Language：Japanese   Publisher：Physical Review B  

In Phys. Rev. Lett. 128, 176402 (2022)0031-900710.1103/PhysRevLett.128.176402, 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%.

DOI： 10.1103/PhysRevB.106.075147

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Scopus

Language：Japanese   Publisher：Physical Review Letters  

A (2+1)-dimensional gapped quantum many-body system can have a topologically protected energy current at its edge. The magnitude of this current is determined entirely by the temperature and the chiral central charge, a quantity associated with the effective field theory of the edge. We derive a formula for the chiral central charge that, akin to the topological entanglement entropy, is completely determined by the many-body ground state wave function in the bulk. According to our formula, nonzero chiral central charge gives rise to a topological obstruction that prevents the ground state wave function from being real valued in any local product basis.

DOI： 10.1103/PhysRevLett.128.176402

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PubMed

Language：Japanese   Publisher：Quantum  

We introduce the concepts of a symmetry-protected sign problem and symmetry-protected magic to study the complexity of symmetry-protected topological (SPT) phases of matter. In particular, we say a state has a symmetry-protected sign problem or symmetry-protected magic, if finite-depth quantum circuits composed of symmetric gates are unable to transform the state into a non-negative real wave function or stabilizer state, respectively. We prove that states belonging to certain SPT phases have these properties, as a result of their anomalous symmetry action at a boundary. For example, we find that one-dimensional Z2 × Z2 SPT states (e.g. cluster state) have a symmetry-protected sign problem, and two-dimensional Z2 SPT states (e.g. Levin-Gu state) have symmetry-protected magic. Furthermore, we comment on the relation between a symmetry-protected sign problem and the computational wire property of one-dimensional SPT states. In an appendix, we also introduce explicit decorated domain wall models of SPT phases, which may be of independent interest.

DOI： 10.22331/q-2021-12-28-612

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Scopus

Language：Japanese   Publisher：Journal of Physics A: Mathematical and Theoretical  

For quantum spin systems in any spatial dimension with a local, translation-invariant Hamiltonian, we prove that asymptotic state convertibility from a quantum state to another one by a thermodynamically feasible class of quantum dynamics, called thermal operations, is completely characterized by the Kullback-Leibler (KL) divergence rate, if the state is translation-invariant and spatially ergodic. Our proof consists of two parts and is phrased in terms of a branch of the quantum information theory called the resource theory. First, we prove that any states, for which the min and max Rényi divergences collapse approximately to a single value, can be approximately reversibly converted into one another by thermal operations with the aid of a small source of quantum coherence. Second, we prove that these divergences collapse asymptotically to the KL divergence rate for any translation-invariant ergodic state. We show this via a generalization of the quantum Stein's lemma for quantum hypothesis testing beyond independent and identically distributed situations. Our result implies that the KL divergence rate serves as a thermodynamic potential that provides a complete characterization of thermodynamic convertibility of ergodic states of quantum many-body systems in the thermodynamic limit, including out-of-equilibrium and fully quantum situations.

DOI： 10.1088/1751-8121/ac333c

Web of Science

Scopus

Language：English  

Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (trade magazine, newspaper, online media)  

Event date： 2022.8

Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Venue：オンライン  

Event date： 2021.11

Language：English   Presentation type：Oral presentation (invited, special)  

Event date： 2021.10

Presentation type：Oral presentation (invited, special)  

Event date： 2021.9

Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Venue：オンライン  

Event date： 2021.3

Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Type：Academic society, research group, etc.