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Title: Symmetry-Enforced Many-Body Separability Transitions

We study quantum many-body mixed states with a symmetry from the perspective of , i.e., whether a mixed state can be expressed as an ensemble of short-range-entangled symmetric pure states. We provide evidence for “symmetry-enforced separability transitions” in a variety of states, where in one regime the mixed state is expressible as a convex sum of symmetric short-range-entangled pure states, while in the other regime, such a representation is not feasible. We first discuss the Gibbs state of Hamiltonians that exhibit spontaneous breaking of a discrete symmetry, and argue that the associated thermal phase transition can be thought of as a symmetry-enforced separability transition. Next we study cluster states in various dimensions subjected to local decoherence, and identify several distinct mixed-state phases and associated separability phase transitions, which also provides an alternative perspective on recently discussed “average symmetry-protected topological order.” We also study decoheredp+ipsuperconductors, and find that if the decoherence breaks the fermion parity explicitly, then the resulting mixed state can be expressed as a convex sum of nonchiral states, while a fermion parity–preserving decoherence results in a phase transition at a nonzero threshold that corresponds to spontaneous breaking of fermion parity. Finally, we briefly discuss systems that satisfy the no low-energy trivial state property, such as the recently discovered good low-density parity-check codes, and argue that the Gibbs state of such systems exhibits a temperature-tuned separability transition.

Published by the American Physical Society2024 
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Award ID(s):
1752417
PAR ID:
10532616
Author(s) / Creator(s):
;
Publisher / Repository:
American Physical Society
Date Published:
Journal Name:
PRX Quantum
Volume:
5
Issue:
3
ISSN:
2691-3399
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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Retrieved from https://par.nsf.gov/biblio/10532616. <em>PRX Quantum</em> 5.3 Web. doi:10.1103/PRXQuantum.5.030310. </div> <div class="modal-footer"> <button class="btn btn-sm btn-default" data-dismiss="modal" aria-hidden="true">Close</button> </div> </div> </div> </div></li> <li class="links-format"><a href="#cite-apa" data-toggle="modal">APA</a> <div id="cite-apa" class="modal" tabindex="-1" role="dialog" aria-labelledby="cite-apa_label" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button> <strong id="cite-apa_label">Cite: APA Format</strong> </div> <div class="modal-body">Chen, Yu-Hsueh, & Grover, Tarun. <em>Symmetry-Enforced Many-Body Separability Transitions</em>. <em>PRX Quantum</em>, <em>5</em> (3). Retrieved from https://par.nsf.gov/biblio/10532616. <a href="https://doi.org/10.1103/PRXQuantum.5.030310">https://doi.org/10.1103/PRXQuantum.5.030310</a> </div> <div class="modal-footer"> <button class="btn btn-sm btn-default" data-dismiss="modal" aria-hidden="true">Close</button> </div> </div> </div> </div></li> <li class="links-format"><a href="#cite-chi" data-toggle="modal">Chicago</a> <div id="cite-chi" class="modal" tabindex="-1" role="dialog" aria-labelledby="cite-chi_label" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button> <strong id="cite-chi_label">Cite: Chicago Format</strong> </div> <div class="modal-body">Chen, Yu-Hsueh, and Grover, Tarun. "Symmetry-Enforced Many-Body Separability Transitions". <em>PRX Quantum</em> 5 (3). Country unknown/Code not available: American Physical Society. <a href="https://doi.org/10.1103/PRXQuantum.5.030310">https://doi.org/10.1103/PRXQuantum.5.030310.</a> <a href="https://par.nsf.gov/biblio/10532616">https://par.nsf.gov/biblio/10532616</a>. </div> <div class="modal-footer"> <button class="btn btn-sm btn-default" data-dismiss="modal" aria-hidden="true">Close</button> </div> </div> </div> </div></li> <li class="links-format"><a href="#cite-bib" data-toggle="modal">BibTeX</a> <div id="cite-bib" class="modal" tabindex="-1" role="dialog" aria-labelledby="cite-bib_label" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button> <strong id="cite-bib_label">Cite: BibTeX Format</strong> </div> <div class="modal-body"> @article{osti_10532616,<br/> place = {Country unknown/Code not available}, title = {Symmetry-Enforced Many-Body Separability Transitions}, url = {https://par.nsf.gov/biblio/10532616}, DOI = {10.1103/PRXQuantum.5.030310}, abstractNote = {We study quantum many-body mixed states with a symmetry from the perspective of , i.e., whether a mixed state can be expressed as an ensemble of short-range-entangled symmetric pure states. We provide evidence for “symmetry-enforced separability transitions” in a variety of states, where in one regime the mixed state is expressible as a convex sum of symmetric short-range-entangled pure states, while in the other regime, such a representation is not feasible. We first discuss the Gibbs state of Hamiltonians that exhibit spontaneous breaking of a discrete symmetry, and argue that the associated thermal phase transition can be thought of as a symmetry-enforced separability transition. Next we study cluster states in various dimensions subjected to local decoherence, and identify several distinct mixed-state phases and associated separability phase transitions, which also provides an alternative perspective on recently discussed “average symmetry-protected topological order.” We also study decoheredp+ipsuperconductors, and find that if the decoherence breaks the fermion parity explicitly, then the resulting mixed state can be expressed as a convex sum of nonchiral states, while a fermion parity–preserving decoherence results in a phase transition at a nonzero threshold that corresponds to spontaneous breaking of fermion parity. Finally, we briefly discuss systems that satisfy the no low-energy trivial state property, such as the recently discovered good low-density parity-check codes, and argue that the Gibbs state of such systems exhibits a temperature-tuned separability transition. Published by the American Physical Society2024}, journal = {PRX Quantum}, volume = {5}, number = {3}, publisher = {American Physical Society}, author = {Chen, Yu-Hsueh and Grover, Tarun}, }</div> <div class="modal-footer"> <button class="btn btn-sm btn-default" data-dismiss="modal" aria-hidden="true">Close</button> </div> </div> </div> </div></li> <li class="divider"></li> </ul> <ul class="nav nav-list" style="font-size: 14px; font-family: Arial Regular;"> <li class="nav-header header-format">Export Metadata</li> <li class="links-format"><a href="https://par.nsf.gov/endnote?osti_id=10532616">EndNote</a></li> <li class="links-format"><a href="https://par.nsf.gov/export/format:excel/osti-id:10532616">Excel</a></li> <li class="links-format"><a href="https://par.nsf.gov/export/format:csv/osti-id:10532616">CSV</a></li> <li class="links-format"><a href="https://par.nsf.gov/export/format:xml/osti-id:10532616">XML</a></li> <li class="divider"></li> </ul> <ul class="nav nav-list" style="font-size: 14px; 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