Restoring number conservation in quadratic bosonic Hamiltonians with dualities

Flynn, Vincent P.; Cobanera, Emilio; Viola, Lorenza

doi:10.1209/0295-5075/131/40006

Cited by 19 publications

(9 citation statements)

References 32 publications

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“…Finally, we note that Ref. [57] presented an approach for unitarily mapping dynamically-stable quadratic bosonic Hamiltonians to particle-conserving models. While this approach could also deal with positive nondefinite systems, it has many crucial differences from our approach.…”

Section: Relation To Previous Workmentioning

confidence: 99%

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A simple approach to characterizing band topology in bosonic pairing Hamiltonians

Chaudhary,

Levin,

Clerk

2021

Preprint

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We revisit the problem of characterizing band topology in dynamically-stable quadratic bosonic Hamiltonians that do not conserve particle number. We show this problem can be rigorously addressed by a smooth and local adiabatic mapping procedure to a particle number conserving Hamiltonian. In contrast to a generic fermionic pairing Hamiltonian, such a mapping can always be constructed for bosons. Our approach shows that particle non-conserving bosonic Hamiltonians can be classified using known approaches for fermionic models. It also provides a simple means for identifying and calculating appropriate topological invariants. We also explicitly study dynamically stable but non-positive definite Hamiltonians (as arise frequently in driven photonic systems). We show that in this case, each band gap is characterized by two distinct invariants.

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Section: Relation To Previous Workmentioning

confidence: 99%

“…Ref. [57] does introduce such a mapping; however, unlike our approach, this map is not guaranteed to be local, nor can it be used in general to address topology.…”

Section: Introductionmentioning

confidence: 99%

A simple approach to characterizing band topology in bosonic pairing Hamiltonians

Chaudhary,

Levin,

Clerk

2021

Preprint

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“…Dynamical stability and perturbations The eigenvalues of a Krein-Hermitian matrix K are either real or come in complex-conjugate pairs [3,10,11,24]. An eigenvector ψ corresponding to a non-real eigenvalue has null signature ( ψ, ψ η = 0), while one corresponding to a real eigenvalue can have positive ( ψ, ψ η > 0), negative ( ψ, ψ η < 0), or null signature.…”

Section: A Krein Spacesmentioning

confidence: 99%

“…Note that in the context of non-Hermitian Hamiltonians, "P T symmetry" has come to refer to any antilinear symmetry of a specific form [10], and not necessarily to space-time inversion symmetry. Both these examples fall into a class of non-Hermitian Hamiltonians called Krein-Hermitian [10,[16][17][18][19][20][21][22][23], also referred to in the literature as "pseudo-Hermitian" [10,11,[16][17][18][19]24] or "para-Hermitian" [25].…”

Section: Introductionmentioning

confidence: 99%

Krein-Hermitian Schrieffer-Wolff transformation and band touchings in bosonic BdG Hamiltonians

Massarelli¹,

Khait²,

Paramekanti³

2022

Preprint

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Krein-Hermitian Hamiltonians have emerged as an important class of non-Hermitian Hamiltonians in physics, encompassing both single-particle bosonic Bogoliubov-de Gennes (BdG) Hamiltonians and so-called "PT-symmetric" non-Hermitian Hamiltonians. In particular, they have attracted considerable scrutiny owing to the recent surge in interest for boson topology. Motivated by these developments, we formulate a perturbative Krein-unitary Schrieffer-Wolff transformation for finite-size dynamically stable Krein-Hermitian Hamiltonians, yielding an effective Hamiltonian for a subspace of interest. The effective Hamiltonian is Krein-Hermitian and, for sufficiently small perturbations, also dynamically stable. As an application, we use this transformation to justify codimension-based analyses of band touchings in bosonic BdG Hamiltonians, which complement topological characterization. We use this simple approach based on symmetry and codimension to revisit known topological magnon band touchings in several materials of recent interest.

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“…In some cases, however, particle interactions play an important role in creating non-trivial topology for both fermion [27][28][29][30][31][32][33] and boson [34][35][36][37][38][39][40][41][42][43][44][45]. Chiral p-wave superfluids are one example where pairing interaction of p-wave symmetry is essential.…”

Section: Introductionmentioning

confidence: 99%

Interaction induced topological Bogoliubov excitations in a spin-orbit coupled Bose-Einstein condensate

Huang,

Luo,

et al. 2021

Preprint

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We study topologically non-trivial excitations of a weakly interacting, spin-orbit coupled Bose-Einstein condensate in a two-dimensional square optical lattice, a system recently realized in experiment [W. Sun et al., Phys. Rev. Lett. 121, 150401 (2018)]. We focus on situations where the system is not subjected to a Zeeman field and thus does not exhibit nontrivial single-particle band topology. Of special interest then is the role of particle interaction as well as its interplay with the symmetry properties of the system in producing topologically non-trivial excitations. We find that the non-interacting system possesses a rich set of symmetries, including the PT symmetry, the modified dihedral point group symmetry D4 and the nonsymmorphic symmetry. These combined symmetries ensure the existence of pairs of degenerate Dirac points at the edge of Brillouin zone for the single-particle energy bands. In the presence of particle interaction and with sufficient spin-orbit coupling, the atoms condense in a ground state with net magnetization which spontaneously breaks the PT and D4 symmetry. We demonstrate that this symmetry breaking leads to a gap opening at the Dirac point for the Bogoliubov spectrum and consequentially topologically non-trivial excitations. We confirm the non-trivial topology by calculating the Chern numbers of the lowest excitation bands and show that gapless edge states form at the interface of systems characterized by different values of the Chern number.

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Restoring number conservation in quadratic bosonic Hamiltonians with dualities

Cited by 19 publications

References 32 publications

A simple approach to characterizing band topology in bosonic pairing Hamiltonians

A simple approach to characterizing band topology in bosonic pairing Hamiltonians

Krein-Hermitian Schrieffer-Wolff transformation and band touchings in bosonic BdG Hamiltonians

Interaction induced topological Bogoliubov excitations in a spin-orbit coupled Bose-Einstein condensate

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