Many-Body Chern Number from Statistical Correlations of Randomized Measurements

Cian, Ze-Pei; Dehghani, Hossein; Elben, Andreas; Vermersch, Benoît; Zhu, Guanyu; Barkeshli, Maissam; Zoller, P.; Hafezi, Mohammad

doi:10.1103/physrevlett.126.050501

Cited by 62 publications

(32 citation statements)

References 49 publications

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“…Randomized measurements have also been used to estimate entanglement entropy [6,21,41,46], topological invariants [9,14], benchmark physical devices [8,12,21,29], and predict outcomes of physical experiments [22]. Derandomization provides a principled approach for adapting randomized measurement pro- cedures to fine-grained structure and is closely related to an algorithmic technique -multiplicative weight update [2] -commonly used in machine learning and game theory.…”

Section: Discussionmentioning

confidence: 99%

Efficient Estimation of Pauli Observables by Derandomization

2021

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Section: Discussionmentioning

confidence: 99%

Efficient Estimation of Pauli Observables by Derandomization

2021

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“…2. Can one deduce symmetry-protected topological invaraints (e.g., [50][51][52][53][54]) of the phase from the modular Hamiltonian?…”

Section: Discussionmentioning

confidence: 99%

“…The last line follows from the vanishing of modular commutators due to the Markov chain condition Eq. (54).…”

Section: Gapped Domain Wallmentioning

confidence: 99%

Modular commutator in gapped quantum many-body systems

Kim,

Shi,

Kato

et al. 2021

Preprint

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In arXiv:2110.06932, we argued that the chiral central charge -a topologically protected quantity characterizing the edge theory of a gapped (2+1)-dimensional system -can be extracted from the bulk by using an order parameter called the modular commutator. In this paper, we reveal general properties of the modular commutator and strengthen its relationship with the chiral central charge. First, we identify connections between the modular commutator and conditional mutual information, time reversal, and modular flow. Second, we prove, within the framework of the entanglement bootstrap program, that two topologically ordered media connected by a gapped domain wall must have the same modular commutator in their respective bulk. Third, we numerically calculate the value of the modular commutator for a bosonic lattice Laughlin state for finite sizes and extrapolate to the infinite-volume limit. The result of this extrapolation is consistent with the proposed formula up to an error of about 0.7%.

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“…Further insights could also be obtained by realizing these phases experimentally with synthetic quantum systems. In particular, protocols have been developed theoretically to characterize non-trivial topological properties of such systems, including the analysis of currents [57][58][59][60][61], randomized measurements [62][63][64], and interferometry [65][66][67][68].…”

Section: Discussionmentioning

confidence: 99%

Characterizing fractional topological phases of lattice bosons near the first Mott lobe

Boesl,

Dilip,

Pollmann

et al. 2021

Preprint

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The Bose-Hubbard model subjected to an effective magnetic field hosts a plethora of phases with different topological orders when tuning the chemical potential. Using the density matrix renormalization group method, we identify several gapped phases near the first Mott lobe at strong interactions. By a particle-hole symmetry, they are connected to a variety of quantum Hall states stabilized at low fillings. We characterize phases of both particle and hole type and identify signatures compatible with Laughlin, Moore-Read, and Bosonic Integer Quantum Hall states by calculating the quantized Hall conductance and by extracting the topological entanglement entropy. Furthermore, we analyze the entanglement spectrum of a Laughlin state of bosonic particles and holes for a range of interaction strengths. These results further corroborate the existence of topological states at high fillings, close to the first Mott lobe, as hole analogues of the respective low-filling states.

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Many-Body Chern Number from Statistical Correlations of Randomized Measurements

Cited by 62 publications

References 49 publications

Efficient Estimation of Pauli Observables by Derandomization

Efficient Estimation of Pauli Observables by Derandomization

Modular commutator in gapped quantum many-body systems

Characterizing fractional topological phases of lattice bosons near the first Mott lobe

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