Berry connection induced anomalous wave-packet dynamics in non-Hermitian systems

Silberstein, Navot; Behrends, Jan; Goldstein, Moshe; Ilan, Roni

doi:10.1103/physrevb.102.245147

Cited by 28 publications

(15 citation statements)

References 91 publications

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“…The Hamiltonian varies slowly in time which suggests the use of the quantum adiabatic theorem. However, the conventional Hermitian derivation relies on the vanishing of both Re(ε(τ )), the real part of the instantaneous eigen-energy, and Im(i Ψ L n |∂ t Ψ R n ), the imaginary part of the Berry connection [74,75]. (Here, L(R) denotes the left(right) eigenstates of the Hamiltonian.)…”

Section: Appendix E: the Full Many-body Systemmentioning

confidence: 99%

Non-Hermitian gap closure and delocalization in interacting directed polymers

Abhijeet¹,

Patapoff²,

Paulose³

2021

Preprint

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We examine the interplay of band theory and non-Hermitian mechanics in a classical system of thermally fluctuating directed polymers subject to shear forces and experiencing a continuum periodic potential in 1+1D. The equilibrium polymer conformations are described by a mapping to a quantum system with a non-Hermitian Hamiltonian and with fermionic statistics generated by noncrossing interactions among polymers. Using molecular dynamics simulations and analytical calculations, we identify a localized and a delocalized phase of the polymer conformations, separated by a delocalization transition which corresponds (in the quantum description) to the breakdown of a band insulator when driven by an imaginary vector potential. We find the critical shear value and the critical exponent by which the shear modulus diverges in terms of the branch points in the complex-valued band structure at which the bandgap closes. We also investigate the combined effects of non-Hermitian delocalization and localization due to both periodicity and disorder, uncovering preliminary evidence that while disorder favours localization at high values, it encourages delocalization at lower values.

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Section: Appendix E: the Full Many-body Systemmentioning

confidence: 99%

Non-Hermitian gap closure and delocalization in interacting directed polymers

Abhijeet¹,

Patapoff²,

Paulose³

2021

Preprint

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“…Especially, dynamical evolution of a wave packet in a disordered system has obtained considerable interest. One tries to understand the relation between the energy spectrum and the dynamical propagation of the wave packet [43][44][45][46][47][48][49][50][51][52][53][54][55][56][57] . Dynamical observation of wave packet evolution and many body localization in one-dimensional incommensurate optical lattices has been also reported in recent works [58][59][60] .…”

Section: Introductionmentioning

confidence: 99%

Dynamical evolution in a one-dimensional incommensurate lattice with $\mathcal{PT}$ symmetry

Xu,

Chen

2021

Preprint

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We investigate the dynamical evolution of a parity-time (PT ) symmetric extension of Aubry-André (AA) model which exhibits the coincidence of localization-delocalization transition point with PT symmetry breaking point. One can apply the evolution of the profile of the wave packet and the long-time survival probability to distinguish the localization regimes in PT symmetric AA model. The results of the mean displacement show that when the system is in the PT symmetry unbroken regime, the wave packet spreading is ballistic which is different from that in PT symmetry broken regime. Furthermore, we discuss the distinctive features of the Loschmidt echo with the post-quench parameter being localized in different PT symmetric regimes.

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“…Similarly, in response to a temperature gradient, without any external magnetic field, it generate a transverse Hall voltage, known as the anomalous Nernst effect [9,[12][13][14]. Coupled with the Boltzmann transport theory, the modified semiclassical equations have been employed to study transport in topological insulators [15], Chern Insulators [16], Weyl Semi-Metals [13,14,[17][18][19][20][21][22], Kondo Insulators [23], Rashba systems [24,25], optical lattices and quasicrystals [26,27], superconductors [28], non-Hermitian systems [29,30], as well as in various other systems [31][32][33][34][35][36][37]. Non-linear effects in transport have also been studied within this formalism [38][39][40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Energy magnetization and transport in systems with a non-zero Berry curvature in a magnetic field

Archisman¹,

Mukerjee²

2021

Preprint

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We demonstrate that the well-known expression for the charge magnetization of a sample with a non-zero Berry curvature can be obtained by demanding that the Einstein relation holds for the electric transport current. We extend this formalism to the transport energy current and show that the energy magnetization must satisfy a particular condition. We provide a physical interpretation of this condition and relate the energy magnetization to circulating energy currents due to chiral edge states. We further obtain an expression for the energy magnetization analogous to the one previously obtained for the charge magnetization. We also solve the Boltzmann Transport Equation for the non-equilibrium distribution function in 2D for systems with a non-zero Berry curvature in a magnetic field. This distribution function can be used to obtain the regular Hall response in time-reversal invariant samples with a non-zero Berry curvature, for which there is no anomalous Hall response.

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Berry connection induced anomalous wave-packet dynamics in non-Hermitian systems

Cited by 28 publications

References 91 publications

Non-Hermitian gap closure and delocalization in interacting directed polymers

Non-Hermitian gap closure and delocalization in interacting directed polymers

Dynamical evolution in a one-dimensional incommensurate lattice with $\mathcal{PT}$ symmetry

Energy magnetization and transport in systems with a non-zero Berry curvature in a magnetic field

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