Non-ergodic delocalized phase with Poisson level statistics
- URL: http://arxiv.org/abs/2112.09700v5
- Date: Thu, 14 Sep 2023 05:57:29 GMT
- Title: Non-ergodic delocalized phase with Poisson level statistics
- Authors: Weichen Tang and Ivan M. Khaymovich
- Abstract summary: We develop a model simulating the same eigenstate structure like in MBL, but in the random-matrix setting.
This model carries non-ergodic eigenstates, delocalized over the extensive number of configurations in the Hilbert space.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Motivated by the many-body localization (MBL) phase in generic interacting
disordered quantum systems, we develop a model simulating the same eigenstate
structure like in MBL, but in the random-matrix setting. Demonstrating the
absence of energy level repulsion (Poisson statistics), this model carries
non-ergodic eigenstates, delocalized over the extensive number of
configurations in the Hilbert space. On the above example, we formulate general
conditions to a single-particle and random-matrix models in order to carry such
states, based on the transparent generalization of the Anderson localization of
single-particle states and multiple resonances.
Related papers
- Localization transitions in quadratic systems without quantum chaos [0.0]
We study the one-dimensional Anderson and Wannier-Stark models that exhibit eigenstate transitions from localization in quasimomentum space to localization in position space.
We show that the transition point may exhibit an unconventional character of Janus type, i.e., some measures hint at the RMT-like universality emerging at the transition point, while others depart from it.
Our results hint at rich diversity of volume-law eigenstate entanglement entropies in quadratic systems that are not maximally entangled.
arXiv Detail & Related papers (2024-10-07T14:29:32Z) - Theory of mobility edge and non-ergodic extended phase in coupled random
matrices [18.60614534900842]
The mobility edge, as a central concept in disordered models for localization-delocalization transitions, has rarely been discussed in the context of random matrix theory.
We show that their overlapped spectra and un-overlapped spectra exhibit totally different scaling behaviors, which can be used to construct tunable mobility edges.
Our model provides a general framework to realize the mobility edges and non-ergodic phases in a controllable way in RMT.
arXiv Detail & Related papers (2023-11-15T01:43:37Z) - Numerical variational simulations of quantum phase transitions in the
sub-Ohmic spin-boson model with multiple polaron ansatz [17.26854451734512]
Dissipative quantum phase transitions in the sub-Ohmic spin-boson model are numerically studied.
quantum-to-classical correspondence is fully confirmed over the entire sub-Ohmic range.
Mean-field and non-mean-field critical behaviors are found in the deep and shallow sub-Ohmic regimes.
arXiv Detail & Related papers (2023-09-02T02:23:54Z) - Canonical typicality under general quantum channels [39.58317527488534]
In the present work we employ quantum channels to define generalized subsystems.
We show that generalized subsystems also display the phenomena of canonical typicality.
In particular we demonstrate that the property regulating the emergence of the canonical typicality behavior is the entropy of the channel used to define the generalized subsystem.
arXiv Detail & Related papers (2023-08-30T21:29:45Z) - Quantum Alchemy and Universal Orthogonality Catastrophe in
One-Dimensional Anyons [2.9491988705158843]
We characterize the geometry of quantum states associated with different values of $kappa$, i.e., different quantum statistics.
We characterize this decay using quantum speed limits on the flow of $kappa$, illustrate our results with a model of hard-core anyons, and discuss possible experiments in quantum simulation.
arXiv Detail & Related papers (2022-10-19T17:59:59Z) - Truncated generalized coherent states [0.0]
A class of generalized coherent states is determined for the distribution of excitations.
The statistics is uniquely sub-Poissonian for large values of the label.
As particular cases, truncated Wright generalized coherent states exhibit uniquely non-classical properties.
arXiv Detail & Related papers (2022-09-29T23:20:25Z) - Deformed Symmetry Structures and Quantum Many-body Scar Subspaces [12.416248333306237]
A quantum many-body scar system usually contains a special non-thermal subspace decoupled from the rest of the Hilbert space.
We propose a general structure called deformed symmetric spaces for the decoupled subspaces hosting quantum many-body scars.
arXiv Detail & Related papers (2021-08-17T18:00:02Z) - Non-equilibrium stationary states of quantum non-Hermitian lattice
models [68.8204255655161]
We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner.
We focus on the quantum steady states of such models for both fermionic and bosonic systems.
arXiv Detail & Related papers (2021-03-02T18:56:44Z) - Long-range level correlations in quantum systems with finite Hilbert
space dimension [0.0]
We study the spectral statistics of quantum systems with finite Hilbert spaces.
We derive a theorem showing that eigenlevels in such systems cannot be globally uncorrelated.
arXiv Detail & Related papers (2020-10-13T15:49:15Z) - Robustness and Independence of the Eigenstates with respect to the
Boundary Conditions across a Delocalization-Localization Phase Transition [15.907303576427644]
We focus on the many-body eigenstates across a localization-delocalization phase transition.
In the ergodic phase, the average of eigenstate overlaps $barmathcalO$ is exponential decay with the increase of the system size.
For localized systems, $barmathcalO$ is almost size-independent showing the strong robustness of the eigenstates.
arXiv Detail & Related papers (2020-05-19T10:19:52Z) - Renormalization to localization without a small parameter [0.0]
We study the wave function localization properties in a d-dimensional model of randomly spaced particles with isotropic hopping potential depending solely on Euclidean interparticle distances.
Due to the generality of this model usually called the Euclidean random matrix model, it arises naturally in various physical contexts such as studies of vibrational modes, artificial atomic systems, liquids and glasses, ultracold gases and photon localization phenomena.
arXiv Detail & Related papers (2020-01-17T19:00:06Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.