| 1. |
- Herviou, Loic, et al.
(författare)
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Bipartite fluctuations and topology of Dirac and Weyl systems
- 2019
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Ingår i: Physical Review B. - : AMER PHYSICAL SOC. - 2469-9950 .- 2469-9969. ; 99:7
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Tidskriftsartikel (refereegranskat)abstract
- Bipartite fluctuations can provide interesting information about entanglement properties and correlations in many-body quantum systems. We address such fluctuations in relation with the topology of Dirac and Weyl quantum systems, in situations where the relevant particle number is not conserved, leading to additional volume laws scaling with the quantum Fisher information. In the case of the p + ip superconductor, we build a relation between charge fluctuations and the associated winding numbers of Dirac cones in the low-energy sector. Topological aspects of the Hamiltonian in the vicinity of these points induce long-range entanglement in real space. We specifically extract analytical expressions for the corner contributions to bipartite fluctuations. We highlight their differences and similarities with the corner functions of the entanglement entropy which characterize the underlying conformal field theory. We provide a detailed analysis of such fluctuation properties, including the role of gap anisotropy, and discuss higher-dimensional Weyl analogs.
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| 2. |
- Herviou, Loic, et al.
(författare)
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Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
- 2019
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Ingår i: Physical Review A: covering atomic, molecular, and optical physics and quantum information. - : AMER PHYSICAL SOC. - 2469-9926 .- 2469-9934. ; 99:5
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Tidskriftsartikel (refereegranskat)abstract
- We address the breakdown of the bulk-boundary correspondence observed in non-Hermitian systems, where open and periodic systems can have distinct phase diagrams. The correspondence can be completely restored by considering the Hamiltonian's singular-value decomposition instead of its eigendecomposition. This leads to a natural topological description in terms of a flattened singular decomposition. This description is equivalent to the usual approach for Hermitian systems and coincides with a recent proposal for the classification of non-Hermitian systems. We generalize the notion of the entanglement spectrum to non-Hermitian systems, and show that the edge physics is indeed completely captured by the periodic bulk Hamiltonian. We exemplify our approach by considering the chiral non-Hermitian Su-Schrieffer-Heger and Chern insulator models. Our work advocates a different perspective on topological non-Hermitian Hamiltonians, paving the way to a better understanding of their entanglement structure.
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| 3. |
- Herviou, Loic, et al.
(författare)
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Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models
- 2019
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Ingår i: SciPost Physics. - : SciPost Foundation. - 2542-4653. ; 7:5
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Tidskriftsartikel (refereegranskat)abstract
- We study the properties of the entanglement spectrum in gapped non-interacting non-Hermitian systems, and its relation to the topological properties of the system Hamiltonian. Two different families of entanglement Hamiltonians can be defined in non-Hermitian systems, depending on whether we consider only right (or equivalently only left) eigenstates or a combination of both left and right eigenstates. We show that their entanglement spectra can still be computed efficiently, as in the Hermitian limit. We discuss how symmetries of the Hamiltonian map into symmetries of the entanglement spectrum depending on the choice of the many-body state. Through several examples in one and two dimensions, we show that the biorthogonal entanglement Hamiltonian directly inherits the topological properties of the Hamiltonian for line gapped phases, with characteristic singular and energy zero modes. The right (left) density matrix carries distinct information on the topological properties of the many-body right (left) eigenstates themselves. In purely point gapped phases, when the energy bands are not separable, the relation between the entanglement Hamiltonian and the system Hamiltonian breaks down.
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| 4. |
- Herviou, Loic, et al.
(författare)
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L-2 localization landscape for highly excited states
- 2020
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Ingår i: Physical Review B. - : AMER PHYSICAL SOC. - 2469-9950 .- 2469-9969. ; 101:22
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Tidskriftsartikel (refereegranskat)abstract
- The localization landscape [M. Filoche and S. Mayboroda, Proc. Natl. Acad. Sci. USA 109, 14761 (2012)] gives direct access to the localization of bottom-of-band eigenstates in noninteracting disordered systems. We generalize this approach to eigenstates at arbitrary energies in systems with or without internal degrees of freedom by introducing a modified L-2 landscape, and we demonstrate its accuracy in a variety of archetypal models of Anderson localization in one and two dimensions. This L-2-landscape function can be efficiently computed using hierarchical methods that allow evaluating the diagonal of a well-chosen Green's function. We compare our approach to other landscape methods, bringing insights on their strengths and limitations. Our approach is general and can in principle be applied to both studies of topological Anderson transitions and many-body localization.
