Unveiling topological order through multipartite entanglement

Patra, Siddhartha; Basu, Somnath; Lal, Siddhartha

doi:10.1103/physreva.105.052428

Cited by 5 publications

(12 citation statements)

References 66 publications

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“…We view (d), which can be generalized to certain non-planar graphs, as the emergence of the Euler characteristic (which is a global topological invariant). This has been shown by some of us recently [34] via computations of multipartite information on a plane, which capture the Topological Entanglement Entropy (TEE) [19,23] of a topologically ordered phases of quantum matter [52,53,54]. We also note that a recent work [46] has shown that the multipartite information between D + 1 partitions of a D-dimensional non-interacting Fermi gas is proportional to the Euler characteristic of the D-dimensional Fermi volume.…”

Section: Introductionsupporting

confidence: 52%

“…Remark 2.12. We have found that the alternative sum of the count D j (C n ), denoted by β Cn (−1) for any planar embedding of C n , is proportional to the n-partite information and topological entanglement entropy [34]. The cycle graph is crucially related to the topological entanglement entropy measure of a collection of subsystems arranged in an annulus.…”

Section: Island Count For Standard Graphsmentioning

confidence: 99%

“…The first equality in (2.9) is the original formula that was predicted in [34], based on an intuitive counting method similar to the inclusion-exclusion principle. However, a simple proof using inclusionexclusion seems elusive.…”

Section: Island Count For Standard Graphsmentioning

confidence: 99%

“…All of the commonly known polynomial invariants (including the celebrated Tutte polynomial) are invariants of the graph and need not admit natural generalizations to embedded graphs. We propose a new graph polynomial β (Γ,σ) (Definition 2.5), heavily borrowing from ideas arising from a recent study of topological entanglement entropy by us [34]. Given a graph Γ embedded in an oriented surface Σ, we define a polynomial built out of signed counts of the number of faces of all induced subgraphs.…”

Section: Introductionmentioning

confidence: 99%

“…Their aim was to study the statistical mechanics of the Potts antiferromagnet in a magnetic field as well as use these weighted graph coloring polynomials to solve problems that have physical applications. A recent study [34] of the entanglement entropy of a topologically ordered state of quantum matter [52,53,54] sheds light on the connection between multipartite quantum information measure and questions in graph theory.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Graph Polynomial for Colored Embedded Graphs: A Topological Approach

Basu¹,

Bhasin²,

Lal³

et al. 2022

Preprint

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We study finite graphs embedded in oriented surfaces by associating a polynomial to it. The tools used in developing a theory of such graph polynomials are algebraic topological while the polynomial itself is inspired from ideas arising in physics. We also analyze a variant of these polynomials for colored embedded graphs. This is used to describe the change in the polynomial under basic graph theoretic operations. We conclude with several applications of this polynomial including detection of certain classes of graphs and the connection of this polynomial with topological entanglement entropy.

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Section: Introductionsupporting

confidence: 52%

Section: Island Count For Standard Graphsmentioning

confidence: 99%

Section: Island Count For Standard Graphsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Graph Polynomial for Colored Embedded Graphs: A Topological Approach

Basu¹,

Bhasin²,

Lal³

et al. 2022

Preprint

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Frustration shapes multi-channel Kondo physics: a star graph perspective

Patra

Mukherjee

et al. 2023

J. Phys.: Condens. Matter

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We study the overscreened multi-channel Kondo (MCK) model using the recently developed unitary renormalization group (URG) technique. Our results display the importance of ground state degeneracy in explaining various important properties like the breakdown of screening and the presence of local non-Fermi liquids. The impurity susceptibility of the intermediate coupling fixed point Hamiltonian in the zero-bandwidth (or star graph) limit shows a power-law divergence at low temperature. Despite the absence of inter-channel coupling in the MCK fixed point Hamiltonian, the study of mutual information between any two channels shows non-zero correlation between them. A spectral flow analysis of the star graph reveals that the degenerate ground state manifold possesses topological quantum numbers. Upon disentangling the impurity spin from its partners in the star graph, we find the presence of a local Mott liquid arising from inter-channel scattering processes. The low energy effective Hamiltonian obtained upon adding a finite non-zero conduction bath dispersion to the star graph Hamiltonian for both the two and three-channel cases displays the presence of local non-Fermi liquids arising from inter-channel quantum fluctuations. Specifically, we confirm the presence of a local marginal Fermi liquid in the two channel case, whose properties show logarithmic scaling at low temperature as expected. Discontinuous behaviour is observed in several measures of ground state entanglement, signalling the underlying orthogonality catastrophe associated with the degenerate ground state manifold. We extend our results to underscreened and perfectly screened MCK models through duality arguments. A study of channel anisotropy under renormalisation flow reveals a series of quantum phase transitions due to the change in ground state degeneracy. Our work thus presents a template for the study of how a degenerate ground state manifold arising from symmetry and duality properties in a multichannel quantum impurity model can lead to novel multicritical phases at intermediate coupling.

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Universal entanglement signatures of quantum liquids as a guide to fermionic criticality

2023

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An outstanding challenge involves understanding the many-particle entanglement of liquid states of quantum matter that arise in systems of interacting electrons. The Fermi liquid (FL) shows a violation of the area-law in real-space entanglement entropy of a subsystem, believed to be a signature of the ground state of a gapless quantum critical system of interacting fermions. Here, we apply a $T=0$ renormalisation group approach to the FL, unveiling the long-wavelength quantum fluctuations from which long-range entanglement arises. A similar analysis of non-Fermi liquids such as the 2D marginal Fermi liquid (MFL) and the 1D Tomonaga-Luttinger liquid (TLL) reveals a universal logarithmic violation of the area-law in gapless electronic liquids, with a proportionality constant that depends on the nature of the underlying Fermi surface. We extend this analysis to classify the gapped quantum liquids emergent from the destabilisation of the Fermi surface by RG relevant quantum fluctuations arising from backscattering processes.

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Unveiling topological order through multipartite entanglement

Cited by 5 publications

References 66 publications

Graph Polynomial for Colored Embedded Graphs: A Topological Approach

Graph Polynomial for Colored Embedded Graphs: A Topological Approach

Frustration shapes multi-channel Kondo physics: a star graph perspective

Universal entanglement signatures of quantum liquids as a guide to fermionic criticality

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