Topological approach to quantum liquid ground states on geometrically frustrated Heisenberg antiferromagnets

Pal, Santanu; Mukherjee, Anirban; Lal, Siddhartha

doi:10.1088/1361-648x/ab670f

Cited by 12 publications

(8 citation statements)

References 73 publications

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“…[1] and references therein). It will also be an interesting challenge to extend these ideas to the topologically ordered phases that have been recently proposed by some of us in strongly correlated electronic (e.g., Mott liquid, Cooper pair insulator [58][59][60][61][62]) and quantum spin systems in frustrated lattice geometries at finite fields [63][64][65].…”

Section: Discussionmentioning

confidence: 97%

Unveiling topological order through multipartite entanglement

Patra,

Basu,

Lal

2021

Preprint

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It is well known that the topological entanglement entropy (Stopo) of a topologically ordered ground state in 2 spatial dimensions can be captured efficiently by measuring the tripartite quantum information (I 3 ) of a specific annular arrangement of three subsystems. However, the nature of the general N-partite information (I N ) and quantum correlation of a topologically ordered ground state remains unknown. In this work, we study such I N measure and its nontrivial dependence on the arrangement of N subsystems. For the collection of subsystems (CSS) forming a closed annular structure, the I N measure (N ≥ 3) is a topological invariant equal to the product of Stopo and the Euler characteristic of the CSS embedded on a planar manifold, |I N | = χStopo. Importantly, we establish that I N is robust against several deformations of the annular CSS, such as the addition of holes within individual subsystems and handles between nearest-neighbour subsystems. While the addition of a handle between further neighbour subsystems causes I N to vanish, the multipartite information measures of the two smaller annular CSS emergent from this deformation again yield the same topological invariant. For a general CSS with multiple holes (n h > 1), we find that the sum of the distinct, multipartite informations measured on the annular CSS around those holes is given by the product of Stopo, χ and n h ,This constrains the concomitant measurement of several multipartite informations on any complicated CSS. The N th order irreducible quantum correlations for an annular CSS of N subsystems is also found to be bounded from above by |I N |, which shows the presence of correlations among subsystems arranged in the form of closed loops of all sizes. Thus, our results offer important insight into the nature of the many-particle entanglement and correlations within a topologically ordered state of matter.

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Section: Discussionmentioning

confidence: 97%

Unveiling topological order through multipartite entanglement

Patra,

Basu,

Lal

2021

Preprint

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“…Indeed, similar conclusions have been reached by some of us for the Mott liquid ground states of the 2D Hubbard model discovered recently in Refs. 46,47 , and the spin liquid ground states of quantum spins coupled through antiferromagnetic exchange on geometrically frustrated lattices 48,78,79 . It should be possible, therefore, to chart out in a similar fashion the microscopic origins of various kinds of topologically ordered quantum liquids.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Origin of Topological Order in a Cooper Pair Insulator