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| 5. |
- Herviou, Loic, et al.
(författare)
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Many-body localization in a fragmented Hilbert space
- 2021
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Ingår i: Physical Review B. - : American Physical Society (APS). - 2469-9950 .- 2469-9969. ; 103:13
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Tidskriftsartikel (refereegranskat)abstract
- We study many-body localization (MBL) in a pair-hopping model exhibiting strong fragmentation of the Hilbert space. We show that several Krylov subspaces have both ergodic statistics in the thermodynamic limit and a dimension that scales much slower than the full Hilbert space but still exponentially. Such a property allows us to study the MBL phase transition in systems including up to 64 spins. The different Krylov spaces that we consider show clear signatures of a many-body localization transition, both in the Kullback-Leibler divergence of the distribution of their level spacing ratio and their entanglement properties. However, they also present distinct scalings with the system size. Depending on the subspace, the critical disorder strength can be nearly independent of the system size or conversely show an approximately linear increase with the number of spins.
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| 6. |
- Herviou, Loic, et al.
(författare)
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Multiscale entanglement clusters at the many-body localization phase transition
- 2019
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Ingår i: Physical Review B. - : AMER PHYSICAL SOC. - 2469-9950 .- 2469-9969. ; 99:13
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Tidskriftsartikel (refereegranskat)abstract
- We numerically study the formation of entanglement clusters across the many-body localization transition. We observe a crossover from strong many-body entanglement in the ergodic phase to weak local correlations in the localized phase, with continuous clusters throughout the phase diagram. Critical states close to the transition have a structure compatible with fractal or multiscale-entangled states, characterized by entanglement at multiple levels: small strongly entangled clusters are weakly entangled together to form larger clusters. The critical point therefore features subthermal entanglement and a power-law distributed cluster size. Upon entering the localized phase, the power-law distribution seems to persist with a varying power that crosses over into a stretched exponent before eventually becoming exponential deep in the localized phase. These results are in agreement with some of the recently proposed phenomenological renormalization-group schemes characterizing the many-body localized critical point, and serve to constrain other such schemes.
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| 7. |
- Klein Kvorning, Thomas, et al.
(författare)
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Time-evolution of local information : Thermalization dynamics of local observables
- 2022
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Ingår i: SciPost Physics. - : Stichting SciPost. - 2542-4653. ; 13:4
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Tidskriftsartikel (refereegranskat)abstract
- Quantum many-body dynamics generically result in increasing entanglement that eventually leads to thermalization of local observables. This makes the exact description of the dynamics complex despite the apparent simplicity of (high-temperature) thermal states. For accurate but approximate simulations one needs a way to keep track of essential (quantum) information while discarding inessential one. To this end, we first introduce the concept of the information lattice, which supplements the physical spatial lattice with an additional dimension and where a local Hamiltonian gives rise to well-defined locally conserved von Neumann information current. This provides a convenient and insightful way of capturing the flow, through time and space, of information during quantum time-evolution, and gives a distinct signature of when local degrees of freedom decouple from long-range entanglement. As an example, we describe such de-coupling of local degrees of freedom for the mixed-field transverse Ising model. Building on this, we secondly construct algorithms to time-evolve sets of local density matrices without any reference to a global state. With the notion of information currents, we motivate algorithms based on the intuition that information for statistical reasons flows from small to large scales. Using this guiding principle, we construct an algorithm that, at worst, shows two-digit convergence in time-evolutions up to very late times for diffusion process governed by the mixed-field transverse Ising Hamiltonian. While we focus on dynamics in 1D with nearest-neighbor Hamiltonians, the algorithms do not essentially rely on these assumptions and can in principle be generalized to higher dimensions and more complicated Hamiltonians.
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