Full-Counting Many-Particle Dynamics: Nonlocal and Chiral Propagation of Correlations

Ashida, Yuto; Ueda, Masahito

doi:10.1103/physrevlett.120.185301

Cited by 80 publications

(71 citation statements)

References 115 publications

(168 reference statements)

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“…(D3) implies that up to a time t * ∼ O( L v E ) the relative deviation is exponentially small, i.e., − ln R(t) ∼ O(L), which is consistent with a naïve expectation from the Lieb-Robinson bound [138]. Nevertheless, we should mention that the Lieb-Robinson picture may break down in some many-particle non-Hermitian systems after a global quench [171].…”

Section: Appendix D: Long-lived Quasi-eigenstates and Their Absence Isupporting

confidence: 69%

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Topological Phases of Non-Hermitian Systems

Gong¹,

Ashida²,

Kawabata³

et al. 2018

Phys. Rev. X

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1,417

1,447

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While Hermiticity lies at the heart of quantum mechanics, recent experimental advances in controlling dissipation have brought about unprecedented flexibility in engineering non-Hermitian Hamiltonians in open classical and quantum systems. Examples include parity-time-symmetric optical systems with gain and loss, dissipative Bose-Einstein condensates, exciton-polariton systems and biological networks. A particular interest centers on the topological properties of non-Hermitian systems, which exhibit unique phases with no Hermitian counterparts. However, no systematic understanding in analogy with the periodic table of topological insulators and superconductors has been achieved. In this paper, we develop a coherent framework of topological phases of non-Hermitian systems. After elucidating the physical meaning and the mathematical definition of non-Hermitian topological phases, we start with one-dimensional lattices, which exhibit topological phases with no Hermitian counterparts and are found to be characterized by an integer topological winding number even with no symmetry constraint, reminiscent of the quantum Hall insulator in Hermitian systems. A system with a nonzero winding number, which is experimentally measurable from the wave-packet dynamics, is shown to be robust against disorder, a phenomenon observed in the Hatano-Nelson model with asymmetric hopping amplitudes. We also unveil a novel bulk-edge correspondence that features an infinite number of (quasi-)edge modes. We then apply the K-theory to systematically classify all the non-Hermitian topological phases in the Altland-Zirnbauer (AZ) classes in all dimensions. The obtained periodic table unifies time-reversal and particle-hole symmetries, leading to highly nontrivial predictions such as the absence of non-Hermitian topological phases in two dimensions. We provide concrete examples for all the nontrivial non-Hermitian AZ classes in zero and one dimensions. In particular, we identify a Z2 topological index for arbitrary quantum channels (CPTP maps). Our work lays the cornerstone for a unified understanding of the role of topology in non-Hermitian systems. *

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Section: Appendix D: Long-lived Quasi-eigenstates and Their Absence Isupporting

confidence: 69%

“…under postselection [97,98,171] or for loss processes of a coherent condensate [72,74,99]. In particular, if we choose…”

Section: Appendix A: Consistency Between the Winding-number Expressionsmentioning

confidence: 99%

Topological Phases of Non-Hermitian Systems

Gong¹,

Ashida²,

Kawabata³

et al. 2018

Phys. Rev. X

Self Cite

1,417

1,447

View full text Add to dashboard Cite

show abstract

“…Although damping matrices with NHSE can arise quite naturally (e.g., in Fig.1), none of the previous models (e.g., Ref. [108]) we have checked has NHSE.…”

mentioning

confidence: 73%

Non-Hermitian Skin Effect and Chiral Damping in Open Quantum Systems

2019

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One of the unique features of non-Hermitian Hamiltonians is the non-Hermitian skin effect, namely that the eigenstates are exponentially localized at the boundary of the system. For open quantum systems, a short-time evolution can often be well described by the effective non-Hermitian Hamiltonians, while long-time dynamics calls for the Lindblad master equations, in which the Liouvillian superoperators generate time evolution. In this Letter, we find that Liouvillian superoperators can exhibit the non-Hermitian skin effect, and uncover its unexpected physical consequences. It is shown that the non-Hermitian skin effect dramatically shapes the long-time dynamics, such that the damping in a class of open quantum systems is algebraic under periodic boundary condition but exponential under open boundary condition. Moreover, the non-Hermitian skin effect and non-Bloch bands cause a chiral damping with a sharp wavefront. These phenomena are beyond the effective non-Hermitian Hamiltonians; instead, they belong to the non-Hermitian physics of full-fledged open quantum dynamics.Model.-The system is illustrated in Fig.1(a). Our Hamiltonian H = ij h ij c † i c j , where c † i , c i are fermion creation and annihilation operators at site i (including

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“…The obtained density matrix can also be used to determine an effective temperature of open many-body systems governed by the Lindblad master equation. Our results can thus be applied to dissipative many-body dynamics of a system coupled to a (not necessarily thermal) Markovian environment [74][75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90] or under noisy unitary operations [98][99][100][101][102][103][104][105][106][107]. We also present numerical evidence of these findings by applying our theory to specific models.…”

mentioning

confidence: 83%

Thermalization and Heating Dynamics in Open Generic Many-Body Systems

2018

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state of the meter such thatP lÂm = δ lmÂm , whereP l 's are projection operators satisfying M l=0P l = 1. After each interaction, we perform a projection measurement {P l } on the meter to read out an outcome l = 0, 1, . . . M . The meter is then reset to the reference stateP 0 , which ensures that the dynamics is Markovian (see the Supplementary Material [109] for discussions on a non-Markovian case). For each measurement process, the meter exhibits either (i) a change in the state of the meter corresponding to outcome m = 1, 2, . . . M or (ii) no change. The case (i) is referred to as a quantum jump process and accompanied by the following nonunitary mappingwhere Tr M [·] denotes the trace over the meter,Û (τ ) = e −iĤtotτ , and γ = v 2 δtTr A [P 0Â

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Full-Counting Many-Particle Dynamics: Nonlocal and Chiral Propagation of Correlations

Cited by 80 publications

References 115 publications

Topological Phases of Non-Hermitian Systems

Topological Phases of Non-Hermitian Systems

Non-Hermitian Skin Effect and Chiral Damping in Open Quantum Systems

Thermalization and Heating Dynamics in Open Generic Many-Body Systems

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