| 1. |
- Colmenarez, Luis, et al.
(författare)
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Subdiffusive Thouless time scaling in the Anderson model on random regular graphs
- 2022
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Ingår i: Physical Review B. - 2469-9950 .- 2469-9969. ; 105:17
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Tidskriftsartikel (refereegranskat)abstract
- The scaling of the Thouless time with system size is of fundamental importance to characterize dynamical properties in quantum systems. In this work, we study the scaling of the Thouless time in the Anderson model on random regular graphs with on-site disorder. We determine the Thouless time from two main quantities: the spectral form factor and the power spectrum. Both quantities probe the long-range spectral correlations in the system and allow us to determine the Thouless time as the timescale after which the system is well described by random matrix theory. We find that the scaling of the Thouless time is consistent with the existence of a subdiffusive regime anticipating the localized phase. Furthermore, to reduce finite-size effects, we break energy conservation by introducing a Floquet version of the model and show that it hosts a similar subdiffusive regime.
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| 2. |
- De Tomasi, Giuseppe, et al.
(författare)
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Non-Hermitian Rosenzweig-Porter random-matrix ensemble : Obstruction to the fractal phase
- 2022
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Ingår i: Physical Review B. - : American Physical Society (APS). - 2469-9950 .- 2469-9969. ; 106:9
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Tidskriftsartikel (refereegranskat)abstract
- We study the stability of nonergodic but extended (NEE) phases in non-Hermitian systems. For this purpose, we generalize the so-called Rosenzweig-Porter random-matrix ensemble, known to carry a NEE phase along with the Anderson localized and ergodic ones, to the non-Hermitian case. We analyze, both analytically and numerically, the spectral and multifractal properties of the non-Hermitian case. We show that the ergodic and localized phases are stable against the non-Hermitian nature of matrix entries. However, the stability of the fractal phase depends on the choice of the diagonal elements. For purely real or imaginary diagonal potential, the fractal phase is intact, while for a generic complex diagonal potential the fractal phase disappears, giving way to a localized one.
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| 3. |
- De Tomasi, Giuseppe, et al.
(författare)
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Non-Hermiticity induces localization: Good and bad resonances in power-law random banded matrices
- 2023
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Ingår i: Physical Review B. - : American Physical Society (APS). - 2469-9950 .- 2469-9969. ; 108:18
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Tidskriftsartikel (refereegranskat)abstract
- The power-law random banded matrix (PLRBM) is a paradigmatic ensemble to study the Anderson localization transition (AT). In d dimensions, the PLRBMs are random matrices with algebraic decaying off-diagonal elements Hnm∼1/|n-m|α, having AT at α=d. In this work, we investigate the fate of the PLRBM to non-Hermiticity (nH). We consider the case where the random on-site diagonal potential takes complex values, mimicking an open system, subject to random gain-loss terms. We understand the model analytically by generalizing the Anderson-Levitov resonance counting technique to the nH case. We identify two competing mechanisms due to nH: favoring localization and delocalization. The competition between the two gives rise to AT at d/2≤α≤d. The value of the critical α depends on the strength of the on-site potential, like in Hermitian disordered short-range models in d>2. Within the localized phase, the wave functions are algebraically localized with an exponent α even for α
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| 4. |
- De Tomasi, Giuseppe, et al.
(författare)
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Stable many-body localization under random continuous measurements in the no-click limit
- 2024
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Ingår i: Physical Review B. - : American Physical Society (APS). - 2469-9950 .- 2469-9969. ; 109:17
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Tidskriftsartikel (refereegranskat)abstract
- In this work, we investigate the localization properties of a paradigmatic model, coupled to a monitoring environment and possessing a many-body localized (MBL) phase. We focus on the postselected no-click limit with quench random rates, i.e., random gains and losses. In this limit, the system is modeled by adding an imaginary random potential, rendering non-Hermiticity in the system. Numerically, we provide evidence that the system is localized for any finite amount of disorder. To analytically understand our results, we extend the quantum random energy model (QREM) to the non-Hermitian scenario. The Hermitian QREM has been used previously as a benchmark model for MBL. The QREM exhibits a size-dependent MBL transition, where the critical value scales as Wc∼LlnL with system size and presenting many-body mobility edges. We reveal that the non-Hermitian QREM with random gain-loss offers a significantly stronger form of localization, evident in the nature of the many-body mobility edges and the value for the transition, which scales as Wc∼ln1/2L with the system size.
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| 5. |
- Deng, Xiaolong, et al.
(författare)
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Anisotropy-mediated reentrant localization
- 2022
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Ingår i: SciPost Physics. - : Stichting SciPost. - 2542-4653. ; 13:5
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Tidskriftsartikel (refereegranskat)abstract
- We consider a 2d dipolar system, d = 2, with the generalized dipole-dipole interaction similar to r(-a), and the power a controlled experimentally in trapped-ion or Rydberg-atom systems via their interaction with cavity modes. We focus on the dilute dipolar excitation case when the problem can be effectively considered as single-particle with the interaction providing long-range dipolar-like hopping. We show that the spatially homogeneous tilt beta of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion, a < d, unlike the models with random dipole orientation. The Anderson transitions are found to occur at the finite values of the tilt parameter beta = a, 0 < a < d, and beta = a =(a d =2), d =2 < a < d, showing the robustness of the localization at small and large anisotropy values. Both exact analytical methods and extensive numerical calculations show power-law localized eigenstates in the bulk of the spectrum, obeying recently discovered duality a <-> 2d -a of their spatial decay rate, on the localized side of the transition, a > a(AT). This localization emerges due to the presence of the ergodic extended states at either spectral edge, which constitute a zero fraction of states in the thermodynamic limit, decaying though extremely slowly with the system size.
