parent Hamiltonians with a non-Abelian (or q-deformed) symmetry, whose eigenspectra are organized as degenerate multiplets that transform as irreducible representations of the symmetry (`tunnels'). We show that large classes of perturbations break the symmetry, but in a manner that preserves a particular low-entanglement multiplet of states -- thereby giving generic, thermal spectra with a `shadow' of the broken symmetry in the form of scars. The generators of the Lie algebra furnish operators with `spectrum generating algebras' that can be used to lift the degeneracy of the scar states and promote them to equally spaced `towers'. Our framework applies to several known models with scars, but we also introduce new models with scars that transform as irreducible representations of symmetries such as SU(3) and q-deformed SU(2), significantly generalizing the types of systems known to harbor this phenomenon. Additionally, we present new examples of generalized AKLT models with scar states that do not transform in an irreducible representation of the relevant symmetry. These are derived from parent Hamiltonians with enhanced symmetries, and bring AKLT-like models intomore » our framework.« less

Authors:
; ; ;
Publication Date:
Research Org.:
Stanford Univ., CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF); US Air Force Office of Scientific Research (AFOSR)
OSTI Identifier:
1730971
Alternate Identifier(s):
OSTI ID: 1785237
Grant/Contract Number:  
SC0021111; DMR-1752759; DMR-1928166; FA9550-20-1-0235
Resource Type:
Published Article
Journal Name:
Physical Review Research
Additional Journal Information:
Journal Name: Physical Review Research Journal Volume: 2 Journal Issue: 4; Journal ID: ISSN 2643-1564
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 74 ATOMIC AND MOLECULAR PHYSICS

Citation Formats

O'Dea, Nicholas, Burnell, Fiona, Chandran, Anushya, and Khemani, Vedika. From tunnels to towers: Quantum scars from Lie algebras and q -deformed Lie algebras. United States: N. p., 2020. Web. https://doi.org/10.1103/PhysRevResearch.2.043305.
O'Dea, Nicholas, Burnell, Fiona, Chandran, Anushya, & Khemani, Vedika. From tunnels to towers: Quantum scars from Lie algebras and q -deformed Lie algebras. United States. https://doi.org/10.1103/PhysRevResearch.2.043305
O'Dea, Nicholas, Burnell, Fiona, Chandran, Anushya, and Khemani, Vedika. Wed . "From tunnels to towers: Quantum scars from Lie algebras and q -deformed Lie algebras". United States. https://doi.org/10.1103/PhysRevResearch.2.043305.
@article{osti_1730971,
title = {From tunnels to towers: Quantum scars from Lie algebras and q -deformed Lie algebras},
author = {O'Dea, Nicholas and Burnell, Fiona and Chandran, Anushya and Khemani, Vedika},
abstractNote = {We present a general symmetry-based framework for obtaining many-body Hamiltonians with scarred eigenstates that do not obey the eigenstate thermalization hypothesis. Our models are derived from parent Hamiltonians with a non-Abelian (or q-deformed) symmetry, whose eigenspectra are organized as degenerate multiplets that transform as irreducible representations of the symmetry (`tunnels'). We show that large classes of perturbations break the symmetry, but in a manner that preserves a particular low-entanglement multiplet of states -- thereby giving generic, thermal spectra with a `shadow' of the broken symmetry in the form of scars. The generators of the Lie algebra furnish operators with `spectrum generating algebras' that can be used to lift the degeneracy of the scar states and promote them to equally spaced `towers'. Our framework applies to several known models with scars, but we also introduce new models with scars that transform as irreducible representations of symmetries such as SU(3) and q-deformed SU(2), significantly generalizing the types of systems known to harbor this phenomenon. Additionally, we present new examples of generalized AKLT models with scar states that do not transform in an irreducible representation of the relevant symmetry. These are derived from parent Hamiltonians with enhanced symmetries, and bring AKLT-like models into our framework.},
doi = {10.1103/PhysRevResearch.2.043305},
journal = {Physical Review Research},
number = 4,
volume = 2,
place = {United States},
year = {2020},
month = {12}
}

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