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arXiv:2006.01182 · Physical review. B./Physical review. B

Many-body topological and skin states without open boundaries

Ching Hua Lee

Published Nov 1, 2021• 79 citations
arXivHTMLPDF

Abstract

Robust boundary states have been the focus of much recent research, both as topologically protected states and as non-Hermitian skin states. In this paper, we show that many-body effects can also induce analogs of these robust states in place of actual physical boundaries. Particle statistics or suitably engineered interactions, i.e., in ultracold atomic lattices can restrict the accessible many-body Hilbert space, and introduce effective boundaries in a spatially periodic higher-dimensional configuration space. We demonstrate the emergence of topological chiral modes in a two-fermion hopping model without open boundaries, with fermion pairs confined and asymmetrically propagated by suitably chosen fluxes. Heterogeneous nonreciprocal hoppings across different particle species can also result in robust particle clumping in a translation invariant setting, reminiscent of skin mode accumulation at an open boundary. But unlike fixed open boundaries, effective boundaries correspond to the locations of impenetrable particles and are mobile, giving rise to fundamentally different many-body versus single-body spectra and corresponding dynamics. Since nonreciprocal accumulation is agnostic to the dimensionality of restricted Hilbert spaces, our many-body skin states generalize directly in the thermodynamic limit. The many-body topological states, however, are nontrivially dimension-dependent, and their detailed exploration will stimulate further studies in higher dimensional topological invariants.