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| 6. |
- Deng, Xiaolong, et al.
(författare)
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Superdiffusion in a random two-dimensional system with time-reversal symmetry and long-range hopping
- 2024
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Ingår i: Physical Review B. - : American Physical Society (APS). - 2469-9950 .- 2469-9969. ; 109:17
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Tidskriftsartikel (refereegranskat)abstract
- Although it is recognized that Anderson localization takes place for all states at a dimension d less than or equal to 2, while delocalization is expected for hopping V(r) decreasing with the distance slower or as r-d, the localization problem in the crossover regime for the dimension d=2 and hopping V(r)â r-2 is not resolved yet. Following earlier suggestions we show that for the hopping determined by two-dimensional anisotropic dipole-dipole interactions in the presence of time-reversal symmetry there exist two distinguishable phases at weak and strong disorder. The first phase is characterized by ergodic dynamics and superdiffusive transport, while the second phase is characterized by diffusive transport and delocalized eigenstates with fractal dimension less than 2. The transition between phases is resolved analytically using the extension of scaling theory of localization and verified numerically using an exact numerical diagonalization.
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| 7. |
- Gonçalves, Miguel, et al.
(författare)
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Quasiperiodicity hinders ergodic Floquet eigenstates
- 2023
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Ingår i: Physical Review B. - : American Physical Society (APS). - 2469-9950 .- 2469-9969. ; 108:10
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Tidskriftsartikel (refereegranskat)abstract
- Quasiperiodic systems in one dimension can host nonergodic states, e.g., states localized in position or momentum. Periodic quenches within localized phases yield Floquet eigenstates of the same nature, i.e., spatially localized or ballistic. However, periodic quenches across these two nonergodic phases were thought to produce ergodic diffusivelike states even for noninteracting particles. We show that this expectation is not met at the thermodynamic limit where the system always attains a nonergodic state. We find that ergodicity may be recovered by scaling the Floquet quenching period with system size and determine the corresponding scaling function. Our results suggest that, while the fraction of spatially localized or ballistic states depends on the model's details, all Floquet eigenstates belong to one of these nonergodic categories. Our findings demonstrate that quasiperiodicity hinders ergodicity and thermalization, even in driven systems where these phenomena are commonly expected.
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| 8. |
- Kochergin, Daniil, et al.
(författare)
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Anatomy of the fragmented Hilbert space : Eigenvalue tunneling, quantum scars, and localization in the perturbed random regular graph
- 2023
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Ingår i: Physical Review B. - : American Physical Society (APS). - 2469-9950 .- 2469-9969. ; 108:9
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Tidskriftsartikel (refereegranskat)abstract
- We consider the properties of the random regular graph with node degree d perturbed by chemical potentials μk for a number of short k-cycles. We analyze both numerically and analytically the phase diagram of the model in the (μk,d) plane. The critical curve separating the homogeneous and clusterized phases is found and it is demonstrated that the clusterized phase itself generically is separated as the function of d into the phase with ideal clusters and phase with coupled ones when the continuous spectrum gets formed. The eigenstate spatial structure of the model is investigated and it is found that there are localized scarlike states in the delocalized part of the spectrum, that are related to the topologically equivalent nodes in the graph. We also reconsider the localization of the states in the nonperturbative band formed by eigenvalue instantons and find the semi-Poisson level spacing distribution. The Anderson transition for the case of combined (k-cycle) structural and diagonal (Anderson) disorders is investigated. It is found that the critical diagonal disorder gets reduced sharply at the clusterization phase transition but does it unevenly in nonperturbative and mid-spectrum bands, due to the scars, present in the latter. The applications of our findings to 2d quantum gravity are discussed.
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| 9. |
- Kochergin, Daniil, et al.
(författare)
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Robust extended states in Anderson model on partially disordered random regular graphs
- 2024
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Ingår i: SciPost Physics. - : SCIPOST FOUNDATION. - 2542-4653. ; 16:4
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Tidskriftsartikel (refereegranskat)abstract
- In this work we analytically explain the origin of the mobility edge in the partially disordered random regular graphs of degree d, i.e., with a fraction beta of the sites being disordered, while the rest remain clean. It is shown that the mobility edge in the spectrum survives in a certain range of parameters (d, beta) at infinitely large uniformly distributed disorder. The critical curve separating extended and localized states is derived analytically and confirmed numerically. The duality in the localization properties between the sparse and extremely dense RRG has been found and understood.
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| 10. |
- Motamarri, Vedant R., et al.
(författare)
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Localization and fractality in disordered Russian Doll model
- 2022
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Ingår i: SciPost Physics. - : Stichting SciPost. - 2542-4653. ; 13:5
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Tidskriftsartikel (refereegranskat)abstract
- Motivated by the interplay of Bethe-Ansatz integrability and localization in the Richardson model of superconductivity, we consider a time-reversal symmetry breaking deformation of this model, known as the Russian Doll Model (RDM), and implement diagonal on-site disorder. The localization and ergodicity-breaking properties of the single-particle spectrum are analyzed using a large-energy renormalization group (RG) over the momentum-space spectrum. Based on the above RG, we derive an effective Hamiltonian of the model, discover a fractal phase of non-ergodic delocalized states with the fractal dimension different from the paradigmatic Rosenzweig-Porter model and explain it in terms of the developed RG equations and the matrix-inversion trick.
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