Modular commutator in gapped quantum many-body systems

Kim, Isaac H.; Shi, B. A.; Kato, Kohtaro; Albert, Victor V.

doi:10.1103/physrevb.106.075147

Cited by 19 publications

(18 citation statements)

References 65 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As mentioned in the introduction, the dimensionless real number c − is known as the chiral central charge, which is related to the thermal Hall conductance at low temperature via κ xy (T ) = π 6 c − T + O(T 2 ). Authors of [11,13] proposed the following formula to compute the chiral central charge c − from the ground state wave-function…”

Section: Thermal Hall Conductancementioning

confidence: 99%

“…To support the conjectures, the authors of [11][12][13][14] provided a few general arguments in addition to the numerical tests. For instance, Ref.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, Ref. [11,13] used a quantum Markov-chain assumption to argue the topological invariance of the above formula. However, that assumption is too strong to hold for a state with a chiral central charge.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Generalized Real-space Chern Number Formula and Entanglement Hamiltonian

Fan¹,

Zhang²,

Gu³

2022

Preprint

View full text Add to dashboard Cite

show abstract

Section: Thermal Hall Conductancementioning

confidence: 99%

“…To support the conjectures, the authors of [11][12][13][14] provided a few general arguments in addition to the numerical tests. For instance, Ref.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Generalized Real-space Chern Number Formula and Entanglement Hamiltonian

Fan¹,

Zhang²,

Gu³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…This formalism provides a useful heuristic picture of entanglement in a topological phase as arising from anyon-antianyon pairs condensed at the entanglement cut, with the topological contributions to entanglement quantities coming from the non-1 See also Refs. [19][20][21][22], which extract the chiral central charge using a quantity known as the modular commutator. local constraint that the net anyon charge in a subregion is fixed.…”

mentioning

confidence: 99%

Entanglement in tripartitions of topological orders: a diagrammatic approach

Sohal¹,

Ryu²

2023

Preprint

View full text Add to dashboard Cite

Recent studies have demonstrated that measures of tripartite entanglement can probe data characterizing topologically ordered phases to which bipartite entanglement is insensitive. Motivated by these observations, we compute the reflected entropy and logarithmic negativity, a mixed state entanglement measure, in tripartitions of bosonic topological orders using the anyon diagrammatic formalism. We consider tripartitions in which three subregions meet at trijunctions and tetrajunctions. In the former case, we find a contribution to the negativity which distinguishes between Abelian and non-Abelian order while in the latter, we find a distinct universal contribution to the reflected entropy. Finally, we demonstrate that the negativity and reflected entropy are sensitive to the F -symbols for configurations in which we insert an anyon trimer, for which the Markov gap, defined as the difference between the reflected entropy and mutual information, is also found to be non-vanishing.

show abstract

“…Even in the absence of charge conservation, systems with nonzero chiral central charge, which signals nonzero thermal Hall conductance, has gapless edge modes [3]. We have a good theoretical understanding of these quantities by way of coarsegrained Chern-Simons theory, and we can extract them from microscopic wavefunctions [4][5][6][7][8][9][10][11][12][13].…”

mentioning

confidence: 99%

Extracting higher central charge from a single wave function

Kobayashi¹,

Wang²,

Soejima³

et al. 2023

Preprint

View full text Add to dashboard Cite

A (2+1)D topologically ordered phase may or may not have a gappable edge, even if its chiral central charge c− is vanishing. Recently, it is discovered that a quantity regarded as a "higher" version of chiral central charge gives a further obstruction beyond c− to gapping out the edge. In this Letter, we show that the higher central charges can be characterized by the expectation value of the partial rotation operator acting on the wavefunction of the topologically ordered state. This allows us to extract the higher central charge from a single wavefunction, which can be evaluated on a quantum computer. Our characterization of the higher central charge is analytically derived from the modular properties of edge conformal field theory, as well as the numerical results with the ν = 1/2 bosonic Laughlin state and the non-Abelian gapped phase of the Kitaev honeycomb model, which corresponds to U(1)2 and Ising topological order respectively. The letter establishes a numerical method to obtain a set of obstructions to the gappable edge of (2+1)D bosonic topological order beyond c−. We also point out that the expectation values of the partial rotation on a single wavefunction put a constraint on the low-energy spectrum of the bulk-boundary system of (2+1)D bosonic topological order, reminiscent of the Lieb-Schultz-Mattis type theorems.

show abstract

Modular commutator in gapped quantum many-body systems

Cited by 19 publications

References 65 publications

Generalized Real-space Chern Number Formula and Entanglement Hamiltonian

Generalized Real-space Chern Number Formula and Entanglement Hamiltonian

Entanglement in tripartitions of topological orders: a diagrammatic approach

Extracting higher central charge from a single wave function

Contact Info

Product

Resources

About