DOI
10.1103/physrevb.104.195102

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Robust boundary states have been the focus of much recent research, both as topologically protected states and as non-Hermitian skin states. In this paper, we show that many-body effects can also induce analogs of these robust states in place of actual physical boundaries. Particle statistics or suitably engineered interactions, i.e., in ultracold atomic lattices can restrict the accessible many-body Hilbert space, and introduce effective boundaries in a spatially periodic higher-dimensional configuration space. We demonstrate the emergence of topological chiral modes in a two-fermion hopping model without open boundaries, with fermion pairs confined and asymmetrically propagated by suitably chosen fluxes. Heterogeneous nonreciprocal hoppings across different particle species can also result in robust particle clumping in a translation invariant setting, reminiscent of skin mode accumulation at an open boundary. But unlike fixed open boundaries, effective boundaries correspond to the locations of impenetrable particles and are mobile, giving rise to fundamentally different many-body versus single-body spectra and corresponding dynamics. Since nonreciprocal accumulation is agnostic to the dimensionality of restricted Hilbert spaces, our many-body skin states generalize directly in the thermodynamic limit. The many-body topological states, however, are nontrivially dimension-dependent, and their detailed exploration will stimulate further studies in higher dimensional topological invariants.
Abstract Strong, non-perturbative interactions often lead to new exciting physics, as epitomized by emergent anyons from the Fractional Quantum hall effect. Within the actively investigated domain of non-Hermitian physics, we discover a new family of states known as non-Hermitian skin clusters. Taking distinct forms as Vertex, Topological, Interface, Extended and Localized skin clusters, they generically originate from asymmetric correlated hoppings on a lattice, in the strongly interacting limit with quenched single-body energetics. Distinct from non-Hermitian skin modes which accumulate at boundaries, our skin clusters are predominantly translation invariant particle clusters. As purely interacting phenomena, they fall outside the purview of generalized Brillouin zone analysis, although our effective lattice formulation provides alternative analytic and topological characterization. Non-Hermitian skin clusters fundamentally originate from the fragmentation structure of the Hilbert space, and may thus be of significant interest in modern many-body contexts like the ETH and quantum scars.
The explorations of non-Hermiticity have been devoted to investigate the disorder-induced many-body localization (MBL). However, the sensitivity of the spatial boundary conditions and the interplay of the non-Hermitian skin effect with many-body phenomena are not yet clear. For a MBL system in the presence of nonreciprocal tunnelings and random disorder potential, we identify two different complex-real spectral transitions, one is present for both open and periodic boundaries while the other is present only for open boundaries of coupled non-Hermitian chains. The later is driven due to the interchain coupling at weak disorder where the level statistics of the real eigenenergy phase follows a Gaussian orthogonal ensemble. We further characterize wave functions through the (biorthogonal) inverse participation ratio and fractal dimension, which reveal the suppression of skin effect in the non-Hermitian MBL phase. Finally, we demonstrate that the quench dynamics of the local particle density, spin imbalance, and entanglement entropy also signify the hallmark of the boundary effects and nonergodic character of many-body localization.
Non-Hermiticity greatly expands existing physical laws beyond the Hermitian framework, revealing various novel phenomena with unique properties. Up to now, most exotic nonHermitian effects, such as exceptional points and non-Hermitian skin effects, are discovered in single-particle systems. The interplay between non-Hermitian and manybody correlation is expected to be a more fascinating but much less explored area. Due to the complexity of the problem, current researches in this field mainly stay at the theoretical level. The experimental observation of predicted non-Hermitian manybody phases is still a great challenging. Here, we report the first experimental simulation of strongly correlated non-Hermitian many-body system, and reveal a new type of nonHermitian many-body skin states toward effective boundaries in Hilbert space. Such an interaction-induced non-Hermitian many-body skin effect represents the aggregation of bosonic clusters with non-identical occupations in the periodic lattice. In particular, by mapping eigen-states of three correlated bosons to modes of the designed threedimensional electric circuit, non-Hermitian many-body skin effects in Hilbert space is verified by measuring the spatial impedance response. Our finding not only discloses a new physical effect in the non-Hermitian many-body system, but also suggests a flexible platform to further investigate other non-Hermitian correlated phases in experiments.
Despite recent intensive research on topological aspects of open quantum systems, effects of strong interactions have not been sufficiently explored. In this paper, we demonstrate that complex-valued interactions induce the Liouvillian skin effect by analyzing a one-dimensional correlated model with two-body loss. We show that, in the presence of complex-valued interactions, eigenmodes and eigenvalues of the Liouvillian strongly depend on boundary conditions. Specifically, we find that complex-valued interactions induce localization of eigenmodes of the Liouvillian around the right edge under open boundary conditions. To characterize the Liouvillian skin effect, we define the topological invariant by using the Liouvillian superoperator. Then, we numerically confirm that the topological invariant captures the Liouvillian skin effect. Furthermore, the presence of the localization of eigenmodes results in the unique dynamics observed only under open boundary conditions: particle accumulation at the right edge in transient dynamics. Our result paves the way to realize topological phenomena in open quantum systems induced by strong interactions.
The non-Hermitian skin effect (NHSE) is a fascinating phenomenon in nonequilibrium systems where eigenstates massively localize at the systems’ boundaries, pumping (quasi-)particles loaded in these systems unidirectionally to the boundaries. Its interplay with many-body effects has been widely explored recently, and inter-particle repulsion or Fermi degeneracy pressure have been shown to limit the boundary accumulation induced by the NHSE both in their eigensolutions and dynamics. However, in this work we find that anyonic statistics can even more profoundly affect the NHSE dynamics, suppressing or even reversing the state dynamics against the localizing direction of the NHSE. This phenomenon is found to be more pronounced when more particles are involved. The spreading of quantum information in this system shows even more exotic phenomena, where NHSE affects only the information dynamics for a thermal ensemble, but not that for a single initial state. Our results open up a new avenue on exploring novel non-Hermitian phenomena arisen from the interplay between NHSE and anyonic statistics, and can potentially be demonstrated in ultracold atomic quantum simulators and quantum computers. Anyons are a general class of particles with unusual statistics beyond conventional bosons and fermions. In this work, the authors reveal that anyonic statistics can profoundly affect the non-Hermitian skin effect (NHSE) dynamically, suppressing or even reversing the NHSE-induced unidirectional evolution of both state dynamics and quantum information spreading, while keeping qualitatively the same skin-localization of static eigensolutions.
Non-Hermitian skin effect, the accumulation of bulk eigenstates at edges under open boundary conditions, has been observed across classical, quantum, and synthetic platforms. Whether it can be generalized to the genuine time dimension remains open. We propose a spatiotemporal NHSE in the Floquet phase space via Floquet engineering of a ring-trapped ultracold atomic gas. Placing spatial and temporal degrees of freedom on an equal footing, we show that a single parent skin effect projects onto either domain. The spatial projection yields an NHSE with arbitrarily tunable skin locations, eliminating the need for physical open boundaries. The temporal projection gives time-domain nonreciprocity and periodic temporal funneling, consistent with causality. This establishes a unified spatiotemporal paradigm for NHSE and opens a route to non-Hermitian topological physics in time.