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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenSat, 13 Apr 2024 00:48:04 +0000Fermion condensation and super pivotal categories
https://resolver.caltech.edu/CaltechAUTHORS:20180129-085443018
Authors: {'items': [{'id': 'Aasen-David', 'name': {'family': 'Aasen', 'given': 'David'}, 'orcid': '0000-0002-6552-488X'}, {'id': 'Lake-Ethan', 'name': {'family': 'Lake', 'given': 'Ethan'}}, {'id': 'Walker-Kevin', 'name': {'family': 'Walker', 'given': 'Kevin'}}]}
Year: 2019
DOI: 10.1063/1.5045669
We study fermionic topological phases using the technique of fermion condensation. We give a prescription for performing fermion condensation in bosonic topological phases that contain a fermion. Our approach to fermion condensation can roughly be understood as coupling the parent bosonic topological phase to a phase of physical fermions and condensing pairs of physical and emergent fermions. There are two distinct types of objects in the resulting fermionic fusion categories, which we call "m-type" and "q-type" objects. The endomorphism algebras of q-type objects are complex Clifford algebras, and they have no analogs in bosonic theories. We construct a fermionic generalization of the tube category, which allows us to compute the quasiparticle excitations arising from the condensed theories. We prove a series of results relating data in fermionic theories to data in their parent bosonic theories; for example, if C is a modular tensor category containing a fermion, then the tube category constructed from the condensed theory satisfies Tube(C/ψ)≅C×(C/ψ). We also study how modular transformations, fusion rules, and coherence relations are modified in the fermionic setting, prove a fermionic version of the Verlinde dimension formula, construct a commuting projector lattice Hamiltonian for fermionic theories, and write down a fermionic version of the Turaev-Viro-Barrett-Westbury state sum. A large portion of this work is devoted to three detailed examples of performing fermion condensation to produce fermionic topological phases: we condense fermions in the Ising theory, the SO(3)₆ theory, and the ½E₆ theory and compute the quasiparticle excitation spectrum in each of the condensed theories.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ew6w9-qcs31Topological defect networks for fractons of all types
https://resolver.caltech.edu/CaltechAUTHORS:20201103-104249449
Authors: {'items': [{'id': 'Aasen-David', 'name': {'family': 'Aasen', 'given': 'David'}, 'orcid': '0000-0002-6552-488X'}, {'id': 'Bulmash-D', 'name': {'family': 'Bulmash', 'given': 'Daniel'}, 'orcid': '0000-0001-8978-4531'}, {'id': 'Prem-Abhinav', 'name': {'family': 'Prem', 'given': 'Abhinav'}, 'orcid': '0000-0003-4438-7107'}, {'id': 'Slagle-K', 'name': {'family': 'Slagle', 'given': 'Kevin'}, 'orcid': '0000-0002-8036-3447'}, {'id': 'Williamson-D-J', 'name': {'family': 'Williamson', 'given': 'Dominic J.'}}]}
Year: 2020
DOI: 10.1103/physrevresearch.2.043165
Fracton phases exhibit striking behavior which appears to render them beyond the standard topological quantum field theory (TQFT) paradigm for classifying gapped quantum matter. Here, we explore fracton phases from the perspective of defect TQFTs and show that topological defect networks—networks of topological defects embedded in stratified 3+1-dimensional (3+1D) TQFTs—provide a unified framework for describing various types of gapped fracton phases. In this picture, the subdimensional excitations characteristic of fractonic matter are a consequence of mobility restrictions imposed by the defect network. We conjecture that all gapped phases, including fracton phases, admit a topological defect network description and support this claim by explicitly providing such a construction for many well-known fracton models, including the X-cube and Haah's B code. To highlight the generality of our framework, we also provide a defect network construction of a fracton phase hosting non-Abelian fractons. As a byproduct of this construction, we obtain a generalized membrane-net description for fractonic ground states as well as an argument that our conjecture implies no topological fracton phases exist in 2+1-dimensional gapped systems. Our paper also sheds light on techniques for constructing higher-order gapped boundaries of 3+1D TQFTs.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2pr2z-y4v69Time-Domain Anyon Interferometry in Kitaev Honeycomb Spin Liquids and Beyond