Patra,

Lal

2021

Preprint

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While a topologically ordered counterpart of the s-wave superconductor has been proposed in the literature on phenomenological grounds, its microscopic origin remains unknown. In meeting this goal, we employ the recently developed unitary renormalisation group (URG) method on a generalised model of electrons in two spatial dimensions with attractive interactions. We show that the effective Hamiltonian obtained at the stable low-energy fixed point of the RG flow corresponds to a gapped, insulating state of quantum matter we call the Cooper pair insulator (CPI). Detailed analyses show that the CPI ground state manifold displays several signatures of topological order, including a four-fold degeneracy when placed on the torus. Spectral flow based arguments reveal the emergent gauge-theoretic structure of the effective theory: the CPI effective Hamiltonian can be written entirely in terms of non-local Wilson loops. Further, it contains a topological θ-term whose coefficient is quantised in keeping with the requirement of invariance of the ground state under large gauge transformations. This θ-term is known to be equivalent to the Chern-Simons term in two spatial dimensions. Passage from the CPI to the metal by tuning the θ coefficient reveals a plateaux structure of the CPI ground state in terms of the steadily decreasing number of condensed Cooper pairs. Investigations reveal that the long-ranged many-particle entanglement content of the CPI ground state is driven by inter-helicity two-particle scattering processes. The plateau with θ = 0 possesses the largest bipartite entanglement entropy (EE), scaling logarithmically with subsystem size (L) and falling rapidly upon tuning θ towards the metal. The bipartite EE for inter-plateau transitions shows universal signatures in its variations with L and θ. While the EE signatures for plateaux and transitions can be distinguished at low temperatures, such distinctions are smeared out as temperature is raised. We also study the passage from the CPI to the s-wave BCS superconducting ground state under RG, and find that the RG flow promotes fluctuations in the number of condensed Cooper pairs and lowers those in the conjugate global phase of the ground state wavefunction. Consequently, we find that the distinct signatures of long-ranged entanglement in the CPI are replaced by the well-known short-ranged entanglement of the BCS state. Analysing the effects of Josephson effects reveals that while a Cooper pair tunnel coupling between two CPI systems does not lead to phase stiffening, breaking the global U (1) phase rotation symmetry in one of them induces a phase coherence in the other. However, the generation of a Josephson current requires the separate breaking of the U (1) symmetry in the two systems. Finally, we study the renormalisation of the entanglement in k-space for both the CPI and BCS ground states. The topologically ordered CPI state is shown to possess an emergent hierarchy of scales of entanglement, and that this hierarchy collapses in the BCS state. Our work offe...

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“…Because the angle (13) depends on neither N 1 nor N 2 , we can take the thermodynamic limit, V → +∞, without any ambiguity. This well-defined thermodynamic limit is a great advantage of the tilted boundary condition over the periodic boundary condition [7,29].…”

Section: Flux Insertionmentioning

confidence: 98%

“…1). When we adopt the flux insertion argument [7] to this system with the periodic boundary condition, we face the previously mentioned problem of the ambiguous thermodynamic limit [29]. In the case of the d-dimensional hyper cubic lattice, this problem can be resolved in Ref.…”

Section: B Symmetriesmentioning

confidence: 99%

Anomalies of kagome antiferromagnets on magnetization plateaus

Furuya¹,

Horinouchi²,

Momoi³

2020

Preprint

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We discuss the ground-state degeneracy of spin-1/2 kagome-lattice quantum antiferromagnets on magnetization plateaus by employing two complementary methods: the adiabatic flux insertion in closed boundary conditions and a 't Hooft anomaly argument on inherent symmetries in a quasi-onedimensional limit. The flux insertion with a tilted boundary condition restricts the lower bound of the ground-state degeneracy on 1/9, 1/3, 5/9, and 7/9 magnetization plateaus under the U(1) spinrotation and the translation symmetries: 3, 1, 3, and 3, respectively. This result motivates us further to develop an anomaly interpretation of the 1/3 plateau. Taking advantage of the insensitivity of anomalies to spatial anisotropies, we examine the existence of the unique gapped ground state on the 1/3 plateau from a quasi-one-dimensional viewpoint. In the quasi-one-dimensional limit, kagome antiferromagnets are reduced to weakly coupled three-leg spin tubes. Here, we point out the following anomaly description of the 1/3 plateau. While a simple S = 1/2 three-leg spin tube cannot have the unique gapped ground state on the 1/3 plateau because of an anomaly between a Z3 × Z3 symmetry and the translation symmetry at the 1/3 filling, the kagome antiferromagnet breaks explicitly one of the Z3 symmetries related to a Z3 cyclic transformation of spins in the unit cell. Hence the kagome antiferromagnet can have the unique gapped ground state on the 1/3 plateau.

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Topological approach to quantum liquid ground states on geometrically frustrated Heisenberg antiferromagnets

Cited by 12 publications

References 73 publications

Unveiling topological order through multipartite entanglement

Unveiling topological order through multipartite entanglement

Origin of Topological Order in a Cooper Pair Insulator

Anomalies of kagome antiferromagnets on magnetization plateaus

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