Interaction induced dynamical $\mathcal{PT}$ symmetry breaking in dissipative Fermi-Hubbard models

Pan, Lei; Wang, Xueliang; Cui, Xiaoling; Chen, Shu

doi:10.48550/arxiv.2003.08864

Cited by 2 publications

(3 citation statements)

References 39 publications

(41 reference statements)

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“…29 for experimental observations). This feature is common both in few-and many-body systems while the latter can lead to rich phenomena such as enhanced particle correlations [597,671,672], the shift of the quantum critical point [589,633], the engineering of non-Abelian gauge fields [612], multiband effects due to lattice confinement [629,630], and (transiently) stabilizing otherwise unstable quantum states [597,[673][674][675][676][677][678][679][680]. Regarding other dynamical aspects, the unconventional Kibble-Zurek mechanism is proposed [681][682][683], and insights from exceptional points in disordered non-Hermitian many-body systems are argued to be useful for understanding transient destabilization of the many-body localization due to environments [145].…”

Section: 32)mentioning

confidence: 99%

Non-Hermitian Physics

Ashida,

Gong,

Ueda

2020

Preprint

129

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A review is given on the foundations and applications of non-Hermitian classical and quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra, including Jordan normal form, biorthogonality, exceptional points, pseudo-Hermiticity and parity-time symmetry, are delineated in a pedagogical and mathematically coherent manner. Building on these, we provide an overview of how diverse classical systems, ranging from photonics, mechanics, electrical circuits, acoustics to active matter, can be used to simulate non-Hermitian wave physics. In particular, we discuss rich and unique phenomena found therein, such as unidirectional invisibility, enhanced sensitivity, topological energy transfer, coherent perfect absorption, single-mode lasing, and robust biological transport. We then explain in detail how non-Hermitian operators emerge as an effective description of open quantum systems on the basis of the Feshbach projection approach and the quantum trajectory approach. We discuss their applications to physical systems relevant to a variety of fields, including atomic, molecular and optical physics, mesoscopic physics, and nuclear physics with emphasis on prominent phenomena/subjects in quantum regimes, such as quantum resonances, superradiance, continuous quantum Zeno effect, quantum critical phenomena, Dirac spectra in quantum chromodynamics, and nonunitary conformal field theories. Finally, we introduce the notion of band topology in complex spectra of non-Hermitian systems and present their classifications by providing the proof, firstly given by this review in a complete manner, as well as a number of instructive examples. Other topics related to non-Hermitian physics, including nonreciprocal transport, speed limits, nonunitary quantum walk, are also reviewed.

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Section: 32)mentioning

confidence: 99%

Non-Hermitian Physics

Ashida,

Gong,

Ueda

2020

Preprint

129

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“…In some previous works 6, [54][55][56][57][58][59][60] on open quantum systems, topological phenomena have been studied for the effective non-Hermitian Hamiltonian,…”

Section: Effective Non-hermitian Hamiltonian For Open Quantum Systemsmentioning

confidence: 99%

“…Among them, open quantum systems [49][50][51][52][53][54] also provide a unique platform of the following intriguing issue: the interplay between correlations and non-Hermitian topology [55][56][57][58][59][60][61] . Such systems interact with the environment and may lose energy or particles.…”

Section: Introductionmentioning

confidence: 99%

Fate of fractional quantum Hall states in open quantum systems: characterization of correlated topological states for the full Liouvillian

Yoshida,

Kudo,

Katsura

et al. 2020

Preprint

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Despite previous extensive analysis of open quantum systems described by the Lindblad equation, it is unclear whether correlated topological states, such as fractional quantum Hall states, are maintained even in the presence of the jump term. In this paper, we introduce the pseudo-spin Chern number of the Liouvillian which is computed by twisting the boundary conditions only for one of the subspaces of the doubled Hilbert space. The existence of such a topological invariant elucidates that the topological properties remain unchanged even in the presence of the jump term which does not close the gap of the effective non-Hermitian Hamiltonian (obtained by neglecting the jump term). In other words, the topological properties are encoded into an effective non-Hermitian Hamiltonian rather than the full Liouvillian. This is particularly useful when the jump term can be written as a strictly block-upper (-lower) triangular matrix in the doubled Hilbert space, in which case the presence or absence of the jump term does not affect the spectrum of the Liouvillian. With the pseudo-spin Chern number, we address the characterization of fractional quantum Hall states with two-body loss but without gain, elucidating that the topology of the non-Hermitian fractional quantum Hall states is preserved even in the presence of the jump term. This numerical result also supports the use of the non-Hermitian Hamiltonian which significantly reduces the numerical cost. Similar topological invariants can be extended to treat correlated topological states for other spatial dimensions and symmetry (e.g., one-dimensional open quantum systems with inversion symmetry), indicating the high versatility of our approach.

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Interaction induced dynamical $\mathcal{PT}$ symmetry breaking in dissipative Fermi-Hubbard models

Cited by 2 publications

References 39 publications

Non-Hermitian Physics

Non-Hermitian Physics

Fate of fractional quantum Hall states in open quantum systems: characterization of correlated topological states for the full Liouvillian

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