https://resolver.caltech.edu/CaltechAUTHORS:20201111-081453060
Authors: {'items': [{'id': 'Klocke-Kai', 'name': {'family': 'Klocke', 'given': 'Kai'}, 'orcid': '0000-0002-9580-8509'}, {'id': 'Aasen-David', 'name': {'family': 'Aasen', 'given': 'David'}, 'orcid': '0000-0002-6552-488X'}, {'id': 'Mong-Roger-S-K', 'name': {'family': 'Mong', 'given': 'Roger S. K.'}}, {'id': 'Demler-Eugene-A', 'name': {'family': 'Demler', 'given': 'Eugene A.'}, 'orcid': '0000-0002-2499-632X'}, {'id': 'Alicea-J', 'name': {'family': 'Alicea', 'given': 'Jason'}, 'orcid': '0000-0001-9979-3423'}]}
Year: 2021
DOI: 10.1103/PhysRevLett.126.177204
Motivated by recent experiments on the Kitaev honeycomb magnet α-RuCl₃, we introduce time-domain probes of the edge and quasiparticle content of non-Abelian spin liquids. Our scheme exploits ancillary quantum spins that communicate via time-dependent tunneling of energy into and out of the spin liquid's chiral Majorana edge state. We show that the ancillary-spin dynamics reveals the edge-state velocity and, in suitable geometries, detects individual non-Abelian anyons and emergent fermions via a time-domain counterpart of quantum-Hall anyon interferometry. We anticipate applications to a wide variety of topological phases in solid-state and cold-atoms settings.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/n35hk-1cx37Spin chains, defects, and quantum wires for the quantum-double edge
https://resolver.caltech.edu/CaltechAUTHORS:20220113-182244311
Authors: {'items': [{'id': 'Albert-Victor-V', 'name': {'family': 'Albert', 'given': 'Victor V.'}, 'orcid': '0000-0002-0335-9508'}, {'id': 'Aasen-David', 'name': {'family': 'Aasen', 'given': 'David'}, 'orcid': '0000-0002-6552-488X'}, {'id': 'Xu-Wenqing-William', 'name': {'family': 'Xu', 'given': 'Wenqing'}}, {'id': 'Ji-Wenjie', 'name': {'family': 'Ji', 'given': 'Wenjie'}}, {'id': 'Alicea-J', 'name': {'family': 'Alicea', 'given': 'Jason'}, 'orcid': '0000-0001-9979-3423'}, {'id': 'Preskill-J', 'name': {'family': 'Preskill', 'given': 'John'}, 'orcid': '0000-0002-2421-4762'}]}
Year: 2021
DOI: 10.48550/arXiv.2111.12096
Non-Abelian defects that bind Majorana or parafermion zero modes are prominent in several topological quantum computation schemes. Underpinning their established understanding is the quantum Ising spin chain, which can be recast as a fermionic model or viewed as a standalone effective theory for the surface-code edge -- both of which harbor non-Abelian defects. We generalize these notions by deriving an effective Ising-like spin chain describing the edge of quantum-double topological order. Relating Majorana and parafermion modes to anyonic strings, we introduce quantum-double generalizations of non-Abelian defects. We develop a way to embed finite-group valued qunits into those valued in continuous groups. Using this embedding, we provide a continuum description of the spin chain and recast its non-interacting part as a quantum wire via addition of a Wess-Zumino-Novikov-Witten term and non-Abelian bosonization.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gnrr3-rdt94Microscopic characterization of Ising conformal field theory in Rydberg chains
https://resolver.caltech.edu/CaltechAUTHORS:20211207-393208000
