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This study utilizes tensor-network methods to directly confirm the condensation of nonlocal composite bosons and long-range correlations in lattice quantum Hall states, addressing a longstanding gap in verifying topological order beyond simple trial states. By defining accessible nonlocal order parameters for both bosonic and fermionic models, the research provides measurable signatures for phase transitions that are feasible for implementation in near-term quantum simulators. This work advances the microscopic understanding of topological quantum matter, offering new pathways for studying strongly correlated systems where traditional solid-state approaches fall short.
Long-Range Order and Composite Boson Condensation in Lattice Quantum Hall States
arXiv:2608.24628v1 Announce Type: cross Abstract: Topological states of matter, such as quantum Hall states, are characterized by the absence of local order parameters. In the continuum, their topological order has been reinterpreted as the condensation of nonlocal composite bosons, but this condensation and the resulting long-range correlations have so far eluded direct confirmation beyond the simplest trial states. Here, we apply tensor-network methods to lattice Hamiltonians hosting quantum Hall states, revealing this exotic order directly in interacting ground states and demonstrating both the long-range correlations and the condensation of composite bosons. These correlations define a nonlocal order parameter that identifies phase transitions between trivial and topological phases, for both bosonic and fermionic models. The corresponding operators are accessible through site-resolved, local measurements on an extensive number of particles, making them directly probable in quantum simulators. Our work opens new avenues for microscopic studies of topological quantum matter beyond the reach of traditional solid-state approaches.
Abstract:Topological states of matter, such as quantum Hall states, are characterized by the absence of local order parameters. In the continuum, their topological order has been reinterpreted as the condensation of nonlocal composite bosons, but this condensation and the resulting long-range correlations have so far eluded direct confirmation beyond the simplest trial states. Here, we apply tensor-network methods to lattice Hamiltonians hosting quantum Hall states, revealing this exotic order directly in interacting ground states and demonstrating both the long-range correlations and the condensation of composite bosons. These correlations define a nonlocal order parameter that identifies phase transitions between trivial and topological phases, for both bosonic and fermionic models. The corresponding operators are accessible through site-resolved, local measurements on an extensive number of particles, making them directly probable in quantum simulators. Our work opens new avenues for microscopic studies of topological quantum matter beyond the reach of traditional solid-state approaches.
Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Gases (cond-mat.quant-gas); Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)
arXiv:2608.24628 [cond-mat.mes-hall]
(or arXiv:2608.24628v1 [cond-mat.mes-hall] for this version)
https://doi.org/10.48550/arXiv.2608.24628 arXiv-issued DOI via DataCite (pending registration)
Full text under the publisher's open licence · 179 words
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