Authors: {'items': [{'id': 'Slagle-Kevin', 'name': {'family': 'Slagle', 'given': 'Kevin'}, 'orcid': '0000-0002-8036-3447'}, {'id': 'Aasen-David', 'name': {'family': 'Aasen', 'given': 'David'}, 'orcid': '0000-0002-6552-488X'}, {'id': 'Pichler-Hannes', 'name': {'family': 'Pichler', 'given': 'Hannes'}, 'orcid': '0000-0003-2144-536X'}, {'id': 'Mong-Roger-S-K', 'name': {'family': 'Mong', 'given': 'Roger S. K.'}}, {'id': 'Fendley-Paul', 'name': {'family': 'Fendley', 'given': 'Paul'}, 'orcid': '0000-0002-7747-0153'}, {'id': 'Chen-Xie', 'name': {'family': 'Chen', 'given': 'Xie'}, 'orcid': '0000-0003-2215-2497'}, {'id': 'Endres-M', 'name': {'family': 'Endres', 'given': 'Manuel'}, 'orcid': '0000-0002-4461-224X'}, {'id': 'Alicea-J', 'name': {'family': 'Alicea', 'given': 'Jason'}, 'orcid': '0000-0001-9979-3423'}]}
Year: 2021
DOI: 10.1103/physrevb.104.235109
Rydberg chains provide an appealing platform for probing conformal field theories (CFTs) that capture universal behavior in a myriad of physical settings. Focusing on a Rydberg chain at the Ising transition separating charge density wave and disordered phases, we establish a detailed link between microscopics and low-energy physics emerging at criticality. We first construct lattice incarnations of primary fields in the underlying Ising CFT including chiral fermions, a nontrivial task given that the Rydberg chain Hamiltonian does not admit an exact fermionization. With this dictionary in hand, we compute correlations of microscopic Rydberg operators, paying special attention to finite, open chains of immediate experimental relevance. We further develop a method to quantify how second-neighbor Rydberg interactions tune the sign and strength of four-fermion couplings in the Ising CFT. Finally, we determine how the Ising fields evolve when four-fermion couplings drive an instability to Ising tricriticality. Our results pave the way to a thorough experimental characterization of Ising criticality in Rydberg arrays, and can inform the design of novel higher-dimensional phases based on coupled critical chains.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bmxdz-db910Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays
https://resolver.caltech.edu/CaltechAUTHORS:20220428-212235605
Authors: {'items': [{'id': 'Slagle-Kevin', 'name': {'family': 'Slagle', 'given': 'Kevin'}, 'orcid': '0000-0002-8036-3447'}, {'id': 'Liu-Yue', 'name': {'family': 'Liu', 'given': 'Yue'}, 'orcid': '0000-0002-5965-0644'}, {'id': 'Aasen-David', 'name': {'family': 'Aasen', 'given': 'David'}, 'orcid': '0000-0002-6552-488X'}, {'id': 'Pichler-Hannes', 'name': {'family': 'Pichler', 'given': 'Hannes'}, 'orcid': '0000-0003-2144-536X'}, {'id': 'Mong-Roger-S-K', 'name': {'family': 'Mong', 'given': 'Roger S. K.'}}, {'id': 'Chen-Xie', 'name': {'family': 'Chen', 'given': 'Xie'}, 'orcid': '0000-0003-2215-2497'}, {'id': 'Endres-M', 'name': {'family': 'Endres', 'given': 'Manuel'}, 'orcid': '0000-0002-4461-224X'}, {'id': 'Alicea-J', 'name': {'family': 'Alicea', 'given': 'Jason'}, 'orcid': '0000-0001-9979-3423'}]}
Year: 2022
DOI: 10.48550/arXiv.2204.00013
Arrays of Rydberg atoms constitute a highly tunable, strongly interacting venue for the pursuit of exotic states of matter. We develop a new strategy for accessing a family of fractionalized phases known as quantum spin liquids in two-dimensional Rydberg arrays. We specifically use effective field theory methods to study arrays assembled from Rydberg chains tuned to an Ising phase transition that famously hosts emergent fermions propagating within each chain. This highly entangled starting point allows us to naturally access spin liquids familiar from Kitaev's honeycomb model, albeit from an entirely different framework. In particular, we argue that finite-range repulsive Rydberg interactions, which frustrate nearby symmetry-breaking orders, can enable coherent propagation of emergent fermions between the chains in which they were born. Delocalization of emergent fermions across the full two-dimensional Rydberg array yields a gapless Z2 spin liquid with a single massless Dirac cone. Here, the Rydberg occupation numbers exhibit universal power-law correlations that provide a straightforward experimental diagnostic of this phase. We further show that explicitly breaking symmetries perturbs the gapless spin liquid into gapped, topologically ordered descendants: Breaking lattice symmetries generates toric-code topological order, whereas introducing chirality generates non-Abelian Ising topological order. In the toric-code phase, we analytically construct microscopic incarnations of non-Abelian defects, which can be created and transported by dynamically controlling the atom positions in the array. Our work suggests that appropriately tuned Rydberg arrays provide a cold-atoms counterpart of solid-state 'Kitaev materials' and, more generally, spotlights a new angle for pursuing experimental platforms for Abelian and non-Abelian fractionalization.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2jegc-73t42Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays
https://resolver.caltech.edu/CaltechAUTHORS:20221031-575177800.11
Authors: {'items': [{'id': 'Slagle-Kevin', 'name': {'family': 'Slagle', 'given': 'Kevin'}, 'orcid': '0000-0002-8036-3447'}, {'id': 'Liu-Yue', 'name': {'family': 'Liu', 'given': 'Yue'}, 'orcid': '0000-0002-5965-0644'}, {'id': 'Aasen-David', 'name': {'family': 'Aasen', 'given': 'David'}, 'orcid': '0000-0002-6552-488X'}, {'id': 'Pichler-Hannes', 'name': {'family': 'Pichler', 'given': 'Hannes'}, 'orcid': '0000-0003-2144-536X'}, {'id': 'Mong-Roger-S-K', 'name': {'family': 'Mong', 'given': 'Roger S. K.'}}, {'id': 'Chen-Xie', 'name': {'family': 'Chen', 'given': 'Xie'}, 'orcid': '0000-0003-2215-2497'}, {'id': 'Endres-M', 'name': {'family': 'Endres', 'given': 'Manuel'}, 'orcid': '0000-0002-4461-224X'}, {'id': 'Alicea-J', 'name': {'family': 'Alicea', 'given': 'Jason'}, 'orcid': '0000-0001-9979-3423'}]}
Year: 2022
DOI: 10.1103/physrevb.106.115122
Arrays of Rydberg atoms constitute a highly tunable, strongly interacting venue for the pursuit of exotic states of matter. We develop a strategy for accessing a family of fractionalized phases known as quantum spin liquids in two-dimensional Rydberg arrays. We specifically use effective field theory methods to study arrays assembled from Rydberg chains tuned to an Ising phase transition that famously hosts emergent fermions propagating within each chain. This highly entangled starting point allows us to naturally access spin liquids familiar from Kitaev's honeycomb model — albeit from an entirely different framework. In particular, we argue that finite-range repulsive Rydberg interactions, which frustrate nearby symmetry-breaking orders, can enable coherent propagation of emergent fermions between the chains in which they were born. Delocalization of emergent fermions across the full two-dimensional Rydberg array yields a gapless ℤ₂ spin liquid with a single massless Dirac cone. Here, the Rydberg occupation numbers exhibit universal power-law correlations that provide a straightforward experimental diagnostic of this phase. We further show that explicitly breaking symmetries perturbs the gapless spin liquid into gapped, topologically ordered descendants: Breaking lattice symmetries generates toric-code topological order, whereas introducing Floquet-mediated chirality generates non-Abelian Ising topological order. In the toric-code phase, we analytically construct microscopic incarnations of non-Abelian defects, which can be created and transported by dynamically controlling the atom positions in the array. Our work suggests that appropriately tuned Rydberg arrays provide a cold-atoms counterpart of solid-state "Kitaev materials" and, more generally, it spotlights a different angle for pursuing experimental platforms for Abelian and non-Abelian fractionalization.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7bhnp-r9z60